{"id":3792,"date":"2017-10-28T01:00:00","date_gmt":"2017-10-27T17:00:00","guid":{"rendered":"http:\/\/swarma.org\/%swarma-paper%\/"},"modified":"2018-12-08T11:41:37","modified_gmt":"2018-12-08T03:41:37","slug":"%e9%87%8d%e7%a3%85science%e8%ae%ba%e6%96%87%ef%bc%9a%e7%94%a8%e4%ba%ba%e5%b7%a5%e7%a5%9e%e7%bb%8f%e7%bd%91%e7%bb%9c%e8%a7%a3%e5%86%b3%e9%87%8f%e5%ad%90%e5%a4%9a%e4%bd%93%e9%97%ae%e9%a2%98","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=3792","title":{"rendered":"\u91cd\u78c5Science\u8bba\u6587\uff1a\u7528\u4eba\u5de5\u795e\u7ecf\u7f51\u7edc\u89e3\u51b3\u91cf\u5b50\u591a\u4f53\u95ee\u9898"},"content":{"rendered":"
\n

\"\u96c6\u667a\"<\/span><\/p>\n

\u8fd1\u5e74\u6765\uff0c\u4eba\u4eec\u53d1\u73b0\u4e86\u8d8a\u6765\u8d8a\u591a\u7684<\/span>\u57fa\u7840\u7269\u7406\u5b66<\/span><\/strong>\u4e0e<\/span>\u4eba\u5de5\u667a\u80fd<\/span><\/strong>\u4e4b\u95f4\u7684\u8054\u7cfb\u3002\u9996\u5148\uff0c\u6df1\u5ea6\u5b66\u4e60\u4e0e\u7269\u7406\u7cfb\u7edf\u5b58\u5728\u7740\u672c\u8d28\u4e0a\u7684\u5bf9\u5e94\u5173\u7cfb\uff0c\u4f8b\u5982\u53d7\u9650\u73bb\u5c14\u5179\u66fc\u673a\u4e0e\u81ea\u65cb\u7cfb\u7edf\uff0c\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc\u4e0e\u91cd\u6574\u5316\u7fa4\uff1b\u5176\u6b21\uff0c\u673a\u5668\u5b66\u4e60\u662f\u4e00\u79cd\u6bd4\u4f20\u7edf\u7684\u6570\u503c\u6a21\u62df\u3001\u8499\u7279\u5361\u6d1b\u6a21\u62df\u66f4\u6709\u6548\u7684\u5bf9\u590d\u6742\u95ee\u9898\u8fd1\u4f3c\u6c42\u89e3\u7684\u65b9\u6cd5\u3002\u8fd9\u79cd\u6709\u6548\u6027\u8ba9\u4eba\u4eec\u5f00\u59cb\u601d\u8003\u7269\u7406\u4e0e\u673a\u5668\u5b66\u4e60\u66f4\u6df1\u5c42\u6b21\u7684\u8054\u7cfb\uff0c\u4e5f\u8bb8\u5b83\u80fd\u5e2e\u6211\u4eec\u83b7\u5f97\u5bf9\u667a\u80fd\u4ee5\u53ca\u5b87\u5b99\u672c\u8d28\u7684\u771f\u77e5\u707c\u89c1\u3002<\/span><\/p>\n

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\u672c\u6587\u662f\u4e8e2017\u5e742\u6708<\/strong>\u53d1\u8868\u5728\u79d1\u5b66\u4e0a\u7684\u91cd\u78c5\u6587\u7ae0\uff0c\u4f5c\u8005\u63d0\u51fa\u4e86\u57fa\u4e8e\u795e\u7ecf\u7f51\u7edc\u7684\u91cf\u5b50\u6001\u8868\u793a\u65b9\u6848<\/strong>\uff0c\u5e76\u5c55\u793a\u4e86\u5b83\u5728\u591a\u4e2a\u7ecf\u5178\u91cf\u5b50\u591a\u4f53\u95ee\u9898\u4e0a\u7684\u9ad8\u7cbe\u5ea6\u548c\u8868\u8fbe\u80fd\u529b\u3002\u8fd9\u7bc7\u6587\u7ae0\u751a\u81f3\u5f15\u53d1\u4e86\u6211\u4eec\u5bf9\u91cf\u5b50\u7cfb\u7edf\u66f4\u672c\u8d28\u7684\u601d\u8003\uff1a\u662f\u5426\u90a3\u4e9b\u8ba9\u6211\u4eec\u56f0\u60d1\u7684\u53cd\u76f4\u89c9\u7684\u91cf\u5b50\u7279\u6027\uff0c\u7279\u522b\u662f\u54e5\u672c\u54c8\u6839\u89e3\u91ca\u538b\u6839\u513f\u5c31\u4e0d\u5b58\u5728\uff0c\u800c\u53ea\u4e0d\u8fc7\u662f\u66f4\u590d\u6742\u7684\u7ecf\u5178\u7cfb\u7edf\u7684\u67d0\u79cd\u8868\u8c61\u5462\uff1f\u800c\u8fd9\u79cd\u8868\u8c61\u5374\u6070\u6070\u80fd\u88ab\u795e\u7ecf\u7f51\u7edc\u5f88\u597d\u5730\u8868\u8fbe\u51fa\u6765\u3002\u6362\u4e2a\u89d2\u5ea6\u601d\u8003\uff0c\u4e00\u4e2a\u7ecf\u5178\u7684\u590d\u6742\u7684\u795e\u7ecf\u7f51\u7edc\u6709\u53ef\u80fd\u5c55\u73b0\u51fa\u90a3\u4e9b\u532a\u5937\u6240\u601d\u7684\u91cf\u5b50\u7cfb\u7edf\u7279\u5f81\uff0c\u5982\u91cf\u5b50\u9042\u7a7f\u3001\u4e0d\u786e\u5b9a\u6027\u539f\u7406\u7b49\u7b49\u3002<\/span><\/strong><\/p>\n<\/section>\n<\/section>\n


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\u7528\u4eba\u5de5\u795e\u7ecf\u7f51\u7edc\u89e3\u51b3\u91cf\u5b50\u591a\u4f53\u95ee\u9898<\/strong><\/span><\/p>\n

Giuseppe Carleo1* and Matthias Troyer1,2<\/strong><\/span><\/p>\n


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\u6458\u8981<\/strong><\/span><\/p>\n


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\u91cf\u5b50\u7269\u7406\u4e2d\u7684\u91cf\u5b50\u591a\u4f53\u95ee\u9898\u7ed9\u6211\u4eec\u5e26\u6765\u7684\u5f88\u591a\u6311\u6218\u90fd\u8d77\u6e90\u4e8e\u5bf9\u7f16\u7801\u5728\u591a\u4f53\u6ce2\u51fd\u6570\u4e2d\u6307\u6570\u7ea7\u590d\u6742\u6027\u4e2d\u7684\u975e\u5e73\u51e1\u5173\u8054\u7279\u6027\u5982\u4f55\u63cf\u8ff0\u3002\u5728\u672c\u6587\u4e2d\uff0c\u6211\u4eec\u5bf9\u4e8e\u51e0\u4e2a\u7269\u7406\u5b66\u611f\u5174\u8da3\u7684\u95ee\u9898\uff0c\u5c55\u793a\u4e86\u5982\u4f55\u901a\u8fc7\u673a\u5668\u5b66\u4e60<\/span><\/strong>\u7684\u65b9\u5f0f\u6765\u5b66\u4e60\u6ce2\u51fd\u6570\uff0c\u4ece\u800c\u53ef\u4ee5\u5c06\u91cf\u5b50\u591a\u4f53\u95ee\u9898\u7684\u590d\u6742\u6027\u7b80\u5316\u4e3a\u53ef\u8ba1\u7b97\u7684\u7a0b\u5ea6\u3002\u6211\u4eec\u5f15\u5165\u4e86\u4e00\u79cd\u91cf\u5b50\u72b6\u6001<\/span><\/strong>\u7684\u53d8\u5206\u8868\u793a\u65b9\u6cd5\uff0c\u8be5\u65b9\u6cd5\u57fa\u4e8e\u9690\u5c42\u795e\u7ecf\u5143\u6570\u91cf\u53ef\u53d8\u7684\u4eba\u5de5\u795e\u7ecf\u7f51\u7edc\u6765\u5b8c\u6210\u3002\u6211\u4eec\u5c06\u8bf4\u660e\u5f3a\u5316\u5b66\u4e60\u65b9\u6848\u65e2\u80fd\u627e\u5230\u57fa\u6001\uff0c\u53c8\u80fd\u63cf\u8ff0\u590d\u6742\u76f8\u4e92\u4f5c\u7528\u7684\u91cf\u5b50\u7cfb\u7edf\u7684\u5e7a\u6b63\u65f6\u95f4\u6f14\u5316\u3002\u6211\u4eec\u7684\u65b9\u6cd5\u5728\u63cf\u8ff0\u4e00\u7ef4\u548c\u4e8c\u7ef4\u7684\u4ea4\u4e92\u81ea\u65cb\u6a21\u578b\u8fd9\u6837\u7684\u7b80\u5355\u7cfb\u7edf\u65f6\uff0c\u8fbe\u5230\u4e86\u5f88\u9ad8\u7684\u7cbe\u5ea6\u3002<\/p>\n


