{"id":32899,"date":"2018-11-20T00:42:47","date_gmt":"2018-11-19T16:42:47","guid":{"rendered":"https:\/\/case.ntu.edu.tw\/blog\/?p=32899"},"modified":"2018-12-14T10:01:37","modified_gmt":"2018-12-14T02:01:37","slug":"hubbard-%e6%a8%a1%e5%9e%8b%ef%bc%88%e3%84%a7%ef%bc%89%ef%bc%9a%e5%8b%95%e6%a9%9f%e8%88%87%e5%ae%9a%e7%be%a9","status":"publish","type":"post","link":"https:\/\/case.ntu.edu.tw\/blog\/?p=32899","title":{"rendered":"Hubbard \u6a21\u578b\uff08\u3127\uff09\uff1a\u52d5\u6a5f\u8207\u5b9a\u7fa9"},"content":{"rendered":"<p><span style=\"color: #333399;\"><strong>\u25a0\u6211\u5011\u5c07\u5229\u7528\u4e00\u500b\u7cfb\u5217\u6587\u8ddf\u5927\u5bb6\u4ecb\u7d39\u4e00\u500b\u5728\u51dd\u614b\u7269\u7406\u4e2d\u5f88\u91cd\u8981\u7684\u6a21\u578b\u5bb6\u65cf\u3002<\/strong><\/span><\/p>\n<p><strong>\u64b0\u6587\uff5c\u856d\u7dad\u7ff0<\/strong><\/p>\n<p>\u524d\u5169\u7bc7\u6587\u7ae0\u8ddf\u8b80\u8005\u5b9a\u6027\u5730\u8b1b\u8ff0\u4e86\u5728\u8a0e\u8ad6\u91d1\u5c6c\u6027\u8cea\u6642\uff0c\u5927\u5bb6\u6240\u8b02\u7684\u5178\u7bc4\u5f0f\u7684\u862d\u9053\u7406\u8ad6\u662f\u4ec0\u9ebc\u610f\u601d\u3002\u7b46\u8005\u9810\u8a08\u518d\u82b1\u81f3\u5c11\u4e00\u5169\u7bc7\u6587\u7ae0\u804a\u804a\u73fe\u5728\u7576\u7d05\u7684\u300c\u602a\u91d1\u5c6c\u300d\uff08Strange metal\uff09\u548c\u300c\u58de\u91d1\u5c6c\u300d\uff08bad metal\uff09\uff0c\u63a2\u8a0e\u5b83\u5011\u8207\u6b63\u5e38\u91d1\u5c6c\u7684\u5dee\u7570\uff0c\u4e26\u76e1\u7b46\u8005\u80fd\u529b\u6240\u53ca\u8ddf\u5927\u5bb6\u8aaa\u660e\u80cc\u5f8c\u7684\u539f\u56e0\u3002<\/p>\n<p>\u5728\u90a3\u4e4b\u524d\uff0c\u7b46\u8005\u60f3\u8ddf\u5927\u5bb6\u82b1\u5e7e\u7bc7\u6587\u7ae0\u7684\u7a7a\u9593\u4f86\u804a\u804a\u4e00\u500b\u4e5f\u53ef\u4ee5\u6709\u975e\u8cbb\u7c73\u6db2\u9ad4\uff08non-Fermi liquid\uff09\u7684\u7c21\u55ae\u6a21\u578b\u3002<\/p>\n<p>\u8aaa\u662f\u4e00\u500b\u6a21\u578b\uff0c\u5176\u5be6\u7cbe\u78ba\u800c\u8a00\u662f\u4e00\u500b\u6a21\u578b\u8207\u5b83\u7684\u5404\u7a2e\u8b8a\u5f62\u3002<\/p>\n<p>\u5728\u79d1\u666e\u6587\u4e2d\u62ff\u7406\u8ad6\u7269\u7406\u7684\u7279\u5b9a\u6a21\u578b\u4f86\u63a2\u8a0e\u5f80\u5f80\u662f\u5f88\u4e0d\u8a0e\u597d\u7684\u3002\u5176\u4e00\uff0c\u6a21\u578b\u5f80\u5f80\u96e2\u73fe\u5be6\u7684\u91cf\u6e2c\u9084\u6709\u4e00\u6bb5\u8ddd\u96e2\uff0c\u6bd4\u8f03\u96e3\u8b93\u4e00\u822c\u4f86\u8aaa\u8b80\u8005\u6709\u76f4\u63a5\u7684\u9ad4\u6703 ; \u5176\u4e8c\uff0c\u5be6\u4f8b\u7684\u4e00\u4e9b\u7279\u5fb5\u5f80\u5f80\u727d\u6d89\u5230\u5b9a\u91cf\u7684\u8a08\u7b97\uff0c\u5c0d\u65bc\u4e00\u822c\u8b80\u8005\uff0c\u9019\u4e26\u4e0d\u662f\u6700\u53cb\u5584\u7684\u5448\u73fe\u65b9\u5f0f\u3002<\/p>\n<p>\u4f46\u5f9e\u53e6\u5916\u4e00\u500b\u89d2\u5ea6\u601d\u8003\uff0c\u9019\u6216\u8a31\u53ef\u4ee5\u8b93\u5927\u5bb6\u7406\u89e3\u7406\u8ad6\u7269\u7406\u5b78\u5bb6\u5728\u9762\u5c0d\u8907\u96dc\u554f\u984c\u6642\uff0c\u5982\u4f55\u53bb\u8403\u53d6\u4e2d\u6700\u95dc\u9375\u7684\u5143\u7d20\uff0c\u53c8\u6216\u662f\u5728\u7814\u7a76\u4e00\u500b\u76f8\u5c0d\u7c21\u55ae\u7684\u6a21\u578b\u6642\uff0c\u5982\u4f55\u63a8\u8ad6\u51fa\u4e00\u4e9b\u9069\u7528\u6027\u66f4\u5ee3\u7684\u7d50\u8ad6\u3002\u81f3\u65bc\u6280\u8853\u6027\u7684\u3001\u5b9a\u91cf\u7684\u8a0e\u8ad6\uff0c\u5728\u96fb\u8166\u6280\u8853\u767c\u9054\u7684\u4eca\u65e5\uff0c\u53ef\u90e8\u5206\u5730\u5c07\u6578\u503c\u5448\u73fe\u6210\u5716\u8868\u4f86\u8b93\u5927\u5bb6\u6709\u66f4\u76f4\u89c0\u7684\u611f\u53d7\u3002<\/p>\n<p>\u9019\u500b\u7cfb\u5217\u6587\u7684\u91cd\u9ede\u5728\u6240\u8b02\u7684 Hubbard \u6a21\u578b\u3002\u9019\u500b\u6a21\u578b\u4e00\u958b\u59cb\u662f\u88ab\u63d0\u51fa\u4f86\u7814\u7a76\u904e\u6e21\u91d1\u5c6c\u4e2d\u7684\u96fb\u5b50\u904b\u52d5\uff0c\u800c\u5f8c\u88ab\u9032\u884c\u5404\u7a2e\u6539\u9020\uff0c\u81f3\u4eca\u4ecd\u662f\u5f37\u95dc\u806f\u7cfb\u7d71\u5167\u4e00\u500b\u91cd\u8981\u7684\u8ab2\u984c\u3002\u5728\u66f4\u7cbe\u78ba\u5730\u5b9a\u7fa9\u4eca\u5929\u7684\u7248\u672c\u524d\uff0c\u8b93\u6211\u5011\u5728\u770b\u770b\u9019\u500b\u554f\u984c\u5167\u7684\u57fa\u672c\u5143\u7d20\u3002<\/p>\n<figure id=\"attachment_32918\" aria-describedby=\"caption-attachment-32918\" style=\"width: 500px\" class=\"wp-caption aligncenter\"><img fetchpriority=\"high\" decoding=\"async\" class=\"wp-image-32918\" src=\"http:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2018\/11\/1-1.jpg\" alt=\"\" width=\"500\" height=\"386\" data-wp-pid=\"32918\" srcset=\"https:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2018\/11\/1-1.jpg 1178w, https:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2018\/11\/1-1-600x463.jpg 600w, https:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2018\/11\/1-1-800x618.jpg 800w\" sizes=\"(max-width: 500px) 