{"id":32900,"date":"2018-11-26T00:42:49","date_gmt":"2018-11-25T16:42:49","guid":{"rendered":"https:\/\/case.ntu.edu.tw\/blog\/?p=32900"},"modified":"2018-12-14T10:01:20","modified_gmt":"2018-12-14T02:01:20","slug":"hubbard-%e6%a8%a1%e5%9e%8b%ef%bc%88%e4%ba%8c%ef%bc%89%ef%bc%9a%e7%8e%bb%e8%89%b2-hubbard-%e6%a8%a1%e5%9e%8b","status":"publish","type":"post","link":"https:\/\/case.ntu.edu.tw\/blog\/?p=32900","title":{"rendered":"Hubbard \u6a21\u578b\uff08\u4e8c\uff09\uff1a\u73bb\u8272 Hubbard \u6a21\u578b"},"content":{"rendered":"<p><span style=\"color: #333399;\"><strong>\u25a0\u7c21\u55ae\u7684\u73bb\u8272 Hubbard \u6a21\u578b\uff0c\u5728 2 \u7dad\u7a7a\u9593\u4e2d\u63d0\u4f9b\u6211\u5011\u4e86\u89e3\u83ab\u7279\u7d55\u7de3\u9ad4\u8207\u8d85\u6d41\u9ad4\u9593\u7684\u76f8\u8b8a\u5316\u3002<\/strong><\/span><\/p>\n<p><strong>\u64b0\u6587\uff5c\u856d\u7dad\u7ff0<\/strong><\/p>\n<p>\u5e0c\u671b\u7b46\u8005\u5728<a href=\"http:\/\/case.ntu.edu.tw\/blog\/?p=32899\" target=\"_blank\" rel=\"noopener noreferrer\">\u524d\u6587\u4e2d<\/a>\u6216\u591a\u6216\u5c11\u7d66\u4e86\u4e00\u9ede\u7406\u7531\u8b93\u5927\u5bb6\u4e00\u8d77\u4f86\u8cde\u73a9\u539f\u672c\u53ea\u5c6c\u65bc\u4e00\u90e8\u5206\u7269\u7406\u5b78\u5bb6\u5011\u7684\u73a9\u5177\u3002\u73fe\u5728\u958b\u59cb\u6211\u5011\u9032\u5165\u6b63\u984c\u4f86\u63a2\u8a0e Hubbard \u6a21\u578b\u5bb6\u65cf\u4e2d\u7684\u5e7e\u500b\u77e5\u540d\u5178\u7bc4\u3002\u660e\u78ba\u7684\u8aaa\uff0c\u9996\u5148\u6211\u5011\u8a0e\u8ad6\u5728\u4e8c\u7dad\u7a7a\u9593\u4e2d\u6b63\u65b9\u6676\u683c\uff08square lattice\uff09\u4e0a\u7684\u73bb\u8272\u5b50\u7248\u672c Hubbard \u6a21\u578b\uff08Bosonic Hubbard Model\uff09[1,2]\u3002<\/p>\n<p>\u4e5f\u5c31\u662f\u8aaa\uff0c\u6211\u5011\u6709\u4e00\u500b\u6b63\u65b9\u5f62\u7684\u6676\u683c\uff0c\u4e26\u6709\u4e00\u4e9b\u73bb\u8272\u5b50\u88ab\u653e\u5728\u7bc0\u9ede x<sub>i&nbsp;<\/sub>\u4e0a\uff0c\u9019\u4e9b\u73bb\u8272\u5b50\u53ef\u4ee5\u76f8\u9130\u7684\u5169\u9ede\u4e0a\u79fb\u52d5\uff0c\u4f46\u7576\u5169\u500b\u73bb\u8272\u5b50\u805a\u96c6\u5728\u540c\u4e00\u500b\u7bc0\u9ede\u6642\uff0c\u4ed6\u5011\u770b\u5f97\u5230\u5f7c\u6b64\u4e26\u4e14\u5169\u8005\u9593\u6703\u611f\u53d7\u5230\u6392\u65a5\u529b\u3002\u4ee3\u6578\u4e0a\uff0c\u73bb\u8272\u5b50\u7684\u6578\u76ee\u3001\u73bb\u8272\u5b50\u5728\u7bc0\u9ede\u4e0a\u79fb\u52d5\u7684\u80fd\u529b\u3001\u8207\u540c\u4e00\u7bc0\u9ede\u4e0a\u5169\u500b\u73bb\u8272\u5b50\u7684\u6392\u65a5\u529b\u53ef\u5206\u5225\u7531\u5316\u5b78\u52e2 \u03bc\uff08chemical potential\uff09\u3001\u8e8d\u9077\u5e38\u6578 t\uff08hopping