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\u6ce2\u51fd\u6570\u03a8\u662f\u91cf\u5b50\u7269\u7406\u5b66\u4e2d\u6700\u57fa\u672c\u7684\u5bf9\u8c61\uff0c\u4e5f\u662f\u4ece\u53e4\u5178\u7269\u7406\u6846\u67b6\u4e0b\u6700\u96be\u88ab\u7406\u89e3\u7684\u4e1c\u897f\u4e86\u3002\u03a8\u662f\u4e00\u4e2a\u5e9e\u5927\u7684\u6570\u5b66\u91cf\uff0c\u56e0\u4e3a\u5b83\u5305\u542b\u4e86\u4e00\u4e2a\u91cf\u5b50\u6001\u7684\u6240\u6709\u4fe1\u606f\uff0c\u65e0\u8bba\u662f\u5355\u4e2a\u7c92\u5b50\u8fd8\u662f\u4e00\u4e2a\u590d\u6742\u7684\u5206\u5b50\u3002\u539f\u5219\u4e0a\uff0c\u5bf9\u901a\u7528\u7684\u591a\u4f53\u91cf\u5b50\u6001\u8fdb\u884c\u5145\u5206\u7f16\u7801\u9700\u8981\u6307\u6570\u7ea7\u6570\u91cf\u7684\u4fe1\u606f\uff1b\u7136\u800c\uff0c\u771f\u5b9e\u7684\u60c5\u51b5\u662f\u63cf\u8ff0\u8bb8\u591a\u7269\u7406\u591a\u4f53\u7cfb\u7edf\u7684\u6ce2\u51fd\u6570\u5374\u53ea\u9700\u8981\u6709\u9650\u7684\u4fe1\u606f\u5c31\u591f\u4e86\uff0c\u5176\u5bb9\u91cf\u8fdc\u6bd4\u76f8\u5e94\u7684Hilbert\u7a7a\u95f4\u6240\u80fd\u5bb9\u7eb3\u7684\u6700\u5927\u5bb9\u91cf\u8981\u5c0f\u5f97\u591a\u3002\u5728\u8fd9\u6837\u7684\u7cfb\u7edf\u4e2d\uff0c\u6211\u4eec\u7528\u73b0\u4ee3\u7684\u65b9\u6cd5\u53ef\u4ee5\u6839\u636e\u6709\u9650\u6570\u91cf\u7684\u91cf\u5b50\u7ea0\u7f20<\/span><\/strong>\u548c\u5c11\u91cf\u7684\u7269\u7406\u72b6\u6001<\/span><\/strong>\u5c31\u80fd\u7528\u6709\u9650\u7684\u7ecf\u5178\u8d44\u6e90\u89e3\u51fa\u591a\u4f53\u7684\u859b\u5b9a\u8c14\u65b9\u7a0b\u3002<\/p>\n


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\"\u96c6\u667a\"<\/p>\n


<\/p>\n

\u4eba\u4eec\u901a\u5e38\u4f1a\u4f7f\u7528\u76f4\u63a5\u4f9d\u8d56\u4e8e\u6ce2\u51fd\u6570\u7684\u6570\u503c\u8fd1\u4f3c\u65b9\u6cd5\uff0c\u6765\u5bf9\u7269\u7406\u76f8\u5173\u6784\u578b\u8fdb\u884c\u6709\u9650\u91c7\u6837\uff0c\u4e5f\u53ef\u4ee5\u5bf9\u91cf\u5b50\u6001\u8fdb\u884c\u6709\u6548\u7684\u538b\u7f29\u3002\u4f8b\u5982\u4eba\u4eec\u5e38\u7528\u7684\u91cf\u5b50\u8499\u7279\u5361\u7f57(Quantum Monte Carlo\uff0cQMC)\u65b9\u6cd5\uff08\u5373\u7edf\u8ba1\u6a21\u62df\u65b9\u6cd5\uff09\u7b49\u968f\u673a\u65b9\u6cd5\u5c31\u5c5e\u4e8e\u7b2c\u4e00\u7c7b\uff0c\u5b83\u4eec\u90fd\u4f9d\u8d56\u4e8e\u6982\u7387\u6846\u67b6\uff0c\u5e76\u901a\u5e38\u8981\u6c42\u4e00\u4e2a\u534a\u6b63\u5b9a\u7684\u6ce2\u51fd\u6570(1-3)\u3002\u800c\u53e6\u4e00\u79cd\u538b\u7f29\u7684\u65b9\u6cd5\u4f9d\u8d56\u4e8e\u6ce2\u51fd\u6570\u7684\u6709\u6548\u8868\u5f81\uff0c\u4f8b\u5982\u77e9\u9635\u4e58\u79ef\u6001(Matrix Product Space, MPS)(4-6)\u6216\u66f4\u5e38\u89c1\u7684\u5f20\u91cf\u7f51\u7edc(Tensor Network\uff0c7-9)\u3002\u7136\u800c\uff0c\u91c7\u7528\u73b0\u6709\u65b9\u6cd5\u4e5f\u6709\u5f88\u591a\u5931\u8d25\u7684\u4f8b\u5b50\uff0c\u8fd9\u4e3b\u8981\u662f\u7531\u4e8eQMC(10)\uff08\u91cf\u5b50\u8499\u7279\u5361\u7f57\u65b9\u6cd5\uff09\u672c\u8eab\u7684\u95ee\u9898\uff0c\u4ee5\u53ca\u5f53\u524d\u7684\u538b\u7f29\u65b9\u6cd5\u5728\u9ad8\u7ef4\u5ea6\u7cfb\u7edf\u4e2d\u8868\u73b0\u4f4e\u6548\u7684\u95ee\u9898\u3002\u56e0\u6b64\uff0c\u5c3d\u7ba1\u8fd9\u4e9b\u65b9\u6cd5\u53d6\u5f97\u4e86\u663e\u8457\u7684\u6210\u529f\uff0c\u4f46\u4ecd\u6709\u5927\u91cf\u672a\u7ecf\u63a2\u7d22\u7684\u7269\u7406\u6761\u4ef6\u5b58\u5728\uff0c\u5176\u4e2d\u4e5f\u5305\u62ec\u8bb8\u591a\u672a\u89e3\u51b3\u7684\u95ee\u9898\uff0c\u4ece\u9ad8\u7ef4\u5ea6\u7cfb\u7edf\u7684\u52a8\u529b\u5b66\u7279\u6027(11\u300112)\u5230\u5f3a\u76f8\u4e92\u4f5c\u7528\u7684\u8d39\u7c73\u5b50(13\u300114)\u7684\u7cbe\u786e\u57fa\u6001\u5c5e\u6027\u8fd9\u6837\u7684\u57fa\u7840\u95ee\u9898\u3002\u8fd9\u79cd\u95ee\u9898\u7684\u6838\u5fc3\u5c31\u5728\u4e8e\u627e\u5230\u4e00\u79cd\u666e\u904d\u7684\u7b56\u7565\uff0c\u4ee5\u51cf\u5c11\u5e9e\u5927\u7684\u591a\u4f53\u6ce2\u51fd\u6570\u7684\u6307\u6570\u7ea7\u590d\u6742\u6027\uff0c\u4ece\u800c\u964d\u4f4e\u5176\u6700\u57fa\u672c\u7684\u7279\u5f81\u7ef4\u5ea6(15)\u3002<\/p>\n