100vw, 500px\" \/><figcaption id=\"caption-attachment-32918\" class=\"wp-caption-text\">Figure1. \uff08photo credit: \u4f5c\u8005\u81ea\u7e6a\uff09<br \/> Hubbard \u6a21\u578b\u793a\u610f\u5716\u3002\u6211\u5011\u4ee5\u85cd\u8272\u5713\u7403\u4ee3\u8868\u7c92\u5b50\uff0cHubbard \u6a21\u578b\u57fa\u672c\u4e0a\u5c31\u662f\u653e\u4e00\u5806\u7c92\u5b50\u5728\u6676\u683c\u7684\u7bc0\u9ede\uff08\u7d05\u8272\u5713\u6846\uff09\u4e0a\u3002\u7c92\u5b50\u53ef\u4ee5\u5728\u76f8\u9130\u7684\u7bc0\u9ede\u9593\u8df3\u8e8d\uff08\u5de6\u4e0a\uff09\uff0c\u7576\u5169\u500b\u7c92\u5b50\u8dd1\u5230\u540c\u4e00\u500b\u7bc0\u9ede\u6642\uff0c\u4ed6\u5011\u6703\u611f\u53d7\u5230\u4ea4\u4e92\u4f5c\u7528\uff08\u53f3\u4e0b\uff09\u3002<\/figcaption><\/figure>\n<p>\u5728 Hubbard \u6a21\u578b\u4e2d\uff0c\u7a7a\u9593\u7684\u80cc\u666f\u662f\u4e00\u500b\u7d66\u5b9a\u7684\u6676\u683c\uff0c\u7a7a\u9593\u7dad\u5ea6\u53ef\u4ee5\u662f 1, 2, 3 \u7dad\uff0c\u5e7e\u4f55\u7d50\u69cb\u53ef\u4ee5\u662f\u6b63\u7acb\u65b9\u9ad4\uff08cubic lattice\uff09\u3001\u4e09\u89d2\u6676\u683c\uff08triangular lattice\uff09\u3001\u8702\u7aa9\u6676\u683c\uff08honeycomb lattice\uff09\u3002\u9032\u800c\u6211\u5011\u5c07\u4e00\u4e9b\u7c92\u5b50\uff08\u8cbb\u7c73\u5b50 (fermion )\u6216\u73bb\u8272\u5b50 (boson)\uff09\u653e\u5230\u7bc0\u9ede\u4e0a\uff0c\u8003\u616e\u4ed6\u5011\u53ef\u80fd\u7684\u52d5\u529b\u5b78\u3002<\/p>\n<p>\u4e00\u500b\u6a21\u578b\u7684\u52d5\u529b\u5b78\u4f9d\u8cf4\u65bc\u6211\u5011\u300c\u5141\u8a31\u300d\u9019\u4e9b\u7c92\u5b50\u505a\u4e9b\u4ec0\u9ebc\u4e8b\u3002\u9996\u5148\u6211\u5011\u8981\u63a7\u5236\u653e\u4e86\u591a\u5c11\u500b\u7c92\u5b50\u9032\u53bb\uff0c\u5728\u7d71\u8a08\u529b\u5b78\u7684\u4e00\u500b\u8868\u8ff0\u5167\uff0c\u5e73\u5747\u7684\u7c92\u5b50\u6578\u53ef\u4ee5\u85c9\u7531\u8abf\u6574\u5316\u5b78\u52e2\uff08chemical potential\uff09\u4f86\u63a7\u5236\u3002\u63a5\u4e0b\u4f86\u6211\u5011\u8b93\u7c92\u5b50\u5011\u6709\u80fd\u529b\u6d3b\u52d5\uff0c\u6700\u7c21\u55ae\u7684\u72c0\u6cc1\u662f\uff0c\u6211\u5011\u8b93\u7c92\u5b50\u53ef\u4ee5\u5728\u9130\u8fd1\u7684\u7bc0\u9ede\u4e0a\u8df3\u8e8d\uff0c\u5728\u4e00\u500b\u9031\u671f\u6027\u7684\u6676\u683c\u4e2d\uff0c\u9019\u6a23\u53ea\u6709\u300c\u52d5\u80fd\u300d\u7684\u554f\u984c\u662f\u53ef\u4ee5\u89e3\u7684\uff0c\u56e0\u70ba\u7c92\u5b50\u5011\u770b\u4e0d\u898b\u5f7c\u6b64\uff0c\u4e00\u500b 