constant\uff09\u3001\u8207\u4ea4\u4e92\u4f5c\u7528\u4f4d\u80fd U \u9019\u4e09\u500b\u53c3\u6578\u6c7a\u5b9a\u3002\u539f\u5247\u4e0a\u6211\u5011\u4e5f\u53ef\u4ee5\u8b93\u55ae\u4e00\u500b\u7c92\u5b50\u5728\u6bcf\u4e0d\u540c\u7bc0\u9ede\u4e0a\u770b\u5230\u4e0d\u540c\u7684\u4f4d\u80fd\u503c V(x<sub>i<\/sub>)\uff0c\u4f46\u9019\u500b\u9805\u5176\u5be6\u53ef\u4ee5\u8ddf\u5316\u5b78\u52e2\u5408\u4f75\u5728\u4e00\u8d77\uff0c\u4e26\u4e14\u70ba\u4e86\u5f97\u5230\u6700\u521d\u6b65\u7684\u7d50\u679c\u6211\u5011\u66ab\u6642\u4e0d\u8003\u616e\u9019\u6a23\u7684\u8907\u96dc\u6027\u3002<\/p>\n<figure id=\"attachment_33154\" aria-describedby=\"caption-attachment-33154\" style=\"width: 700px\" class=\"wp-caption aligncenter\"><img fetchpriority=\"high\" decoding=\"async\" class=\"wp-image-33154\" src=\"http:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2018\/11\/001.png\" alt=\"\" width=\"700\" height=\"317\" data-wp-pid=\"33154\" srcset=\"https:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2018\/11\/001.png 1136w, https:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2018\/11\/001-800x362.png 800w\" sizes=\"(max-width: 700px) 100vw, 700px\" \/><figcaption id=\"caption-attachment-33154\" class=\"wp-caption-text\">Figure1.\u5728\u73bb\u8272\u5b50\u7684\u554f\u984c\u4e2d\uff0c\u7531\u65bc\u6c92\u6709\u4e0d\u76f8\u5bb9\u539f\u7406\uff0c\u4e26\u6c92\u6709\u4e00\u500b\u8ecc\u57df\u53ea\u80fd\u586b\u4e00\u500b\u7c92\u5b50\u7684\u9650\u5236\uff0c\u601d\u8003\u73bb\u8272\u554f\u984c\u57fa\u614b\u7684\u76f4\u89ba\u4e00\u90e8\u5206\u53ef\u7531\u600e\u9ebc\u5206\u4f48\u6703\u4f7f\u5f97\u80fd\u91cf\u8b8a\u4f4e\u6c7a\u5b9a\u3002\uff08photo credit: \u4f5c\u8005\u81ea\u7e6a\uff09<\/figcaption><\/figure>\n<p>\u5c0d\u65bc\u7406\u8ad6\u7269\u7406\u5b78\u5bb6\u5011\u800c\u8a00\uff0c\u7d66\u5b9a\u9019\u6a23\u4e00\u500b\u6a21\u578b\uff0c\u6211\u5011\u4e26\u4e0d\u5962\u671b\u76f4\u63a5\u53ef\u4ee5\u5206\u6790\u5b83\u7684\u6240\u6709\u52d5\u529b\u5b78\u6027\u8cea\uff0c\u5728\u5c11\u6578\u7684\u76f8\u5c0d\u7c21\u55ae\u7684\u554f\u984c\u4e2d\uff0c\u5176\u4e2d\u4e00\u500b\u6211\u5011\u6709\u5e0c\u671b\u80fd\u56de\u7b54\u7684\u662f\uff1a\u9019\u500b\u6a21\u578b\u7684\u57fa\u614b\u7684\u300c\u76f8\u300d\u662f\u4ec0\u9ebc\uff1f\u5728\u505a\u4efb\u4f55\u8a08\u7b97\u4e4b\u524d\uff0c\u6211\u5011\u53ef\u4ee5\u5148\u770b\u4e00\u4e9b\u6975\u9650\u7684\u4f8b\u5b50\uff0c\u4e26\u5617\u8a66\u5b9a\u6027\u5730\u53bb\u63a8\u6572\u9019\u4e9b\u6975\u9650\u7684\u76f8\uff0c\u63a5\u8457\u7528\u6bd4\u8f03\u7cbe\u78ba\u7684\u5b9a\u91cf\u5206\u6790\u4f86\u5167\u63d2\u89e3\u6790\u51fa\u662f\u54ea\u4e9b\u76f8\u9023\u63a5\u9019\u4e9b\u6975\u9650\u7684\u4f8b\u5b50\u3002<\/p>\n<p>\u8b93\u6211\u5011\u770b\u770b\u7b2c\u4e00\u500b\u6975\u9650\uff1aU\/t\u226a1 \u6216 U=0\u3002<\/p>\n<p>\u5728\u9019\u500b\u6975\u9650\uff0c\u73bb\u8272\u5b50\u5011\u5176\u5be6\u770b\u4e0d\u898b\u5c0d\u65b9\uff0c\u4e5f\u5c31\u662f\u8aaa\u591a\u7c92\u5b50\u554f\u984c\u8b8a\u56de\u4e86\u55ae\u7c92\u5b50\u554f\u984c\uff0c\u540c\u6642\uff0c\u6211\u5011\u6709\u80fd\u529b\u53bb\u8a08\u7b97\u55ae\u4e00\u500b\u73bb\u8272\u5b50\u7684\u80fd\u968e\uff0c\u63a5\u4e0b\u4f86\u8981\u56de\u7b54\u7684\uff0c\u5c31\u662f\u7576\u6709\u5f88\u591a\u73bb\u8272\u5b50\u8981\u586b\u9032\u9019\u500b\u80fd\u968e\u6642\u5b83\u5011\u8981\u600e\u9ebc\u5206\u4f48\u3002\u5c0d\u65bc\u81ea\u7531\u7684\u73bb\u8272\u5b50\u800c\u8a00\uff0c\u9019\u500b\u554f\u984c\u7684\u7b54\u6848\u662f\u5df2\u77e5\u7684\uff0c\u56e0\u70ba\u5b83\u5011\u4e0d\u9700\u8981\u9075\u5b88\u5e96\u7acb\u4e0d\u76f8\u5bb9\u539f\u7406\uff0c\u5927\u5bb6\u53ef\u4ee5\u4e00\u8d77\u64e0\u5230\u6700\u4f4e\u7684\u80fd\u614b\u53bb\uff0c\u4e5f\u56e0\u6b64\uff0c\u5168\u90e8\u7684\u4eba\u5171\u4eab\u540c\u4e00\u500b\u6ce2\u51fd\u6578\uff0c\u9019\u6a23\u7684\u7269\u7406\u76f8\u4fe1\u6709\u4e9b\u8b80\u8005\u80fd\u5920\u5fc3\u9818\u795e\u6703\uff0c\u9019\u4e5f\u5c31\u662f\u6240\u8b02\u7684\u73bb\u8272\u611b\u56e0\u65af\u5766\u51dd\u805a\uff08Bose-Einstein condensation\uff09\uff0c\u4e5f\u5c31\u662f\u8aaa\uff0c\u57fa\u614b\u662f\u500b\u8d85\u6d41\u9ad4\uff08Superfluid\uff09\u3002<\/p>\n<p>\u53e6\u5916\u4e00\u500b\u6975\u9650\u662f t\/U\u226a1 \u6216&nbsp; U=0\u3002<\/p>\n<p>\u5728\u9019\u500b\u6975\u9650\u4e2d\uff0c\u73bb\u8272\u5b50\u5011\u4e00\u4f46\u88ab\u653e\u5230\u67d0\u500b\u7bc0\u9ede\u4e0a\uff0c\u5c31\u6c92\u6709\u79fb\u52d5\u7684\u80fd\u529b\u3002\u8981\u6c7a\u5b9a <em>N<\/em> \u500b\u7c92\u5b50\u7684\u57fa\u614b\uff0c\u7b49\u540c\u65bc\u8003\u616e\u8981\u628a\u9019\u4e9b\u7c92\u5b50\u4ee5\u964d\u4f4e\u80fd\u91cf\u70ba\u8003\u91cf\u5206\u914d\u5230\u6240\u6709\u7bc0\u9ede\u4e0a\u3002\u8b80\u8005\u81ea\u5df1\u53ef\u4ee5\u4f30\u8a08\u5e7e\u500b\u7c21\u55ae\u7684\u7c92\u5b50\uff0c\u6bd4\u5982\u628a 2 \u500b\u7c92\u5b50\u5206\u5230 2 \u500b\u7bc0\u9ede\u4e0a\uff0c\u6216\u628a 4 \u500b\u7c92\u5b50\u5206\u5230 2 \u500b\u7bc0\u9ede\u4e0a\u3002\u5728\u7b2c\u4e00\u500b\u4f8b\u5b50\u4e2d\uff0c\u7576\u5169\u500b\u7c92\u5b50\u5728\u5169\u500b\u7bc0\u9ede\u4e0a\u7684\u6642\u5019\uff0c\u4ea4\u4e92\u4f5c\u7528\u662f 0 \u4e5f\u56e0\u6b64\u80fd\u91cf\u70ba 0\uff0c\u4f46\u7576\u5169\u500b\u7c92\u5b50\u653e\u5728\u540c\u4e00\u500b\u9ede\u4e0a\u6642\uff0c\u80fd\u91cf\u70ba <em>U<\/em>\u3002\u591a\u770b\u770b\u5e7e\u500b\u4f8b\u5b50\uff0c\u5927\u5bb6\u5f88\u5feb\u4fbf\u53ef\u4ee5\u8aaa\u670d\u81ea\u5df1\uff0c\u7576\u6bcf\u500b\u7bc0\u9ede\u90fd\u6709\u4e00\u6a23\u6578\u76ee\u7684\u7c92\u5b50\uff0c\u7cfb\u7d71\u7684\u80fd\u91cf\u6700\u4f4e\u3002\u9019\u7a2e\u5f9e\u80fd\u5e36\u7406\u8ad6\u4e0a\u770b\u662f\u5c0e\u9ad4\uff0c\u4f46\u56e0\u70ba\u4ea4\u4e92\u4f5c\u7528\u5931\u53bb\u5c0e\u96fb\u6027\u7684\u72c0\u614b\uff0c\u6211\u5011\u7a31\u70ba\u83ab\u7279\u7d55\u7de3\u9ad4\uff08Mott Insulator\uff09\u3002<\/p>\n<p>\u56e0\u70ba\u6208\u767b\u65af\u901a\u73bb\u8272\u5b50\uff08Goldstone Boson\uff09\u7684\u7de3\u6545\uff0c\u8d85\u6d41\u9ad4\u662f\u6c92\u6709\u80fd\u9699\uff08energy gap\uff09\u7684\uff0c\u610f\u601d\u662f\u6211\u5011\u4e0d\u9700\u8981\u65bd\u52a0\u5f88\u5927\u7684\u80fd\u91cf\u624d\u53ef\u4ee5\u6fc0\u767c\u8d85\u6d41\u9ad4\u7684\u57fa\u614b\uff0c\u53e6\u4e00\u65b9\u9762\u800c\u8a00\uff0c\u7d55\u7de3\u9ad4\u662f\u6709\u80fd\u9699\u7684\uff0c\u6211\u5011\u5fc5\u9808\u65bd\u52a0\u67d0\u500b\u91cf\u503c\u4ee5\u4e0a\u7684\u80fd\u91cf\u624d\u80fd\u628a\u7cfb\u7d71\u5f9e\u57fa\u614b\u5e36\u5230\u53e6\u5916\u4e00\u500b\u614b\uff0c\u4e5f\u5c31\u662f\u8aaa\uff0c\u5f9e\u80fd\u8b5c\u7684\u89d2\u5ea6\uff0c\u9019\u5169\u500b\u57fa\u614b\u5728\u4e0d\u540c\u7684\u7269\u8cea\u76f8\u88e1\u9762\uff0c\u4f46\u56e0\u70ba\u5b83\u5011\u5c6c\u65bc\u5169\u500b\u6975\u7aef\u7684\u72c0\u6cc1\uff0c\u7576 t\/U \u8655\u65bc 0 \u548c\u7121\u9650\u5927\u4e2d\u9593\u67d0\u500b\u503c\u6642\uff0c\u5fc5\u7136\u8981\u5b58\u5728\u4e00\u500b\u76f8\u8b8a\u5316\u3002<\/p>\n<p>\u5728\u9032\u5165\u4e0b\u4e00\u500b\u8ab2\u984c\u524d\uff0c\u8b80\u8005\u5011\u53ef\u4ee5\u7a0d\u7a0d\u56de\u9867\uff0c\u7b46\u8005\u524d\u9762\u5728\u8ad6\u8ff0\u8d85\u6d41\u9ad4\u548c\u7d55\u7de3\u9ad4\u9019\u5169\u500b\u76f8\u7684\u5b58\u5728\u6642\uff0c\u57fa\u672c\u4e0a\u6c92\u6709\u9032\u884c\u4ec0\u9ebc\u8a8d\u771f\u7684\u8a08\u7b97\uff0c\u800c\u662f\u7531\u8003\u616e\u7cfb\u7d71\u7684\u67d0\u4e9b\u6975\u9650\uff0c\u4e26\u900f\u904e\u66f4\u57fa\u790e\u4e00\u5c64\u7684\u77e5\u8b58\u53bb\u5224\u65b7\u8a72\u6709\u7684\u7d50\u679c\u3002\u7576\u7136\uff0c\u66f4\u7cbe\u78ba\u7684\u76f8\u5206\u4f48\u9084\u662f\u9700\u8981\u900f\u904e\u8a08\u7b97\u5f97\u5230\u3002\u5728\u5716 2 \u4e2d\uff0c\u6211\u5011\u7d04\u7565\u63cf\u7e6a\u4e86\u5728\u5e73\u5747\u5834\uff08mean field\uff09\u7684\u8a08\u7b97\u4e0b\uff0c\u73bb\u8272 Hubbard \u6a21\u578b\u7684\u57fa\u614b\u6839\u64da\u7d66\u5b9a\u7684\u5316\u5b78\u52e2\u3001\u8e8d\u9077\u5e38\u6578\u8207\u4ea4\u4e92\u4f5c\u7528\u6240\u8655\u7684\u7269\u8cea\u76f8\u3002<\/p>\n<figure