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\u5e7f\u4e49\u5730\u770b\uff0c\u5b9e\u9645\u4e0a\u8fd9\u4e9b\u95ee\u9898\u7684\u672c\u8d28\u5c31\u662f\u5bf9\u6570\u636e\u8fdb\u884c\u964d\u7ef4\u548c\u7279\u5f81\u63d0\u53d6<\/span><\/strong>\u3002\u800c\u8fd9\u6070\u6070\u5c31\u662f\u4eba\u5de5\u795e\u7ecf\u7f51\u7edc\u6700\u64c5\u957f\u7684\u4e8b\u60c5(16)\u3002\u5b83\u4eec\u5df2\u7ecf\u5728\u5404\u79cd\u5404\u6837\u7684\u95ee\u9898\u548c\u73af\u5883\uff0c\u5305\u62ec\u56fe\u50cf\u548c\u8bed\u97f3\u8bc6\u522b(17)\u518d\u5230\u535a\u5f08(18)\u4e2d\u8868\u73b0\u7a81\u51fa\u3002\u6700\u8fd1\uff0c\u795e\u7ecf\u7f51\u7edc\u88ab\u5f15\u5165\u5230\u4e86\u7269\u7406\u5b66\u7814\u7a76\u4e2d(19-23)\uff0c\u4f46\u8fd9\u4e9b\u7814\u7a76\u90fd\u96c6\u4e2d\u5728\u5bf9\u7269\u76f8\u7684\u5206\u7c7b\u4e0a\uff0c\u524d\u63d0\u6761\u4ef6\u662f\u4ece\u8fd9\u4e9b\u7269\u76f8\u7684\u72b6\u6001\u4e2d\u8fdb\u884c\u7cbe\u786e\u91c7\u6837\u662f\u53ef\u80fd\u7684\u3002\u800c\u5728\u6ca1\u6709\u7cbe\u786e\u6837\u672c\u7684\u5148\u9a8c\u77e5\u8bc6\u7684\u60c5\u51b5\u4e0b\uff0c\u89e3\u51b3\u591a\u4f53\u95ee\u9898\u7684\u6311\u6218\u6027\u76ee\u6807\u4ecd\u7136\u672a\u88ab\u63a2\u7d22\uff0c\u800c\u8fd9\u6070\u6070\u662f\u4eba\u5de5\u667a\u80fd\u6709\u53ef\u80fd\u53d1\u6325\u4f5c\u7528\u7684\u9886\u57df\u3002\u56e0\u6b64\uff0c\u8ba4\u8bc6\u4eba\u5de5\u795e\u7ecf\u7f51\u7edc\u662f\u5426\u80fd\u591f\u4fee\u6539\u548c\u8c03\u6574\u81ea\u5df1\u4ee5\u9002\u5e94\u5206\u6790\u548c\u63cf\u8ff0\u8fd9\u6837\u7684\u91cf\u5b50\u591a\u4f53\u7cfb\u7edf<\/span><\/strong>\u662f\u4e00\u4e2a\u975e\u5e38\u57fa\u672c\uff0c\u4e5f\u662f\u5177\u6709\u5b9e\u9645\u610f\u4e49\u7684\u95ee\u9898\u3002\u8fd9\u79cd\u80fd\u529b\u53ef\u4ee5\u88ab\u7528\u6765\u89e3\u51b3\u5728\u67d0\u79cd\u7269\u7406\u6761\u4ef6\u4e0b\uff0c\u90a3\u4e9b\u7528\u73b0\u6709\u7684\u7cbe\u786e\u6570\u503c\u65b9\u6cd5\u96be\u4ee5\u89e3\u51b3\u7684\u91cf\u5b50\u591a\u4f53\u95ee\u9898\u3002<\/p>\n


<\/p>\n

\u8fd9\u91cc\u6211\u4eec\u4ecb\u7ecd\u4e00\u79cd\u7528\u4eba\u5de5\u795e\u7ecf\u7f51\u7edc\u65b9\u6cd5<\/span><\/strong>\u6765\u8868\u8fbe\u6ce2\u51fd\u6570\u7684\u65b9\u6cd5\uff0c\u5b83\u7531\u4e00\u7ec4\u5185\u90e8\u53c2\u6570W\u6307\u5b9a\u3002\u6211\u4eec\u7ed9\u51fa\u4e86\u4e00\u4e2a\u968f\u673a\u6846\u67b6\uff0c\u7528\u4e8e\u52a0\u5f3a\u5bf9\u53c2\u6570W\u7684\u5f3a\u5316\u5b66\u4e60\uff0c\u4f7f\u7ed9\u5b9a\u91cf\u5b50\u54c8\u5bc6\u987f\u91cfH\u7684\u57fa\u6001\u548c\u65f6\u95f4\u4f9d\u8d56\u7684\u7269\u7406\u72b6\u6001\u80fd\u5f97\u5230\u6700\u597d\u7684\u8868\u793a\uff0c\u7136\u540e\u5bf9\u795e\u7ecf\u7f51\u7edc\u7684\u53c2\u6570\u8fdb\u884c\u8bad\u7ec3\u3002\u6216\u8005\u5f53\u6211\u4eec\u5bf9\u52a8\u6001\u5c5e\u6027\u611f\u5174\u8da3\u65f6\uff0c\u6211\u4eec\u8fd8\u53ef\u4ee5\u901a\u8fc7\u9759\u6001\u53d8\u5206\u8499\u7279\u5361\u7f57(Varational Monte Carlo\uff0cVMC)\u91c7\u6837(24)\u6216\u65f6\u95f4\u4f9d\u8d56\u7684VMC(25\uff0c26)\u65b9\u6cd5\u6765\u6c42\u89e3\u3002\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u5c31\u901a\u8fc7\u5bf9\u4e00\u7ef4\u548c\u4e8c\u7ef4Ising(\u4f0a\u8f9b)\u6a21\u578b\u548c\u6d77\u68ee\u5821(Heisenberg)\u6a21\u578b\u6765\u9a8c\u8bc1\u8fd9\u79cd\u65b9\u6cd5\u7684\u6b63\u786e\u6027\u3002\u6211\u4eec\u8bc1\u660e\u4e86\u795e\u7ecf\u7f51\u7edc\u91cf\u5b50\u6001(Neural network Quantum State\uff0cNQS)\u7684\u5f3a\u5927\u80fd\u529b\uff0c\u5e76\u5728\u57fa\u6001\u548c\u975e\u5e73\u8861\u52a8\u529b\u5b66\u7b49\u95ee\u9898\u4e2d\u83b7\u5f97\u4e86\u76ee\u524d\u6240\u80fd\u8fbe\u5230\u7684\u6700\u597d\u7684\u7cbe\u5ea6\u3002 <\/p>\n


<\/p>\n

\"\u96c6\u667a\"<\/p>\n


<\/p>\n


    <\/strong><\/strong><\/p>\n
\n
\n
\u795e\u7ecf\u7f51\u7edc\u91cf\u5b50\u6001  <\/strong><\/span><\/section>\n<\/section>\n

   <\/section>\n

   <\/section>\n


<\/p>\n

\u8003\u8651\u4e00\u4e2a\u91cf\u5b50\u7cfb\u7edf, \u8fd9\u4e2a\u7cfb\u7edf\u6709N\u4e2a\u79bb\u6563\u53d6\u503c\u7684\u81ea\u7531\u5ea6S=(S1,S2,…,SN), \u8fd9\u4e9b\u81ea\u7531\u5ea6\u6709\u53ef\u80fd\u662f\u81ea\u65cb, \u73bb\u8272\u5b50\u5360\u636e\u6570, \u6216\u8005\u5176\u4ed6\u7c7b\u4f3c\u7684\u503c. \u8be5\u7cfb\u7edf\u7684\u591a\u4f53\u6ce2\u51fd\u6570\u662f\u4e00\u4e2a\u4eceN\u7ef4\u7684\u96c6\u5408S(\u6570\u91cf\u5448\u6307\u6570\u589e\u957f\u7684)\u5230\u590d\u6570\u4e4b\u95f4\u7684\u6620\u5c04, \u8fd9\u4e9b\u590d\u6570\u80fd\u591f\u5b8c\u5168\u8868\u5f81\u91cf\u5b50\u6001\u7684\u632f\u5e45\u548c\u76f8\u4f4d\u3002\u6211\u4eec\u770b\u5f85\u8fd9\u4e2a\u95ee\u9898\u7684\u89c6\u89d2\u662f, \u5c06\u6ce2\u51fd\u6570\u7406\u89e3\u6210\u4e00\u4e2a\u53ef\u8ba1\u7b97\u7684\u9ed1\u5323\u5b50, \u8fd9\u4e2a\u9ed1\u5323\u5b50\u80fd\u591f\u5bf9\u7ed9\u5b9a\u7684\u591a\u4f53\u7cfb\u7edf\u7684\u6784\u578bS, \u4f9d\u636e\u03a8(S)\u8fd4\u56de\u4e00\u7ec4\u76f8\u4f4d\u548c\u632f\u5e45. \u6211\u4eec\u7684\u76ee\u6807\u662f\u7528\u4e00\u4e2a\u795e\u7ecf\u7f51\u7edc\u6765\u8fd1\u4f3c\u8fd9\u4e2a\u80fd\u8fdb\u884c\u8ba1\u7b97\u7684\u9ed1\u5323\u5b50, \u4f7f\u5f97\u5b83\u7ecf\u8fc7\u8bad\u7ec3\u540e\u53ef\u4ee5\u6781\u597d\u5730\u8868\u5f81\u6211\u4eec\u5173\u5fc3\u7684\u7cfb\u7edf\u3002\u9488\u5bf9\u7279\u5b9a\u7684\u4efb\u52a1, \u4eba\u4eec\u5df2\u7ecf\u63d0\u51fa\u4e86\u4e0d\u540c\u7684\u4eba\u5de5\u795e\u7ecf\u7f51\u7edc\u7ed3\u6784\u4f5c\u4e3a\u5907\u9009\u65b9\u6cd5.\u3002\u540c\u7406, \u7528\u6765\u63cf\u8ff0\u4e00\u4e2a\u591a\u4f53\u7cfb\u7edf\u6240\u9700\u8981\u7684\u6700\u597d\u7684(\u795e\u7ecf\u7f51\u7edc)\u7ed3\u6784\u4e5f\u56e0\u95ee\u9898\u800c\u5f02\u3002\u66f4\u5177\u4f53\u5730\u8bf4, \u6211\u4eec\u5c06\u8ba8\u8bba\u9650\u5b9a\u5728\u53d7\u9650\u73bb\u5c14\u5179\u66fc\u673a<\/strong><\/span>(Ristricted Boltzman Machine\uff0cRBM)\u8fd9\u79cd\u7279\u6b8a\u7684\u7ed3\u6784\u4e0a, \u7528\u5b83\u6765\u63cf\u8ff0\u81ea\u65cb1\/2\u7684\u91cf\u5b50\u7cfb\u7edf\u3002<\/span><\/p>\n