1,000 \u500b\u7c92\u5b50\u7684\u554f\u984c\u57fa\u672c\u4e0a\u53ea\u662f 1,000 \u500b\u4e00\u500b\u7c92\u5b50\u7684\u554f\u984c\u3002\u4e0b\u4e00\u6b65\u5c31\u662f\u8b93\u7c92\u5b50\u5011\u300c\u770b\u898b\u5f7c\u6b64\u300d\uff0c\u73fe\u5be6\u4e16\u754c\u4e2d\u96fb\u5b50\u5011\u770b\u5f97\u898b\u5c0d\u65b9\uff0c\u662f\u56e0\u70ba\u4ed6\u5011\u4e4b\u9593\u6709\u5eab\u502b\u4f4d\u80fd\uff0c\u5eab\u502b\u4f4d\u80fd\u662f\u4e00\u500b\u9060\u8ddd\u96e2\u7684\u4ea4\u4e92\u4f5c\u7528\uff0c\u5c0d\u6211\u5011\u4f86\u8aaa\u9084\u662f\u8907\u96dc\u4e86\u9ede\uff0c\u4f5c\u70ba\u7b2c\u4e00\u6b65\uff0c\u6211\u5011\u8003\u616e\u4e00\u500b\u6975\u9650\u7684\u72c0\u6cc1\uff0c\u4e5f\u5c31\u662f\u5169\u500b\u7c92\u5b50\u9593\u5177\u6709\u4ea4\u4e92\u4f5c\u7528\u50c5\u50c5\u7576\u4ed6\u5011\u8655\u5728\u540c\u4e00\u500b\u7bc0\u9ede\u4e0a\u3002\uff08\u9019\u6a23\u7684\u7c21\u5316\u4e26\u4e0d\u6703\u904e\u65bc\u4e0d\u5207\u5be6\u969b\uff0c\u56e0\u70ba\u5728\u5be6\u969b\u7684\u554f\u984c\u4e2d\uff0c\u5eab\u502b\u529b\u5e38\u5e38\u88ab\u5c4f\u853d\uff0c\u4e5f\u56e0\u6b64\u6c92\u6709\u90a3\u9ebc\u9577\u8ddd\u3002\uff09<\/p>\n<p>\u9019\u5c31\u662f\u6211\u5011\u7684 Hubbard \u6a21\u578b\uff0c\u5b83\u5177\u6709\u4e09\u500b\u53c3\u6578\uff1a\u5316\u5b78\u52e2 \u03bc\uff0c\u6c7a\u5b9a\u5e73\u5747\u800c\u8a00\u6211\u5011\u653e\u4e86\u591a\u5c11\u7c92\u5b50\u9032\u53bb\u9019\u500b\u7cfb\u7d71\uff0c\u8e8d\u9077\u5e38\u6578 t\uff08hopping constant\uff09\u6c7a\u5b9a\u7c92\u5b50\u5728\u76f8\u9130\u5169\u6676\u683c\u9ede\u9593\u8df3\u8e8d\u7684\u80fd\u529b\uff08\u5fae\u89c0\u4e0a\uff0c\u9019\u500b\u6578\u5b57\u53ef\u4ee5\u5c0d\u61c9\u5230\u4e00\u500b\u7c92\u5b50\u5f9e\u4e00\u500b\u9ede\u4e0a\u7a7f\u96a7\u5230\u53e6\u5916\u4e00\u500b\u9ede\u7684\u7a0b\u5ea6\u3002\uff09\uff0c\u4f4d\u80fd U\uff0c\u6c7a\u5b9a\u7576\u5169\u500b\u7c92\u5b50\u4f4d\u65bc\u540c\u4e00\u500b\u6676\u683c\u4e0a\u7684\u6642\u5019\uff0c\u4ed6\u5011\u4e4b\u9593\u4ea4\u4e92\u4f5c\u7528\u7684\u7a0b\u5ea6\u3002\u6700\u5f8c\u9084\u6709\u4e00\u500b\u71b1\u529b\u5b78\u53c3\u6578\u662f\u6eab\u5ea6 