id=\"attachment_33152\" aria-describedby=\"caption-attachment-33152\" style=\"width: 500px\" class=\"wp-caption aligncenter\"><img decoding=\"async\" class=\"wp-image-33152\" src=\"http:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2018\/11\/002.png\" alt=\"\" width=\"500\" height=\"340\" data-wp-pid=\"33152\"><figcaption id=\"caption-attachment-33152\" class=\"wp-caption-text\">Figure2. \u672c\u5716\u4e2d\u6211\u5011\u8003\u616e\u4e0d\u540c\u7684\u5316\u5b78\u52e2\u8207\u8e8d\u9077\u5e38\u6578\u4e0b\u73bb\u8272Hubbard\u6a21\u578b\u7684\u57fa\u614b\u7269\u8cea\u76f8\u3002\uff08photo credit: \u4f5c\u8005\u81ea\u7e6a\uff09<\/figcaption><\/figure>\n<p>\u76ee\u524d\u70ba\u6b62\uff0c\u6211\u5011\u8aaa\u660e\u4e86\u672c\u7cfb\u7d71\u5728\u5169\u500b\u6975\u9650\u4e2d\u7684\u7269\u8cea\u76f8\uff0c\u4ee5\u53ca\u76f8\u8b8a\u5316\u7684\u5b58\u5728\u3002\u5c0d\u65bc\u7406\u8ad6\u7269\u7406\u5b78\u5bb6\u800c\u8a00\uff0c\u4e0b\u4e00\u500b\u554f\u984c\u5c31\u662f\u5f80\u76f8\u8b8a\u5316\u7684\u9818\u57df\u524d\u9032\uff0c\u7814\u7a76\u9019\u500b\u7cfb\u7d71\u7684\u81e8\u754c\u73fe\u8c61\uff08critical phenamonon\uff09\u8981\u59a5\u5584\u5beb\u4e0b\u7cbe\u78ba\u63cf\u8ff0\u9019\u500b\u7bc4\u570d\u7269\u7406\u7684\u6a21\u578b\u662f\u6bd4\u8f03\u6280\u8853\u6027\u7684\uff0c\u6211\u5011\u4e0d\u6703\u947d\u5165\u8a73\u7d30\u7684\u91cf\u5b50\u5834\u8ad6\u5206\u6790\uff0c\u4f46\u6211\u60f3\u8981\u9673\u8ff0\u4e00\u500b\u554f\u984c\uff0c\u4e26\u756b\u51fa\u91cf\u5b50\u7406\u8ad6\u8a08\u7b97\u51fa\u7684\u7d50\u679c\u3002<\/p>\n<p>\u9996\u5148\u4e00\u500b\u6211\u6c92\u6709\u8b49\u660e\u7684\u4e8b\u5be6\u662f\uff0c\u9019\u500b\u81e8\u754c\u9ede\u7684\u6709\u6548\u7406\u8ad6\u88ab\u8a8d\u70ba\u662f\u4e00\u500b\u300c\u76f8\u5c0d\u8ad6\u6027\u300d\uff08relativistic\uff09\u7684\u7406\u8ad6\uff0c\u56e0\u800c\u5728\u8d85\u6d41\u9ad4\u614b\u4e2d\uff0c\u6211\u5011\u9664\u4e86\u6709\u7121\u8cea\u91cf\u7684\u6208\u5fb7\u65af\u901a\u7c92\u5b50\uff0c\u63a5\u8fd1\u76f8\u8b8a\u5316\u6642\uff0c\u9084\u6703\u7372\u5f97\u53e6\u4e00\u500b\u6709\u8cea\u91cf\u7684\uff08\u985e\u6bd4\u7684\uff09<a href=\"#_ftn1\" name=\"_ftnref1\"><sup>[1]<\/sup><\/a>\u300c\u5e0c\u683c\u65af\u73bb\u8272\u5b50\u300d\uff08Higgs Boson\uff09\u3002\u56e0\u70ba\u9019\u662f\u8d85\u6d41\u9ad4\u7684\u4e00\u500b\u7279\u5fb5\uff0c\u6211\u5011\u76f8\u4fe1\u9019\u500b\u5e0c\u683c\u65af\u73bb\u8272\u5b50\u7684\u8cea\u91cf \u2206<sub>H<\/sub> &nbsp;\u5728\u63a5\u8fd1\u76f8\u8b8a\u5316\u7684\u6642\u5019\u6703\u8d8a\u4f86\u8d8a\u5c0f\uff0c\u4e26\u4e14\u5728\u81e8\u754c\u9ede\u6642\u70ba 