<\/p>\n

\"\u96c6\u667a\"<\/p>\n

\u56fe1\uff1a\u4eba\u5de5\u795e\u7ecf\u7f51\u7edc\u7f16\u7801\u4e86N\u4e2a\u81ea\u65cb\u7684\u591a\u4f53\u91cf\u5b50\u6001<\/span><\/p>\n


<\/p>\n

\u8fd9\u662f\u4e00\u4e2a\u53d7\u9650\u73bb\u8033\u5179\u66fc\u673a\u7684\u4f53\u7cfb\u7ed3\u6784\uff0c\u5b83\u662f\u7531N\u4e2a\u53ef\u89c1\u7684\u4eba\u5de5\u795e\u7ecf\u5143(\u9ec4\u70b9)\u548cM\u4e2a\u9690\u85cf\u5c42\u795e\u7ecf\u5143(\u7070\u70b9)\u7ec4\u6210\u7684\u3002\u5bf9\u4e8e\u591a\u4f53\u81ea\u65cb\u72b6\u6001\u7684\u6bcf\u4e00\u4e2a\u503cS=(\u03c3^z_1\uff0c\u03c3^z_2\uff0c\u2026\uff0c\u03c3^z_N)\uff0c\u4eba\u5de5\u795e\u7ecf\u7f51\u7edc\u8ba1\u7b97\u6ce2\u51fd\u6570\u03a8(S)\u7684\u503c\u3002<\/p>\n


<\/p>\n

\u5728\u8fd9\u4e2a\u60c5\u51b5\u4e0b, RBM\u4eba\u5de5\u7f51\u7edc\u62e5\u6709\u4e00\u5c42\u5177\u6709N\u4e2a\u8282\u70b9\u7684\u53ef\u89c1\u5c42, \u53ef\u89c1\u5c42\u5bf9\u5e94\u4e00\u7ec4\u9009\u5b9a\u57fa\u77e2\u4e0b\u7684\u81ea\u65cb\u7269\u7406\u91cf(\u5982: S=(\u03c3^z_1\uff0c\u03c3^z_2\uff0c\u2026\uff0c\u03c3^z_N) , \u8fd8\u62e5\u6709\u4e00\u5c42\u5177\u6709M\u4e2a\u8f85\u52a9\u53d8\u91cf\u7684\u9690\u85cf\u5c42(h1,h2,…,hM) (\u56fe1). \u8fd9\u6837\u7684\u63cf\u8ff0\u5bf9\u5e94\u91cf\u5b50\u6001\u7684\u53d8\u5206\u8868\u8fbe\u5f0f:<\/p>\n


<\/p>\n

\"\u96c6\u667a\"<\/p>\n

\u8fd9\u91cc\uff0chi={-1,1}\u662f\u4e00\u7ec4M\u4e2a\u9690\u542b\u81ea\u65cb\u53d8\u91cf\uff0c\u7f51\u7edc\u53c2\u6570\uff1aW={a,b,W}\u5b8c\u5168\u8868\u5f81\u4e86\u8fd9\u4e2a\u7f51\u7edc\u5bf9\u4e8e\u4e00\u4e2a\u7ed9\u5b9a\u7684\u8f93\u5165\u72b6\u6001S\u7684\u54cd\u5e94\u3002\u7531\u4e8e\u8fd9\u4e2a\u7ed3\u6784\u7684\u7279\u70b9\u662f\u6ca1\u6709\u5c42\u5185\u90e8\u7684\u76f8\u4e92\u4f5c\u7528, \u8fd9\u4e9b\u9690\u53d8\u91cf\u53ef\u4ee5\u663e\u5f0f\u5730\u901a\u8fc7\u6c42\u8ff9\u6765\u6d88\u9664, \u6c42\u8ff9\u540e\u6ce2\u51fd\u6570\u5c31\u53d8\u6210\u4e86:<\/p>\n


<\/p>\n

\"\u96c6\u667a\"<\/p>\n

\u4e14\u6709<\/p>\n

\"\u96c6\u667a\"<\/p>\n

\u8fd9\u4e2a\u7f51\u7edc\u7684\u6743\u91cd\u4e00\u822c\u6765\u8bf4\u53d6\u590d\u6570, \u8fd9\u6837\u80fd\u540c\u65f6\u5b8c\u6574\u63cf\u8ff0\u6ce2\u51fd\u6570\u7684\u632f\u5e45\u548c\u76f8\u4f4d\u3002<\/p>\n


<\/p>\n

\u6570\u5b66\u4e0a\u4eba\u4eec\u5df2\u7ecf\u8bc1\u660e\u4e86\u6240\u8c13\u7684”\u8868\u793a\u5b9a\u7406”(27-29)\uff0c\u8fd9\u4e2a\u5b9a\u7406\u80fd\u591f\u4fdd\u8bc1\u7528(\u795e\u7ecf)\u7f51\u7edc\u6765\u8fd1\u4f3c\u8db3\u591f\u5149\u6ed1\u4e14\u89c4\u5219\u7684\u9ad8\u7ef4\u51fd\u6570\u3002\u8be5\u5b9a\u7406\u540c\u6837\u80fd\u591f\u4fdd\u8bc1NQS<\/span><\/strong>(Neural network Quantum States\uff0c\u795e\u7ecf\u7f51\u7edc\u91cf\u5b50\u6001)\u80fd\u591f\u63cf\u8ff0\u9519\u7efc\u590d\u6742\u7684\u591a\u4f53\u6ce2\u51fd\u6570, \u53ea\u8981\u591a\u4f53\u6ce2\u51fd\u6570\u6ee1\u8db3\u8fd9\u4e9b\u6761\u4ef6\u3002\u6211\u4eec\u6709\u7406\u7531\u76f8\u4fe1NQS\u7ed3\u6784\u662f\u4e00\u4e2a\u5408\u7406\u7684\u9009\u62e9\u3002<\/p>\n


<\/p>\n

\u8fd9\u4e2a\u8868\u8ff0\u65b9\u5f0f\u7684\u4e00\u4e2a\u5b9e\u9645\u597d\u5904\u662f, \u539f\u5219\u4e0a\u5b83\u7684(\u8bad\u7ec3)\u6548\u679c\u80fd\u591f\u901a\u8fc7\u589e\u52a0\u9690\u53d8\u91cf\u7684\u6570\u91cf\u5f97\u5230\u7cfb\u7edf\u6027\u7684\u63d0\u9ad8. \u6570\u91cfM(\u6216\u8005, \u7b49\u4ef7\u7684\u8bf4, \u6bd4\u4f8ba = M\/N\uff0c\u5176\u4e2dM\u4e3a\u9690\u542b\u5c42\u5355\u5143\u6570\u91cf\uff0cN\u4e3a\u53ef\u89c1\u5c42\u5355\u5143\u6570\u91cf)\u626e\u6f14\u4e86\u7c7b\u4f3cMPS\u91cc\u6210\u952e\u7ef4\u5ea6\u7684\u89d2\u8272\u3002\u4f46\u662f, \u8fd9\u4e9b\u9690\u5c42\u5355\u5143\u5bfc\u81f4\u7684\u5173\u8054\u672c\u8d28\u4e0a\u662f\u975e\u5c40\u57df\u7684, \u56e0\u6b64, \u8fd9\u79cd\u5173\u8054\u5341\u5206\u9002\u5408\u63cf\u8ff0\u5177\u6709\u4efb\u610f\u7ef4\u5ea6\u7684\u91cf\u5b50\u7cfb\u7edf\u3002<\/p>\n