T\u3002\uff08\u5728\u7406\u8ad6\u7684\u8a0e\u8ad6\u4e2d\uff0c\u6211\u5011\u7576\u7136\u53ef\u4ee5\u4efb\u6027\u5730\u8003\u616e\u7d55\u5c0d\u96f6\u5ea6\u7684\u7269\u7406\uff0c\u4f46\u7576\u8981\u5728\u5be6\u9a57\u4e0a\u6e96\u5099\u9019\u6a23\u7684\u7cfb\u7d71\u6642\uff0c\u6211\u5011\u5fc5\u9808\u78ba\u4fdd\u6eab\u5ea6\u5920\u4f4e\u4ee5\u81f3\u65bc\u91cf\u5b50\u6548\u61c9\u53ef\u4ee5\u5448\u73fe\u51fa\u4f86\u3002\uff09<\/p>\n<p>\u9019\u500b\u6a21\u578b\u770b\u8d77\u4f86\u5f88\u55ae\u7d14\uff0c\u7136\u800c\uff0c\u5728\u4efb\u610f\u7dad\u5ea6\u7684\u6676\u683c\u4e0a\uff0c\u4eba\u5011\u8fc4\u4eca\u4e26\u6c92\u6709\u7c21\u55ae\u800c\u4e14\u5b8c\u6574\u7684\u4e86\u89e3\u3002\u4f46\u5f9e\u5df2\u7d93\u638c\u63e1\u7684\u77e5\u8b58\u4e2d\uff0c\u6211\u5011\u77e5\u9053\u8cbb\u7c73\u5b50\u7248\u672c\u7684 Hubbard \u6a21\u578b\u5728\u4e0d\u540c\u7684\u6eab\u5ea6\u548c\u647b\u96dc\u689d\u4ef6\u4e0b\u5b83\u7684\u57fa\u614b\u81f3\u5c11\u53ef\u4ee5\u5448\u73fe\u53cd\u9435\u78c1\uff08antiferromagnet\uff09\u3001\u8d17\u9699\uff08pseudogap\uff09\u3001\u975e\u5e38\u898f\u8d85\u5c0e\u6027\uff08unconventional superconductivity\uff09\u3001\u8cbb\u7c73\u6db2\u9ad4\u3001\u602a\u91d1\u5c6c\u7b49\u76f8\u3002\u73bb\u8272\u5b50\u7248\u672c\u7684 Hubbard \u6a21\u578b\u5247\u63d0\u4f9b\u6211\u5011\u4e00\u500b\u7c21\u55ae\u7684\u6a21\u578b\u4f86\u7814\u7a76\u8d85\u6d41\u9ad4\u8207 Mott \u7d55\u7de3\u9ad4\uff08Mott insulator\uff09\u9593\u7684\u76f8\u8b8a\u5316\uff0c\u751a\u81f3\u5728\u76f8\u8b8a\u5316\u7684\u81e8\u754c\u9ede(critical point)\u5be6\u73fe\u4f4e\u80fd\u91cf\u7248\u672c\u7684\u5e0c\u683c\u65af\u7c92\u5b50 (Higgs particle)\u3002<\/p>\n<p>\u5728\u5be6\u9a57\u4e0a\uff0c\u96d6\u7136\u4ed6\u5011\u4e26\u4e0d\u76f4\u63a5\u5c0d\u61c9\u5230\u5be6\u969b\u7684\u91d1\u5c6c\u8207\u96fb\u5b50\u7cfb\u7d71\uff0c\u4f46\u4eca\u65e5\u8d85\u51b7\u539f\u5b50\uff08ultracold atoms\uff09\u5be6\u9a57\u7684\u6280\u8853\u5df2\u7d93\u53ef\u4ee5\u5728\u5149\u5b78\u6676\u683c\uff08optical lattice\uff09\u4e2d\u5206\u5225\u5be6\u73fe\u73bb\u8272\u8ddf\u8cbb\u7c73\u7248\u672c\u7684 Hubbard \u6a21\u578b\uff0c\u8b93\u6574\u500b\u6545\u4e8b\u66f4\u6709\u8da3\u7684\u662f\uff0c\u5be6\u9a57\u5b78\u5bb6\u5011\u6709\u80fd\u529b\u7cbe\u78ba\u5730\u63a7\u5236\u5316\u5b78\u52e2\u3001\u8e8d\u9077\u5e38\u6578\u8207\u4f4d\u80fd\uff0c\u751a\u81f3\u53ef\u4ee5\u900f\u904e\u63a7\u5236\u4e0d\u540c\u65b9\u5411\u7684\u8e8d\u9077\u5e38\u6578\u4f86\u6f38\u9032\u5730\u8b8a\u5316\u7a7a\u9593\u7dad\u5ea6\uff0c\u9019\u5141\u8a31\u4e86\u6211\u5011\u5728\u5be6\u8b49\u7684\u7a0b\u5ea6\u4e0a\u6975\u5927\u53ef\u80fd\u5730\u53bb\u63a2\u7d22\u7c21\u55ae\u6a21\u578b\u4e2d\u7684\u7269\u8cea\u76f8\uff0c\u4e5f\u8b93\u7406\u8ad6\u8a08\u7b97\u4e0a\u7684\u9810\u6e2c\u7d50\u679c\u6709\u4e86\u8a31\u591a\u76f4\u63a5\u7684\u6bd4\u8f03\u5c0d\u8c61\u3002<\/p>\n<p>\u5728\u672c\u7cfb\u5217\u4e2d\uff0c\u6211\u5011\u5c07\u5206\u5225\u8003\u616e\u73bb\u8272\u5b50\u8207\u8cbb\u7c73\u5b50\u7684 