0\u3002\u53e6\u4e00\u65b9\u9762\u800c\u8a00\uff0c\u5728\u83ab\u7279\u7d55\u7de3\u9ad4\u7684\u76f8\u4e2d\uff0c\u6211\u5011\u4e5f\u6709\u4e00\u500b\u80fd\u91cf\u5c3a\u5ea6\u662f\u7d55\u7de3\u9ad4\u7684\u80fd\u9699 \u2206<sub>M<\/sub>\uff0c\u56e0\u7232\u9019\u500b\u80fd\u9699\u662f\u7d55\u7de3\u9ad4\u7684\u7279\u5fb5\uff0c\u6211\u5011\u4e5f\u671f\u5f85\u5728\u63a5\u8fd1\u76f8\u8b8a\u5316\u6642\uff0c\u9019\u500b\u503c\u6703\u6108\u4f86\u6108\u5c0f\uff0c\u4e26\u5728\u81e8\u754c\u9ede\u70ba 0\u3002<\/p>\n<p>\u5be6\u969b\u7684\u8a08\u7b97\u88ab\u5448\u73fe\u5728\u5716 3 \u4e4b\u4e2d\u3002\u4f46\u66f4\u5f15\u4eba\u5165\u52dd\u7684\u662f\uff0c\u9019\u6a23\u7684\u8a08\u7b97\u7d50\u679c\u76ee\u524d\u5df2\u7d93\u88ab\u51b7\u539f\u5b50\u5be6\u9a57\u5be6\u73fe [3]\uff0c\u88ab\u8a8d\u70ba\u662f\u5728\u975e\u57fa\u672c\u7c92\u5b50\u5be6\u9a57\u4e2d\u5c0b\u7372\u7684\u5e0c\u683c\u65af\u7c92\u5b50\u3002<\/p>\n<p>\u5728\u672c\u6587\u4e2d\u6211\u5011\u8a0e\u8ad6\u4e86\u7c21\u55ae\u7684\u73bb\u8272 Hubbard \u6a21\u578b\uff0c\u4e26\u7528\u7269\u7406\u7684\u8ad6\u8ff0\u8a0e\u8ad6\u4e86\u57fa\u614b\u6240\u8655\u7684\u7269\u8cea\u76f8\u3002\u6211\u5011\u4e5f\u5448\u73fe\u4e86\u5728\u76f8\u8b8a\u5316\u9644\u8fd1\u7684\u8a08\u7b97\u7d50\u679c\uff0c\u800c\u9019\u4e9b\u7d50\u679c\u4e0d\u53ea\u662f\u7406\u8ad6\u4e0a\u7684\u5ba3\u8a00\uff0c\u540c\u6642\u4e5f\u5df2\u88ab\u5be6\u9a57\u6240\u9a57\u8b49\u3002<\/p>\n<figure id=\"attachment_33153\" aria-describedby=\"caption-attachment-33153\" style=\"width: 500px\" class=\"wp-caption aligncenter\"><img decoding=\"async\" class=\"wp-image-33153\" src=\"http:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2018\/11\/003.png\" alt=\"\" width=\"500\" height=\"285\" data-wp-pid=\"33153\"><figcaption id=\"caption-attachment-33153\" class=\"wp-caption-text\">Figure3. \u672c\u5716\u4e2d\u6211\u5011\u5448\u73fe\u5728\u4e0d\u540c\u53c3\u6578\u4e0b\uff0c\u8d85\u6d41\u614b\u4e2d\u5e0c\u683c\u65af\u7c92\u5b50\u7684\u8cea\u91cf\u4ee5\u53ca\u7d55\u7de3\u614b\u4e2d\u7d55\u7de3\u9ad4\u7684\u80fd\u9699\u3002\u5982\u672c\u6587\u6240\u89e3\u91cb\uff0c\u9019\u5169\u500b\u6578\u503c\u5728\u63a5\u8fd1\u76f8\u8b8a\u5316\u7684\u6642\u5019\u90fd\u6703\u8b8a\u5c0f\uff0c\u4e26\u4e14\u5728\u81e8\u754c\u9ede\u6b78\u96f6\u3002(Photo credit: \u4f5c\u8005\u81ea\u7e6a)<\/figcaption><\/figure>\n<p><strong>\u53c3\u8003\u8cc7\u6599\uff1a<\/strong><\/p>\n<p>[1] S. Sachdev, Quantum Phase Transitions, 2ed Ed (2011).