<\/p>\n

NQS\u53e6\u4e00\u4e2a\u4fbf\u5229\u4e4b\u5904\u662f, \u7279\u5b9a\u7684\u5bf9\u79f0\u6027\u4f1a\u964d\u4f4e<\/span><\/strong>\uff0c\u4f8b\u5982, \u5177\u6709\u5e73\u79fb\u4e0d\u53d8\u6027\u7684\u53d7\u9650\u6ce2\u5c14\u5179\u66fc\u673a\u4e2d\u8003\u8651\u6676\u683c\u5e73\u79fb\u5bf9\u79f0\u6027\u53ef\u4ee5\u51cf\u5c11NQS\u65b9\u6848\uff08NQS Ansatz\uff09\u7684\u53d8\u5206\u53c2\u6570\u7684\u6570\u91cf\u3002\u5177\u4f53\u70b9\u6765\u8bf4, \u5bf9\u4e8e\u6574\u6570\u7684\u9690\u53d8\u91cf\u5bc6\u5ea6a = 1,2,…, \u6743\u91cd\u77e9\u9635\u53d6\u7279\u5f81\u8fc7\u6ee4\u5668\u7684\u5f62\u5f0fW_j^{f}\uff0c\u5176\u4e2df\u5c5e\u4e8e[1,a]\u3002\u8fd9\u4e9b\u8fc7\u6ee4\u5668\u603b\u5171\u6709aN\u4e2a\u53d8\u5206\u5143\u7d20, \u800c\u4e0d\u662f\u975e\u5bf9\u79f0\u60c5\u51b5\u4e0b\u7684aN^2\u4e2a\u5143\u7d20\u3002<\/p>\n

\u5982\u679c\u73b0\u5728\u7ed9\u5b9a\u4e00\u4e2a\u4e00\u822c\u7684\u91cf\u5b50\u591a\u4f53\u6001\u7684\u8868\u8fbe\u5f0f, \u6211\u4eec\u4f59\u4e0b\u7684\u4efb\u52a1\u5c31\u662f\u7528\u673a\u5668\u5b66\u4e60,\u901a\u8fc7\u6700\u4f18\u5316\u7f51\u7edc\u53c2\u6570W, \u6765\u6c42\u89e3\u591a\u4f53\u95ee\u9898\u3002\u4e00\u4e2a\u975e\u5e38\u6709\u610f\u601d\u7684\u5e94\u7528\u662f, \u5177\u4f53\u7684\u591a\u4f53\u72b6\u6001\u6211\u4eec\u5e76\u4e0d\u77e5\u9053, \u4e00\u822c\u6211\u4eec\u901a\u8fc7\u7ed9\u5b9a\u7684\u54c8\u5bc6\u987f\u91cfH\u6765\u6c42\u89e3\u9759\u6001\u859b\u5b9a\u8c14\u65b9\u7a0bH|\u03a8>=E|\u03a8>\u6216\u542b\u65f6\u65b9\u7a0b\uff1aH|\u03a8(t)>=id\/dt |\u03a8>\u3002\u5728\u6ca1\u6709\u771f\u5b9e\u7684\u6ce2\u51fd\u6570\u63d0\u4f9b\u6837\u672c\u7684\u60c5\u51b5\u4e0b,\u901a\u8fc7\u76d1\u7763\u5b66\u4e60\u5f97\u5230\u03a8\u5e76\u4e0d\u53ef\u884c\u3002\u4f46\u662f, \u6211\u4eec\u63a8\u51fa\u4e86\u4e00\u4e2a\u81ea\u6070\u7684\u5f3a\u5316\u5b66\u4e60\u65b9\u6cd5. \u5728\u8fd9\u4e2a\u65b9\u6cd5\u4e2d, \u57fa\u6001\u6ce2\u51fd\u6570\u6216\u8005\u542b\u65f6\u6ce2\u51fd\u6570\u53ef\u4ee5\u57fa\u4e8e\u53d8\u5206\u539f\u7406\u63d0\u4f9b\u7684\u53cd\u9988\u8fdb\u884c\u5b66\u4e60\u5f97\u5230.<\/p>\n


<\/p>\n

          <\/span><\/p>\n
\n
\n
\u57fa\u6001<\/span><\/strong><\/section>\n<\/section>\n

   <\/section>\n

   <\/section>\n


<\/p>\n

\u4e3a\u4e86\u8bc1\u660eNQS\u5728\u590d\u6742\u591a\u4f53\u91cf\u5b50\u6001\u7684\u63cf\u8ff0\u4e2d\u7684\u51c6\u786e\u6027\uff0c\u6211\u4eec\u9996\u5148\u5173\u6ce8\u4e8e\u627e\u5230\u7ed9\u5b9a\u54c8\u5bc6\u987f\u51fd\u6570H\u7684\u672a\u77e5\u57fa\u6001\u7684\u6700\u597d\u7684\u795e\u7ecf\u7f51\u7edc\u8868\u793a\u7684\u76ee\u6807\u3002\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u5b9e\u73b0\u5f3a\u5316\u5b66\u4e60\u9700\u8981\u901a\u8fc7\u4f7f\u7f51\u7edc\u6743\u91cdW\u7684\u80fd\u91cfE(W) = <\u03a8_M|H|\u03a8_M >\/<\u03a8_M |\u03a8_M>\u7684\u671f\u671b\u503c\u6700\u5c0f\u5316\u6765\u8fbe\u5230\u3002\u5728\u968f\u673a\u8bbe\u7f6e\u4e0b\uff0c\u8fd9\u662f\u901a\u8fc7\u8fed\u4ee3\u65b9\u6848<\/span><\/strong>\u5b9e\u73b0\u7684\u3002\u5728\u6bcf\u6b21\u8fed\u4ee3k\u4e2d\uff0c\u5bf9\u4e8e\u7ed9\u5b9a\u7684\u4e00\u7ec4\u53c2\u6570W_k\u5b9e\u73b0|\u03a8_M(S;W_k)|^2\u7684\u8499\u7279\u5361\u7f57\u91c7\u6837\u3002\u540c\u65f6\uff0c\u83b7\u5f97\u80fd\u91cf\u68af\u5ea6\u7684\u968f\u673a\u4f30\u8ba1\u3002\u7136\u540e\uff0c\u4f7f\u7528\u4e00\u79cd\u6539\u8fdb\u7684\u68af\u5ea6\u4e0b\u964d\u4f18\u5316\uff0832\uff09\u6765\u7ed9\u51fa\u4e0b\u4e00\u7ec4\u6743\u91cdW_{k+1}\u3002\u8fd9\u4e2a\u65b9\u6cd5\u7684\u603b\u4f53\u8ba1\u7b97\u6210\u672c\u4e0e\u6807\u51c6\u57fa\u6001\u91cf\u5b50\u8499\u7279\u5361\u7f57\u6a21\u62df\u7684\u603b\u4f53\u8ba1\u7b97\u6210\u672c\u76f8\u5f53\uff08\u53c2\u89c1\u539f\u8bba\u6587\u8865\u5145\u6750\u6599\uff09\u3002<\/p>\n


<\/p>\n

\u4e3a\u4e86\u9a8c\u8bc1\u6211\u4eec\u7684\u65b9\u6848\uff0c\u6211\u4eec\u8003\u8651\u4e86\u4e24\u4e2a\u5178\u578b\u7684\u81ea\u65cb\u6a21\u578b\u7684\u57fa\u6001\u95ee\u9898\uff0c\u6a2a\u5411\u573aIsing (TFI)\u6a21\u578b\u548c\u53cd\u94c1\u78c1\u6d77\u68ee\u5821 (AFH)\u6a21\u578b\u3002\u4ed6\u4eec\u7684\u54c8\u5bc6\u5c14\u987f\u7b97\u5b50<\/span><\/strong>\u5206\u522b\u662f:<\/p>\n


<\/p>\n

\"\u96c6\u667a\"<\/p>\n

\u548c:<\/p>\n


<\/p>\n

\"\u96c6\u667a\"<\/p>\n

\u5176\u4e2d\u03c3_x\uff0c\u03c3_y\u548c\u03c3_z\u662f\u6ce1\u5229\u77e9\u9635\u3002<\/p>\n


<\/p>\n

\"\u96c6\u667a\"<\/p>\n

\u56fe2: \u591a\u4f53\u57fa\u6001\u7684\u795e\u7ecf\u7f51\u7edc\u8868\u793a<\/span><\/p>\n