Hubbard \u6a21\u578b\uff0c\u4e26\u5c31\u4eba\u5011\u76ee\u524d\u5df2\u7d93\u4e86\u89e3\u7684\u7269\u7406\uff0c\u4e5f\u5c31\u662f\u524d\u9762\u51fa\u73fe\u7684\u90a3\u4e9b\u5c08\u6709\u540d\u8a5e\uff0c\u76e1\u53ef\u80fd\u8ddf\u8b80\u8005\u89e3\u8aaa\u5df2\u77e5\u7684\u73fe\u5be6\u3001\u5df2\u7d93\u5728\u5be6\u9a57\u4e0a\u9a57\u8b49\u7684\u73fe\u8c61\u8207\u671f\u5f85\u7684\u767c\u5c55\u3002<\/p>\n<figure id=\"attachment_32922\" aria-describedby=\"caption-attachment-32922\" style=\"width: 500px\" class=\"wp-caption aligncenter\"><img decoding=\"async\" class=\"wp-image-32922\" src=\"http:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2018\/11\/1-2.jpg\" alt=\"\" width=\"500\" height=\"314\" data-wp-pid=\"32922\"><figcaption id=\"caption-attachment-32922\" class=\"wp-caption-text\">Figure1. \uff08photo credit: \u4f5c\u8005\u81ea\u7e6a\uff09<br \/> Hubbard \u6a21\u578b\u793a\u610f\u5716\u3002\u6211\u5011\u4ee5\u85cd\u8272\u5713\u7403\u4ee3\u8868\u7c92\u5b50\uff0cHubbard \u6a21\u578b\u57fa\u672c\u4e0a\u5c31\u662f\u653e\u4e00\u5806\u7c92\u5b50\u5728\u6676\u683c\u7684\u7bc0\u9ede\uff08\u7d05\u8272\u5713\u6846\uff09\u4e0a\u3002\u7c92\u5b50\u53ef\u4ee5\u5728\u76f8\u9130\u7684\u7bc0\u9ede\u9593\u8df3\u8e8d\uff08\u5de6\u4e0a\uff09\uff0c\u7576\u5169\u500b\u7c92\u5b50\u8dd1\u5230\u540c\u4e00\u500b\u7bc0\u9ede\u6642\uff0c\u4ed6\u5011\u6703\u611f\u53d7\u5230\u4ea4\u4e92\u4f5c\u7528\uff08\u53f3\u4e0b\uff09\u3002<br \/> Figure2. \uff08photo credit: \u4f5c\u8005\u81ea\u7e6a\uff09<br \/> \u5728\u5b78\u8853\u6f14\u8b1b\u4e2d\u5e38\u898b\u7684\u8cbb\u7c73\u5b50 Hubbard \u6a21\u578b\u7684\u7269\u8cea\u76f8\u5716\uff08\u4ee5\u6eab\u5ea6\u548c\u4ea4\u4e92\u4f5c\u7528\u70ba\u53c3\u6578\uff09\u3002<\/figcaption><\/figure>\n<p>&nbsp;<\/p>\n<figure id=\"attachment_32923\" aria-describedby=\"caption-attachment-32923\" style=\"width: 500px\" class=\"wp-caption aligncenter\"><img decoding=\"async\" class=\"wp-image-32923\" src=\"http:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2018\/11\/1-3.jpg\" alt=\"\" width=\"500\" height=\"348\" data-wp-pid=\"32923\"><figcaption