<\/p>\n<p>[2] M. P. A. Fisher, P. B. Weichman, G. Grinstein, and D. S. Fisher, Phys. Rev. B <strong>40<\/strong>, 546 (1989).<\/p>\n<p>[3] M. Endres <em>et al<\/em>, Nature <strong>487<\/strong>, 454 (2012).<\/p>\n<p>--<\/p>\n<p><a href=\"#_ftnref1\" name=\"_ftn1\"><sup>[1]<\/sup><\/a> \u9019\u4e0d\u662f\u6211\u5011\u5728 LHC \u88e1\u627e\u7684\u90a3\u500b\u5e0c\u683c\u65af\u73bb\u8272\u5b50\uff0c\u9019\u908a\u4e4b\u6240\u4ee5\u9019\u6a23\u7a31\u547c\u662f\u56e0\u70ba\u5b83\u5011\u5728\u985e\u4f3c\uff0c\u4f46\u4e0d\u540c\u6a21\u578b\u4e2d\u626e\u6f14\u985e\u6bd4\u7684\u89d2\u8272\u3002<\/p>\n<p>&nbsp;<\/p>\n<p><strong>--<br \/>\n\u672c\u7cfb\u5217\u5168\u6587\uff1a<\/strong><\/p>\n<p><a href=\"http:\/\/case.ntu.edu.tw\/blog\/?p=32899\" target=\"_blank\" rel=\"noopener noreferrer\">Hubbard \u6a21\u578b\uff08\u3127\uff09\uff1a\u52d5\u6a5f\u8207\u5b9a\u7fa9<\/a><\/p>\n<p><a href=\"http:\/\/case.ntu.edu.tw\/blog\/?p=32900\" target=\"_blank\" rel=\"noopener noreferrer\">Hubbard \u6a21\u578b\uff08\u4e8c\uff09\uff1a\u73bb\u8272 Hubbard \u6a21\u578b<\/a><\/p>\n<p><a href=\"http:\/\/case.ntu.edu.tw\/blog\/?p=32901\" target=\"_blank\" rel=\"noopener noreferrer\">Hubbard \u6a21\u578b\uff08\u4e09\uff09\uff1a\u8cbb\u7c73 Hubbard \u6a21\u578b\uff1a\u7c21\u55ae\u7684\u89e3\u6790\u4e8b\u5be6\uff08\u4e0a\uff09<\/a><\/p>\n<p><a href=\"http:\/\/case.ntu.edu.tw\/blog\/?p=33329\" target=\"_blank\" rel=\"noopener noreferrer\">Hubbard \u6a21\u578b\uff08\u56db\uff09\uff1a\u8cbb\u7c73 Hubbard \u6a21\u578b\uff1a\u7c21\u55ae\u7684\u89e3\u6790\u4e8b\u5be6\uff08\u4e0b\uff09<\/a><\/p>\n<p><a href=\"http:\/\/case.ntu.edu.tw\/blog\/?p=33391\" target=\"_blank\" rel=\"noopener noreferrer\">Hubbard \u6a21\u578b\uff08\u4e94\uff09\uff1a\u81ea\u65cb\u6db2\u9ad4\u8207\u50f9\u9375\u56fa\u9ad4<\/a><\/p>\n<p><strong>--<br \/>\n\u4f5c\u8005\uff1a\u856d\u7dad\u7ff0\uff0c\u81fa\u5927\u7269\u7406\u7cfb\u7562\u696d\u5f8c\u9003\u5230\u829d\u52a0\u54e5\uff0c\u5439\u98a8\u5439\u96ea\u4e4b\u9918\uff0c\u505a\u7814\u7a76\u8b80\u535a\u58eb\u73ed\u3002\u53ef\u60dc\u96e2\u958b\u81fa\u7063\u5f8c\u7121\u6d77\u53ef\u770b\uff0c\u53ea\u80fd\u5728\u5bc6\u897f\u6839\u6e56\u65c1\u63c0\u4e00\u65b9\u5824\u5cb8\uff0c\u507d\u88dd\u6210\u770b\u6d77\u7684\u4eba\u3002\u79d1\u6559\u4e2d\u5fc3\u7279\u7d04\u5beb\u624b\uff0c\u5f9e\u4e8b\u79d1\u666e\u6587\u7ae0\u5beb\u4f5c\u3002<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p><a href=\"https:\/\/line.me\/R\/ti\/p\/%40fcx6182w\" target=\"_blank\" rel=\"noopener