<\/p>\n

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<\/p>\n

\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u5c06\u8003\u8651\u5177\u6709\u5468\u671f\u8fb9\u754c\u6761\u4ef6(PBCs)\u7684\u4e00\u7ef4\u548c\u4e8c\u7ef4\uff081D\u548c2D\uff09\u6676\u683c\u7684\u60c5\u51b5\u3002\u5728\u56fe2\u4e2d\uff0c\u6211\u4eec\u5c55\u793a\u4e86\u4e24\u4e2a\u9690\u542b\u53d8\u91cf\u5bc6\u5ea6\u03b1 = 4\u7684\u4e24\u4e2a\u81ea\u65cb\u6a21\u578b\u7684\u57fa\u6001\u7684\u6700\u4f18\u7f51\u7edc\u7ed3\u6784\uff0c\u5e76\u4e14\u6211\u4eec\u89c4\u5b9a\u8fd9\u4e9b\u7ed3\u6784\u5177\u6709\u5e73\u79fb\u5bf9\u79f0\u6027\u3002\u6211\u4eec\u53d1\u73b0\u6bcf\u4e2a\u8fc7\u6ee4\u5668f = [1,…\u03b1]\u80fd\u591f\u5b66\u4e60\u5728\u57fa\u6001\u6ce2\u51fd\u6570\u4e2d\u6d8c\u73b0\u7684\u7279\u5b9a\u7684\u5173\u8054\u7279\u5f81\u3002\u4f8b\u5982\uff0c\u5728\u4e8c\u7ef4\u60c5\u51b5\u4e0b\uff08\u5982\u56fe2\u6240\u793a\uff0c\u53f3\u8fb9\u7684\u9762\u677f\uff09\u795e\u7ecf\u7f51\u7edc\u5b66\u4e60\u4e0e\u53cd\u94c1\u78c1\u6027\u5173\u8054\u7684\u6a21\u5f0f\u3002NQS\u7684\u4e00\u822c\u884c\u4e3a\u5b8c\u5168\u7c7b\u4f3c\u4e8e\u5728\u5377\u79ef\u795e\u7ecf\u7f51\u7edc\u4e2d\u89c2\u5bdf\u5230\u7684\u90a3\u6837\uff0c\u5728\u4e0d\u540c\u5c42\u6b21\u5b66\u4e60\u8f93\u5165\u6570\u636e\u7684\u7279\u5b9a\u7ed3\u6784\u3002<\/p>\n


<\/p>\n

\"\u96c6\u667a\"<\/p>\n

\u56fe3.\u7528\u795e\u7ecf\u7f51\u7edc\u91cf\u5b50\u6001\uff08NQS\uff09\u5bfb\u627e\u591a\u4f53\u57fa\u6001\u80fd\u91cf<\/span><\/p>\n


<\/p>\n

\u51e0\u4e2a\u6d4b\u8bd5\u7528\u4f8b\u663e\u793a\u4e86NQS\u57fa\u6001\u80fd\u91cf\u76f8\u5bf9\u4e8e\u7cbe\u786e\u503c\u7684\u8bef\u5dee\u3002\u53ef\u4ee5\u901a\u8fc7\u589e\u52a0\u9690\u85cf\u5355\u5143\u5bc6\u5ea6\u03b1\u83b7\u5f97\u57fa\u6001\u80fd\u91cf\u7684\u4efb\u610f\u7cbe\u5ea6\u3002(A) \u5728\u7ed9\u5b9a\u78c1\u573a\u5f3a\u5ea6h\u7684\u51e0\u4e2a\u4e0d\u540c\u53d6\u503c\u4e0b\uff0c1\u7ef4TFI\u6a21\u578b\u7684\u7cbe\u5ea6\uff0c\u8be5\u6a21\u578b\u753180\u4e2a\u683c\u70b9\u7ec4\u6210\u81ea\u65cb\u94fe\uff0c\u5177\u6709\u5468\u671f\u6027\u8fb9\u754c\u6761\u4ef6\uff08PBCs\uff09\uff08\u6211\u4eec\u9690\u53bb\u4e86\u4f4e\u4e8e10^{\u20138} \u7684\u70b9\u4ee5\u63d0\u9ad8\u53ef\u8bfb\u6027\uff09\u3002(B) 80\u4e2a\u683c\u70b9\u5177\u6709\u5468\u671f\u8fb9\u754c\u6761\u4ef6\u7684\u81ea\u65cb\u94fe\u5f97\u5230\u7684\u7cbe\u5ea6\u4e0eJastrow \u5047\u8bbe\u7684\u7cbe\u5ea6\uff08\u6c34\u5e73\u865a\u7ebf\uff09\u5bf9\u6bd4\u3002(C) \u572810\u00d710\u683c\u70b9\u4e0a\u5177\u6709\u5468\u671f\u8fb9\u754c\u6761\u4ef6\u7684AFH\u6a21\u578b\u7cbe\u5ea6\u4e0e\u91c7\u7528EPS [\u4e0a\u865a\u7ebf\uff0835\uff09]\u548cPEPS [\u4e0b\u865a\u7ebf\uff0836\uff09]\u7684\u7cbe\u5ea6\u5bf9\u6bd4\u3002\u5bf9\u4e8e\u8fd9\u91cc\u8003\u8651\u7684\u6240\u6709\u60c5\u51b5\uff0cNQS\u65b9\u6cd5\u5728\u4e00\u7ef4\u4e0a\u8fbe\u5230\u4e86MPS\u7ea7\u7cbe\u5ea6\uff0c\u5e76\u7cfb\u7edf\u6027\u5730\u6539\u8fdb\u4e862\u7ef4\u6709\u9650\u683c\u70b9\u7cfb\u7edf\u7684\u6700\u4f73\u5df2\u77e5\u53d8\u5206\u72b6\u6001\u3002 <\/p>\n


<\/p>\n

\u5728\u56fe3\u4e2d\uff0c\u6211\u4eec\u5c55\u793a\u4e86NQS\u7684\u7cbe\u5ea6\uff0c\u5c06\u5176\u91cf\u5316\u4e3a\u57fa\u6001\u80fd\u91cfE_{rel} = (E_{NQS}(\u03b1)-E_{exact})\/|E_{exact}|\u76f8\u5bf9\u8bef\u5dee\u5728\u4e0d\u540c\u03b1\u548c\u6a21\u578b\u53c2\u6570\u4e0b\u7684\u53d6\u503c\u3002\u5728\u56fe3A\uff0c\u6211\u4eec\u5728\u5177\u6709PBCs\u76841\u7ef4\u94fe\u4e0a\u7528\u8d39\u7c73\u5316\u7684TFI\u6a21\u578b\u7684\u7cbe\u786e\u7ed3\u679c\u4e0eNQS\u7684\u80fd\u91cf\u53d8\u5316\u8fdb\u884c\u4e86\u6bd4\u8f83\u3002\u6700\u660e\u663e\u7684\u7ed3\u679c\u662f\uff0cNQS\u5b9e\u73b0\u4e86\u4e00\u4e2a\u53ef\u63a7\u4e14\u4efb\u610f\u7cbe\u51c6\u7684\u51c6\u786e\u6027\uff0c\u4e0e\u5bf9\u4e8e\u03b1\u7684\u5e42\u5f8b\u884c\u4e3a\u76f8\u7b26\u3002\u6700\u96be\u5b66\u4e60\u7684\u57fa\u6001\u662f\u5728\u91cf\u5b50\u4e34\u754c\u70b9h = 1\u9644\u8fd1\uff0c\u5c3d\u7ba1\u5982\u6b64\uff0c\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u76f8\u5bf9\u9002\u5ea6\u7684\u9690\u85cf\u5355\u5143\u5bc6\u5ea6\u8f7b\u677e\u5b9e\u73b0\u6bcf\u4e00\u4e2a\u767e\u4e07\u5206\u4e4b\u4e00\u7684\u663e\u8457\u7cbe\u5ea6\u3002\u540c\u6837\u7684\u7cbe\u5ea6\u53ef\u4ee5\u5728\u66f4\u590d\u6742\u7684\u4e00\u7ef4AFH\u6a21\u578b\u4e2d\u5f97\u5230\uff08\u56fe3B\uff09\u3002\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u6211\u4eec\u8fd8\u89c2\u5bdf\u5230\u57fa\u6001\u80fd\u91cf\u8bef\u5dee\u7684\u7cfb\u7edf\u6027\u4e0b\u964d\uff0c\u5bf9\u4e8e\u5c0f\u7684\u03b1 = 4\uff0c\u5728\u4e34\u754c\u70b9\u83b7\u5f97\u4e0eTFI\u6a21\u578b\u76f8\u540c\u7684\u9ad8\u7cbe\u5ea6\u3002\u6211\u4eec\u7684\u6a21\u578b\u7684\u7cbe\u5ea6\u6bd4\u81ea\u65cbJastrow \u65b9\u6848\u9ad8\u51e0\u4e2a\u6570\u91cf\u7ea7\uff08\u865a\u7ebf\u56fe3B\uff09\u3002\u540c\u6837\u6709\u8da3\u7684\u662f\u5c06\u03b1\u503c\u4e0e\u80fd\u591f\u8fbe\u5230\u76f8\u540c\u7cbe\u5ea6\u6c34\u5e73\u6240\u9700\u8981\u7684MPS\u7ea6\u675f\u7ef4\u5ea6M\u8fdb\u884c\u6bd4\u8f83\u3002\u4f8b\u5982\uff0c\u5728\u6709PBCs\u7684AFH\u6a21\u578b\u4e2d\uff0c\u6211\u4eec\u53d1\u73b0\u5982\u679c\u5e94\u7528\u6807\u51c6\u7684\u5bc6\u5ea6\u77e9\u9635\u91cd\u6574\u5316\u7fa4(Density Matrix Renormalization Group\uff0cDMRG)\uff0833\uff09\uff0c\u6211\u4eec\u9700\u8981M~160\u624d\u80fd\u8fbe\u5230NQS\u5728\u03b1 = 4\u7684\u51c6\u786e\u5ea6\u3002\u8fd9\u8868\u660e\u4e86NQS\u65b9\u6848\u53ef\u4ee5\u5bf9\u591a\u4f53\u72b6\u6001\u8fdb\u884c\u66f4\u7d27\u51d1\u7684\u8868\u793a\uff0c\u8fd9\u6bd4\u76f8\u5e94\u7684MPS\u65b9\u6848\u6240\u9700\u8981\u7684\u53d8\u5206\u53c2\u6570\u5c11\u4e86\u7ea6\u4e09\u4e2a\u6570\u91cf\u7ea7\u3002<\/p>\n