id=\"caption-attachment-32923\" class=\"wp-caption-text\"><br \/> Figure3. (Photo credit: \u4f5c\u8005\u81ea\u7e6a)<br \/> \u5728\u5b78\u8853\u6f14\u8b1b\u4e2d\u5e38\u898b\u7684\u8cbb\u7c73\u5b50 Hubbard \u6a21\u578b\u7684\u7269\u8cea\u76f8\u5716\uff08\u4ee5\u6eab\u5ea6\u548c\u647b\u96dc\u70ba\u53c3\u6578\uff09\u3002<\/figcaption><\/figure>\n<p>&nbsp;<\/p>\n<p><strong>\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\u6211\u5011\u5c07\u5229\u7528\u4e00\u500b\u7cfb\u5217\u6587\u8ddf\u5927\u5bb6\u4ecb\u7d39\u4e00\u500b\u5728\u51dd\u614b\u7269\u7406\u4e2d\u5f88\u91cd\u8981\u7684\u6a21\u578b\u5bb6\u65cf\u3002\u5728 Hubbard \u6a21\u578b\u4e2d\uff0c\u7a7a\u9593\u7684\u80cc\u666f\u662f\u4e00\u500b\u7d66\u5b9a\u7684\u6676\u683c\uff0c\u7a7a\u9593\u7dad\u5ea6\u53ef\u4ee5\u662f 1, 2, 3 \u7dad\uff0c\u5e7e\u4f55\u7d50\u69cb\u53ef\u4ee5\u662f\u6b63\u7acb\u65b9\u9ad4\uff08cubic lattice\uff09\u3001\u4e09\u89d2\u6676\u683c\uff08triangular lattice\uff09\u3001\u8702\u7aa9\u6676\u683c\uff08honeycomb lattice\uff09\u3002\u9032\u800c\u6211\u5011\u5c07\u4e00\u4e9b\u7c92\u5b50\uff08\u8cbb\u7c73\u5b50 (fermion )\u6216\u73bb\u8272\u5b50 (boson)\uff09\u653e\u5230\u7bc0\u9ede\u4e0a\uff0c\u8003\u616e\u4ed6\u5011\u53ef\u80fd\u7684\u52d5\u529b\u5b78\u3002<\/p>\n","protected":false},"author":20,"featured_media":32918,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3293,39],"tags":[3998,1536,2793],"aioseo_notices":[],"jetpack_featured_media_url":"https:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2018\/11\/1-1.jpg","_links":{"self":[{"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=\/wp\/v2\/posts\/32899"}],"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=32899"}],"version-history":[{"count":7,"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=\/wp\/v2\/posts\/32899\/revisions"}],"predecessor-version":[{"id":33401,"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=\/wp\/v2\/posts\/32899\/revisions\/33401"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=\/wp\/v2\/media\/32918"}],"wp:attachment":[{"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=32899"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=32899"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=32899"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}