noreferrer\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/scdn.line-apps.com\/n\/line_add_friends\/btn\/zh-Hant.png\" alt=\"\u52a0\u5165\u597d\u53cb\" width=\"212\" height=\"36\" border=\"0\"><\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u25a0\u5728\u9019\u500b\u6975\u9650\uff0c\u73bb\u8272\u5b50\u5011\u5176\u5be6\u770b\u4e0d\u898b\u5c0d\u65b9\uff0c\u4e5f\u5c31\u662f\u8aaa\u591a\u7c92\u5b50\u554f\u984c\u8b8a\u56de\u4e86\u55ae\u7c92\u5b50\u554f\u984c\uff0c\u540c\u6642\uff0c\u6211\u5011\u6709\u80fd\u529b\u53bb\u8a08\u7b97\u55ae\u4e00\u500b\u73bb\u8272\u5b50\u7684\u80fd\u968e\uff0c\u63a5\u4e0b\u4f86\u8981\u56de\u7b54\u7684\uff0c\u5c31\u662f\u7576\u6709\u5f88\u591a\u73bb\u8272\u5b50\u8981\u586b\u9032\u9019\u500b\u80fd\u968e\u6642\u5b83\u5011\u8981\u600e\u9ebc\u5206\u4f48\u3002\u5c0d\u65bc\u81ea\u7531\u7684\u73bb\u8272\u5b50\u800c\u8a00\uff0c\u9019\u500b\u554f\u984c\u7684\u7b54\u6848\u662f\u5df2\u77e5\u7684\uff0c\u56e0\u70ba\u5b83\u5011\u4e0d\u9700\u8981\u9075\u5b88\u5e96\u7acb\u4e0d\u76f8\u5bb9\u539f\u7406\uff0c\u5927\u5bb6\u53ef\u4ee5\u4e00\u8d77\u64e0\u5230\u6700\u4f4e\u7684\u80fd\u614b\u53bb\uff0c\u4e5f\u56e0\u6b64\uff0c\u5168\u90e8\u7684\u4eba\u5171\u4eab\u540c\u4e00\u500b\u6ce2\u51fd\u6578\uff0c\u9019\u6a23\u7684\u7269\u7406\u76f8\u4fe1\u6709\u4e9b\u8b80\u8005\u80fd\u5920\u5fc3\u9818\u795e\u6703\uff0c\u9019\u4e5f\u5c31\u662f\u6240\u8b02\u7684\u73bb\u8272\u611b\u56e0\u65af\u5766\u51dd\u805a\uff08Bose-Einstein condensation\uff09\uff0c\u4e5f\u5c31\u662f\u8aaa\uff0c\u57fa\u614b\u662f\u500b\u8d85\u6d41\u9ad4\uff08Superfluid\uff09\u3002<\/p>\n","protected":false},"author":20,"featured_media":33155,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3293,39],"tags":[3998,1536,4071],"aioseo_notices":[],"jetpack_featured_media_url":"https:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2018\/11\/001-1.png","_links":{"self":[{"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=\/wp\/v2\/posts\/32900"}],"collection":[{"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=\/wp\/v2\/users\/20"}],"replies":[{"embeddable":true,"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=32900"}],"version-history":[{"count":5,"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=\/wp\/v2\/posts\/32900\/revisions"}],"predecessor-version":[{"id":33400,"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=\/wp\/v2\/posts\/32900\/revisions\/33400"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=\/wp\/v2\/media\/33155"}],"wp:attachment":[{"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=32900"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=32900"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=32900"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}