<\/p>\n

\"\u96c6\u667a\"<\/p>\n


<\/p>\n

\u6211\u4eec\u63a5\u4e0b\u6765\u7814\u7a76\u4e86\u4e8c\u7ef4\u6b63\u65b9\u5f62\u9635\u5217\u4e0a\u7684AFH\u6a21\u578b\uff08\u4e0eQMC\u7ed3\u679c\u7684\u6bd4\u8f83\uff0c\u89c1\u56fe3C\uff09\uff0834\uff09\u3002\u8003\u8651\u5230\u91cf\u5b50\u6001\u6709\u7ea0\u7f20\uff0c\u5bf9\u4e8eNQS\u6765\u8bf4\uff0c\u7814\u7a76\u4e8c\u7ef4\u60c5\u51b5\u4f1a\u66f4\u52a0\u56f0\u96be\u3002\u5c3d\u7ba1\u5982\u6b64\uff0c\u968f\u7740\u03b1\u7684\u589e\u52a0\uff0c\u6211\u4eec\u603b\u80fd\u53d1\u73b0\u53d8\u91cf\u4f1a\u6709\u7cfb\u7edf\u6027\u7684\u6539\u8fdb\uff0c\u5b9a\u91cf\u4e0a\u8fd9\u4e0e\u4e00\u7ef4\u60c5\u51b5\u7c7b\u4f3c\u3002\u96be\u5ea6\u589e\u52a0\u53cd\u6620\u5728\u6536\u655b\u6027\u66f4\u6162\u4e86\u3002\u5f53\u7136\uff0c\u6211\u4eec\u8fd8\u662f\u80fd\u5f97\u5230\u548c\u73b0\u6709\u6700\u5148\u8fdb\u65b9\u6cd5\u4e0d\u76f8\u4e0a\u4e0b\u7684\u7ed3\u679c\u7684\uff0c\u751a\u81f3\u66f4\u597d\u3002\u7279\u522b\u662f\u5728\u9690\u5355\u5143\u5bc6\u5ea6\u76f8\u5bf9\u8f83\u5c0f\u7684\u60c5\u51b5\u4e0b\uff08\u03b1\u301c4\uff09\uff0c\u6211\u4eec\u5df2\u7ecf\u83b7\u5f97\u4e86\u4e0e\u6700\u6709\u540d\u7684\u6709\u9650\u5927\u5c0f\u96c6\u7fa4\u53d8\u5206\u65b9\u7a0b\uff08variational results\uff09\u76f8\u540c\u7684\u7ed3\u679c[\uff0835\uff09\u7684\u7ea0\u7f20plaquette\u72b6\u6001(EPS)\u548c\uff0836\uff09\u6295\u5f71\u7ea0\u7f20\u5bf9\u72b6\u6001(PEPS)]\u3002\u8fdb\u4e00\u6b65\u589e\u52a0\u03b1\u80fd\u5f97\u5230\u4e00\u4e2a\u53ef\u89c2\u7684\u6539\u8fdb\uff0c\u6700\u7ec8\u4ea7\u751f\u8fc4\u4eca\u4e3a\u6b62\u5728\u6709\u9650\u7f51\u683c\u4e0a\u8be52\u7ef4\u6a21\u578b\u7684\u6700\u4f73\u53d8\u5206\u7ed3\u679c\u3002<\/p>\n


<\/p>\n

\n
\n
\n
\u5e7a\u6b63\uff08\u6216\u9149\uff0cUnitary\uff09\u52a8\u529b\u5b66 <\/span>    <\/strong><\/section>\n<\/section>\n

   <\/section>\n

 <\/section>\n


<\/p>\n

\u795e\u7ecf\u7f51\u7edc\u91cf\u5b50\u6001\uff08NQS\uff09\u5e76\u4e0d\u4ec5\u9650\u4e8e\u57fa\u6001\u95ee\u9898\u7684\u7814\u7a76\uff0c\u8fd8\u53ef\u4ee5\u6269\u5c55\u5230\u542b\u65f6\u7684\u859b\u5b9a\u8c14\u65b9\u7a0b\u3002\u5173\u4e8e\u8fd9\u4e2a\u95ee\u9898\uff0c\u6211\u4eec\u5b9a\u4e49\u4e86\u590d\u6570\u57df\u4e0a\u7684\u542b\u65f6\u7f51\u7edc\u6743\u503cW(t)\u3002\u5728\u4e0d\u540c\u7684\u65f6\u95f4t\u4e0b\uff0c\u6839\u636e\u72c4\u62c9\u514b\u7684\u975e\u5b9a\u6001\u539f\u7406(37, 38)\uff0c\u53ef\u4ee5\u8bad\u7ec3W(t)\u5e76\u884d\u751f\u51fa\u6700\u597d\u7684\u91cf\u5b50\u52a8\u529b\u5b66\u3002\u5728\u8fd9\u4e2a\u6761\u4ef6\u4e0b\uff0c\u53d8\u5206\u6b8b\u5dee\uff1a<\/p>\n

\"\u96c6\u667a\"<\/p>\n

\u6210\u4e3a\u4e86\u5173\u4e8e\u65f6\u95f4\u6743\u503c\u5bfc\u6570\u7684\u76ee\u6807\u51fd\u6570\uff0c\u8981\u901a\u8fc7\u8bad\u7ec3\u6c42\u5176\u6700\u5c0f\u503c\u6765\u627e\u5230\u3002\u5728\u968f\u673a\u7ed3\u6784\u4e2d\uff0c\u8fd9\u4e2a\u8fc7\u7a0b\u901a\u8fc7\u5305\u542b\u65f6\u95f4\u7684VMC\u65b9\u6cd5\uff0825,26\uff09\u6765\u5b9e\u73b0\u3002\u5728\u6bcf\u4e00\u4e2a\u65f6\u95f4\u90fd\u5bf9|\u03a8_M(S;W(t))|^2\u8fdb\u884c\u91c7\u6837\uff0c\u968f\u540e\u901a\u8fc7\u8ba1\u7b97\u7ed9\u51fa\u4f7f\u635f\u5931R(t)^2\u6700\u5c0f\u7684W(t)\u7684\u968f\u673a\u4f30\u91cf\uff0c\u5176\u8ba1\u7b97\u6210\u672c\u4e3aO(aN^2)\u3002\u5f53\u7531\u65f6\u95f4\u4ea7\u751f\u7684\u9644\u52a0\u9879\u5f97\u5230\u786e\u5b9a\uff0c\u5e76\u4e14\u5bf9\u65f6\u95f4\u6574\u5408\u540e\uff0c\u5c31\u53ef\u4ee5\u901a\u8fc7\u8fd9\u4e2a\u65b9\u6cd5\u65b9\u4fbf\u7684\u83b7\u5f97\u5168\u90e8\u7684\u65f6\u95f4\u6f14\u5316\u7ed3\u679c\u3002<\/p>\n


<\/p>\n

\"\u96c6\u667a\"<\/p>\n

\u56fe4\uff1aNQS\u7684\u591a\u4f53\u5e7a\u6b63\u65f6\u95f4\u6f14\u5316<\/span><\/p>\n


<\/span><\/p>\n

\u8be5\u56fe\u663e\u793a\u4e86\u7531\u91cf\u5b50\u9000\u706b<\/span><\/strong>\uff08Quantum quench\uff09\u5f15\u8d77\u7684NQS\u65f6\u95f4\u6f14\u5316\u7ed3\u679c\uff08\u5b9e\u7ebf\uff09\u3002(A)TFI\u968f\u65f6\u95f4\u6539\u53d8\u7684\u6a2a\u5411\u81ea\u65cb\u6781\u5316\uff0c\u4e0e\u51c6\u786e\u7ed3\u679c\uff08\u865a\u7ebf\uff09\u5bf9\u6bd4\u3002(B)AFH\u6a21\u578b\u4e2d\u6f14\u5316\u540e\u7684\u4f9d\u8d56\u8fd1\u90bb\u81ea\u65cb\u7edf\u8ba1\uff0c\u4e0e\u5728t-DMRG\u4e2d\u83b7\u5f97\u7684\u51c6\u786e\u7ed3\u679c\uff08\u865a\u7ebf\uff09\u5bf9\u6bd4\u3002\u6240\u6709\u7684\u7ed3\u679c\u90fd\u53c2\u7167\u70ed\u529b\u5b66\u9650\u5b9a\u7684\u4e00\u7ef4\u94fe\u4ee3\u8868\uff0c\u540c\u65f6\u6709\u9650\u5c3a\u5bf8\u4fee\u6b63\u5c0f\u4e8e\u7ebf\u5bbd\u3002<\/p>\n


<\/p>\n

\u4e3a\u4e86\u8bc1\u660e\u5728\u52a8\u529b\u5b66\u73af\u5883\u4e0bNQS\u7684\u6548\u7387\uff0c\u6211\u4eec\u8003\u8651\u5728\u81ea\u65cb\u6a21\u578b\u4e2d\u7684\u8026\u5408\u5e38\u6570<\/span><\/strong>\u8fdb\u884c\u91cf\u5b50\u9000\u706b\u6240\u8bf1\u5bfc\u51fa\u7684\u5e7a\u6b63\u52a8\u529b\u5b66<\/span><\/strong>\u3002\u5728TFI\u6a21\u578b\u4e2d\uff0c\u6211\u4eec\u901a\u8fc7\u8fc5\u901f\u6539\u53d8\u6a2a\u5411\u573a\u7684\u65b9\u6cd5\u5f15\u8d77\u975e\u7ebf\u6027\u7684\u91cf\u5b50\u52a8\u529b\u5b66\uff1a\u8fd9\u4e2a\u7cfb\u7edf\u9996\u5148\u5904\u5728\u67d0\u4e00\u4e2a\u573ahi\u7684TFI\u6a21\u578b\u57fa\u6001\uff0c\u7136\u540e\u5728\u6a2a\u5411\u573ahf<>hi\u4e0b\u6f14\u5316\u3002\u6211\u4eec\u5c06\u6211\u4eec\u7684\u7ed3\u679c\u548c\u5728\u63a7\u5236\u7cfb\u7edf\u4e2d\u7684\u5177\u6709PBCs\u7684\u4e00\u7ef4\u94fe\u7684\u8d39\u7c73\u5316\u7684TFI\u6a21\u578b\u83b7\u5f97\u7684\u89e3\u6790\u89e3\u5bf9\u6bd4\u3002\u5728\u56fe4A\u4e2d\uff0c\u51c6\u786e\u7684\u7531\u65f6\u95f4\u51b3\u5b9a\u7684\u6a2a\u5411\u81ea\u65cb\u6781\u5316\u7684\u7ed3\u679c\u4e0e\u5728\u03b1=4\u65f6\u7684NQS\u7cfb\u7edf\u8fdb\u884c\u4e86\u5bf9\u6bd4\u3002\u5728AFH\u6a21\u578b\u4e2d\uff08\u56fe4B\uff09\uff0c\u6211\u4eec\u7814\u7a76\u4e86\u7eb5\u5411\u8026\u5408Jz\u7684\u91cf\u5b50\u9000\u706b\uff0c\u5e76\u4e14\u76d1\u63a7\u4e86\u6700\u8fd1\u90bb\u7684\u65f6\u95f4\u6f14\u5316\u76f8\u5173\u6027\u3002\u6211\u4eec\u5c06\u65f6\u95f4\u6f14\u5316\u7ed3\u679c(\u03b1=4)\u548c\u5df2\u7ecf\u5b58\u5728\u6570\u5b57\u7684\u5f00\u653e\u8fb9\u754c\u7684MPS\u52a8\u529b\u5b66\u7cfb\u7edf(39-41)\u76f8\u5bf9\u6bd4(\u56fe4B)\u3002<\/p>\n


<\/p>\n

\u7ed3\u679c\u8868\u660e\uff0c\u5e7a\u6b63\u52a8\u529b\u5b66\u7684\u9884\u6d4b\u4ecd\u7136\u53ef\u4ee5\u83b7\u5f97\u5f88\u9ad8\u7684\u7cbe\u5ea6\uff0c\u8fd9\u66f4\u52a0\u8bc1\u5b9e\u4e86\u4ee5\u795e\u7ecf\u7f51\u7edc\u6cd5\u4e3a\u57fa\u7840\u7684\u9014\u5f84\u53ef\u4ee5\u7528\u6765\u89e3\u51b3\u91cf\u5b50\u591a\u4f53\u95ee\u9898\uff0c\u4e0d\u4ec5\u5728\u57fa\u6001\u4e0b\u9002\u7528\uff0c\u5728\u5efa\u7acb\u7684\u7531\u590d\u6742\u539f\u56e0\u5f15\u8d77\u7684\u6fc0\u53d1\u6001\u6a21\u578b\u4e5f\u9002\u7528\u3002<\/span><\/strong><\/p>\n


<\/span><\/strong><\/p>\n

\u5c55\u671b<\/strong><\/span><\/p>\n


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\u9ec4\u6668 <\/strong>\u7269\u7406\u5b66\u535a\u58eb\u5728\u8bfb\uff0c\u4e3b\u8981\u65b9\u5411\u4e3a\u51dd\u805a\u6001\u7269\u7406\uff0c\u5bf9\u91cf\u5b50\u8ba1\u7b97\u548c\u673a\u5668\u5b66\u4e60\u611f\u5174\u8da3\u3002\uff08\u540c\u65f6\u4e5f\u662f\u672c\u671f\u7684\u4f18\u79c0\u8bd1\u8005\uff0c\u6492\u82b1\uff01\uff09<\/strong><\/span><\/span><\/p>\n

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\u674e\u4e3d\u4eac\uff0c<\/strong>\u670d\u88c5\u8bbe\u8ba1\u5e08\uff0c\u611f\u5174\u8da3\u7684\u65b9\u5411\u662f\u590d\u6742\u79d1\u5b66\u3001\u4eba\u5de5\u667a\u80fd\u3001\u8ba4\u77e5\u795e\u7ecf\u79d1\u5b66\u7b49\u3002<\/span><\/p>\n


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\u60f3\u52a0\u5165\u96c6\u667a\u4ff1\u4e50\u90e8\uff0c\u6210\u4e3a\u7ffb\u8bd1\u5fd7\u613f\u8005\uff1f\u626b\u7801\u5373\u53ef\u7533\u8bf7~<\/span><\/strong><\/p>\n

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\u53c2\u8003\u6587\u732e\u4e0e\u6ce8\u8bb0<\/span><\/strong><\/p>\n


<\/span><\/strong><\/p>\n

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42. B. Bauer et al., J. Stat. Mech. 2011, P05001 (2011). <\/p>\n


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\u4eba\u5de5\u667a\u80fd\u5728\u91cf\u5b50\u7269\u7406\u4e2d\u7684\u5e94\u7528 | \u4e0a\u6d77\u6d3b\u52a8<\/a><\/strong><\/p>\n<\/section>\n<\/section>\n

\u5bf9\u673a\u5668\u5b66\u4e60\u3001\u5f20\u91cf\u7f51\u7edc\u548c\u7269\u7406\u7684\u4e00\u4e9b\u770b\u6cd5 <\/a><\/strong>
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\u7528\u6df1\u5ea6\u5b66\u4e60\u89e3\u8bfb\u91cf\u5b50\u5b87\u5b99\u5965\u79d8<\/strong><\/a>
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\u7528\u6df1\u5ea6\u5b66\u4e60\u89e3\u8bfb\u91cf\u5b50\u5b87\u5b99\u5965\u79d8<\/a><\/strong><\/span><\/p>\n

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\u4e3a\u4ec0\u4e48\u4ed6\u4eec\u8981\u6765\u96c6\u667aAI\u5b66\u56ed\u5b66\u4e60 PyTorch\uff1f<\/a><\/strong>
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\u96c6\u667aQQ\u7fa4\uff5c292641157
\u5546\u52a1\u5408\u4f5c\uff5czhangqian@swarma.org
\u6295\u7a3f\u8f6c\u8f7d\uff5cwangting@swarma.org<\/span><\/strong>
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\u25c6 <\/span>\u25c6 <\/span>\u25c6<\/span><\/span><\/strong><\/strong><\/h1>\n<\/section>\n

\u641c\u7d22\u516c\u4f17\u53f7\uff1a\u96c6\u667a\u4ff1\u4e50\u90e8<\/span><\/strong><\/span><\/p>\n


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\u52a0\u5165\u201c\u6ca1\u6709\u56f4\u5899\u7684\u7814\u7a76\u6240\u201d<\/span><\/strong><\/span><\/p>\n

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\"\u96c6\u667a\"<\/p>\n<\/section>\n

\u8ba9\u82f9\u679c\u7838\u5f97\u66f4\u731b\u70c8\u4e9b\u5427\uff01<\/span><\/p>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n

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