{"id":31598,"date":"2018-09-11T00:00:36","date_gmt":"2018-09-10T16:00:36","guid":{"rendered":"https:\/\/case.ntu.edu.tw\/blog\/?p=31598"},"modified":"2018-09-07T15:22:07","modified_gmt":"2018-09-07T07:22:07","slug":"v52-%e9%87%8f%e5%ad%90%e9%9c%8d%e7%88%be%e6%85%8b%e4%b9%8b%e8%ac%8e%ef%bc%88%e4%b8%ad%ef%bc%89","status":"publish","type":"post","link":"https:\/\/case.ntu.edu.tw\/blog\/?p=31598","title":{"rendered":"\u00a0v=5\/2 \u91cf\u5b50\u970d\u723e\u614b\u4e4b\u8b0e\uff08\u4e2d\uff09"},"content":{"rendered":"<p><span style=\"color: #333399;\"><strong>\u25a0\u8ab0\u662f\u63cf\u8ff0v=5\/2\u57fa\u614b\u7684\u6ce2\u51fd\u6578\uff1f\u66fe\u7d93\u6211\u5011\u90fd\u5feb\u8981\u76f8\u4fe1\u5c31\u662f Pfaffian \u6ce2\u51fd\u6578\uff0c\u76f4\u5230 ...... \u3002<\/strong><\/span><\/p>\n<figure id=\"attachment_31601\" aria-describedby=\"caption-attachment-31601\" style=\"width: 450px\" class=\"wp-caption alignleft\"><img fetchpriority=\"high\" decoding=\"async\" class=\"wp-image-31601\" src=\"http:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2018\/07\/pfaffian2-fig1.png\" alt=\"\" width=\"450\" height=\"255\" data-wp-pid=\"31601\"><figcaption id=\"caption-attachment-31601\" class=\"wp-caption-text\">Figure1. 2+1 \u7dad\u6d41\u9ad4\u4e2d\u53ef\u80fd\u7684\u6f29\u6e26\u7d44\u614b\u3002\uff08photo credit: \u4f5c\u8005\u81ea\u7e6a\uff09<\/figcaption><\/figure>\n<p><strong>\u64b0\u6587\uff5c\u856d\u7dad\u7ff0<\/strong><\/p>\n<p>\u8ab0\u662f\u63cf\u8ff0v=5\/2\u57fa\u614b\u7684\u6ce2\u51fd\u6578\uff1f\u66fe\u7d93\u6211\u5011\u90fd\u5feb\u8981\u76f8\u4fe1\u5c31\u662f Pfaffian \u6ce2\u51fd\u6578\uff0c\u76f4\u5230 ...... \u3002<\/p>\n<p>\u5728<a href=\"http:\/\/case.ntu.edu.tw\/blog\/?p=31580\" target=\"_blank\" rel=\"noopener noreferrer\">\u524d\u6587<\/a>\u4e2d\u6211\u5011\u8907\u7fd2\u4e86\u91cf\u5b50\u970d\u723e\u6548\u61c9\uff0c\u4e26\u5728\u6587\u7ae0\u7684\u4e0b\u534a\u6bb5\u4ecb\u7d39 v=5\/2 \u614b\uff0c\u4e26\u8aaa\u660e\u70ba\u4ec0\u9ebc\u4ed6\u662f\u500b\u6709\u8da3\u7684\u554f\u984c\uff0c\u4e26\u4e14\u7528\u4e00\u500b\u554f\u984c\u7d50\u5c3e \u2014\u2014 \u6211\u5011\u6709\u6c92\u6709\u4e00\u500b\u985e\u4f3c Laughlin \u6ce2\u51fd\u6578\u7684\u8a66\u9a57\u6ce2\u51fd\u6578\u4f86\u4ee3\u8868\u9019\u500b\u72c0\u614b\u3002\u800c\u5728\u672c\u6587\u4e2d\u6211\u5011\u5c07\u66f4\u6df1\u5165\u5730\u8a0e\u8ad6\u9019\u500b\u61f8\u554f\u3002<\/p>\n<p>\u5728\u9019\u4e4b\u524d\uff0c\u7b46\u8005\u60f3\u5148\u91d0\u6e05\u524d\u6587\u7684\u4e00\u6bb5\u6558\u8ff0\u3002<\/p>\n<p>\u4e0a\u6587\u7684\u5f8c\u6bb5\u4e2d\uff0c\u6211\u63d0\u53ca\u9019\u500bv=5\/2\u614b\u53ef\u4ee5\u60f3\u6210\u662f\u8907\u5408\u8cbb\u7c73\u5b50\u5f62\u6210\u7684\u8d85\u5c0e\u9ad4\u614b\uff0c\u4e26\u4e14\u6211\u8072\u7a31\uff0c\u9019\u4e9b\u8907\u5408\u8cbb\u7c73\u5b50\u5fc5\u9808\u4ee5 <em>p<\/em> \u3001<em>f<\/em> \u6ce2\u6216\u5176\u4ed6\u5947\u6578\u89d2\u52d5\u91cf\u7684\u65b9\u5f0f\u914d\u5c0d\u3002\u6211\u5fc5\u9808\u627f\u8a8d\u5728\u5beb\u4e0b\u9019\u6bb5\u6558\u8ff0\u6642\uff0c\u6211\u5fc3\u4e2d\u5df2\u7d93\u6709\u67d0\u4e9b\u6ce2\u51fd\u6578\uff0c\u4e26\u4e14\u9019\u500b\u5ba3\u544a\u6697\u81ea\u5730\u5047\u8a2d\u4e86 (1) \u5728\u90a3\u4e00\u5c64\u862d\u9053\u968e\u7684\u96fb\u5b50\u5011\u7684\u81ea\u65cb\u90fd\u5728\u540c\u4e00\u500b\u65b9\u5411\u4e0a\uff0c\u800c\u4e14 (2) \u8907\u5408\u8cbb\u7c73\u5b50\u662f\u975e\u76f8\u5c0d\u8ad6\u6027\u7684\u8cbb\u7c73\u5b50\u3002\u7b2c\u4e00\u500b\u689d\u4ef6\u5728\u6587\u4e2d\u4e5f\u6709\u63d0\u53ca\uff0c\u4f46\u5176\u5be6\u6700\u65e9\u7684\u7814\u7a76\u4e2d\uff0c\u5b78\u8005\u5011\u4e5f\u66fe\u8003\u616e\u904e\u96fb\u5b50\u81ea\u65cb\u672a\u6975\u5316\u7684\u72c0\u6cc1\uff0c\u5728\u90a3\u6a23\u7684\u5047\u8a2d\u5e95\u4e0b\uff0c\u8907\u5408\u8cbb\u7c73\u5b50\u4e5f\u80fd\u4ee5 <em>s<\/em> \u6ce2\u914d\u5c0d\u3002\u95dc\u65bc\u5be6\u9a57\u4e0a\u5c0d\u9019\u500b\u5047\u8a2d\u7684\u6700\u65b0\u5831\u5c0e\uff0c\u53ef\u4ee5\u53c3\u8003 [1]\u3002\u7b2c\u4e8c\u500b\u5047\u8a2d\u5247\u662f\u8fd1\u5e74\u4f86\u5f15\u8d77\u8a31\u591a\u8a0e\u8ad6\uff0c\u56e0\u70ba\u5728\u829d\u52a0\u54e5\u5927\u5b78\u7684 Son \u5728 2015 \u5e74\u63d0\u51fa\u8907\u5408\u8cbb\u7c73\u5b50\u5176\u5be6\u4e5f\u53ef\u4ee5\u662f\u72c4\u62c9\u514b\u8cbb\u7c73\u5b50 [2]\uff0c\u9019\u500b\u72c4\u62c9\u514b\u8cbb\u7c73\u5b50\u53ef\u4ee5\u5f62\u6210 <em>s<\/em> \u6ce2\u914d\u5c0d\u3002<\/p>\n<p>\u70ba\u4e86\u4e0d\u6df7\u6dc6\u5927\u5bb6\uff0c\u5728\u63a5\u4e0b\u4f86\u7684\u8a0e\u8ad6\u4e2d\uff0c\u82e5\u7121\u7279\u5225\u8aaa\u660e\uff0c\u6211\u90fd\u5c07\u7dad\u6301 (1) \u8ddf (2) \u7684\u5047\u8a2d\u3002<\/p>\n<p><span style=\"color: #008080;\"><strong>\u25cfPfaffian \u6ce2\u51fd\u6578<\/strong><\/span><\/p>\n<p>\u56de\u5230 v=5\/2\u91cf\u5b50\u614b\uff0c\u6211\u5011\u7684\u554f\u984c\u662f\uff1a\u6709\u6c92\u6709\u4e00\u500b\u50cf Laughlin \u6ce2\u51fd\u6578\u7684\u6ce2\u51fd\u6578\uff0c\u53ef\u4ee5\u5e6b\u52a9\u6211\u5011\u4e86\u89e3\u9019\u500b\u91cf\u5b50\u614b\uff1f\u5728 1991 \u5230 2007 \u9593\uff0c\u5728\u6578\u503c\u7d50\u679c\u4e0a\u547c\u8072\u6700\u9ad8\u7684\u5019\u9078\u4eba\u662f\u6240\u8b02\u7684 Moore-Read \u6ce2\u51fd\u6578 [3]\uff0c\u53c8\u7a31\u4f5c Pfaffian \u614b\uff08\u7c21\u5beb\u6210 Pf\uff09\u3002<\/p>\n<p>Moore \u8ddf Read \u986f\u7136\u662f\u63d0\u51fa\u7684\u5169\u4f4d\u7269\u7406\u5b78\u5bb6\uff0c\u90a3\u4ec0\u9ebc\u662f Pfaffian?<\/p>\n<p>\u5beb\u4f5c\u7684\u6642\u5019\u6211\u624d\u767c\u73fe\u9019\u500b\u8a5e\u6c92\u6709\u4e2d\u6587\u7684\u7dad\u57fa\u7db2\u9801\u3002\u7528\u6700\u7c21\u55ae\u7684\u65b9\u6cd5\u8b1b\uff0c\u7d66\u5b9a\u4e00\u500b\u5076\u6578\u7dad\u5ea6\u7684\u53cd\u5c0d\u7a31\u77e9\u9663\uff0c\u9019\u500b\u77e9\u9663\u7684 Pfaffian \u7d04\u7565\u5c31\u662f\u884c\u5217\u5f0f\u958b\u6839\u865f\u3002\u9019\u500b\u540d\u7a31\u8207\u6ce2\u51fd\u6578\u7684\u5177\u9ad4\u5f62\u5f0f\u6709\u95dc\u4fc2\uff0c\u5728\u5f8c\u7e8c\u7684\u6bb5\u843d\u4e2d\uff0c\u6211\u90fd\u5c07\u4e4b\u7c21\u5beb\u70ba Pf \u614b\u3002<\/p>\n<p>\u9664\u4e86\u662fv=5\/2\u7684\u5f37\u529b\u5019\u9078\u4eba\uff0cPf \u614b\u672c\u8eab\u5c31\u662f\u4e00\u500b\u6545\u4e8b\u5f88\u8c50\u5bcc\u7684\u6ce2\u51fd\u6578\u3002\u751a\u81f3\u53ef\u4ee5\u8aaa\uff0c\u4eba\u5011\u5bc4\u8a17\u65bcv=5\/2\u91cf\u5b50\u970d\u723e\u614b\u7684\u8a31\u591a\u60f3\u50cf\uff0c\u90fd\u4f86\u81ea\u65bc Pf \u614b\u3002\u4ee5\u4e0b\u5c31\u8b93\u6211\u5011\u4f86\u9673\u8ff0\u5b83\u7684\u6027\u8cea\u3002<\/p>\n<p><strong>(i)&nbsp;<\/strong>\u5206\u6578\u96fb\u8377\uff1a\u56de\u60f3\u9996\u5148\u8072\u540d\u5927\u566a\u7684 Laughlin \u6ce2\u51fd\u6578\uff0c\u9019\u500b\u6ce2\u51fd\u6578\u5176\u4e2d\u4e00\u500b\u8ca2\u737b\u5c31\u662f\uff0c\u4ed6\u8aaa\u660e\u4e86\u5728\u7cfb\u7d71\u4e2d\u7684\u6e96\u7c92\u5b50\u53ef\u4ee5\u5e36\u6709\u5206\u6578\u96fb\u8377\uff0c\u4ee5v=1\/3\u7684\u91cf\u5b50\u970d\u723e\u614b\u800c\u8a00\uff0c\u88e1\u9762\u7684\u6e96\u7c92\u5b50\u5e36\u7684\u96fb\u8377\u662fq=e\/3 \uff0c\u4e5f\u5c31\u662f\u4e09\u5206\u4e4b\u4e00\u7684\u96fb\u5b50\u96fb\u8377\u3002\u5229\u7528 Pf \u6ce2\u51fd\u6578\uff0cMoore \u8ddf Read \u4e5f\u53ef\u4ee5\u9032\u884c\u985e\u4f3c\u7684\u8a08\u7b97\uff0c\u4e26\u4e14\u767c\u73fe\u9019\u88e1\u9762\u7684\u6e96\u7c92\u5b50\u6709<\/p>\n<p style=\"text-align: center;\">q=e\/4<\/p>\n<p><strong>(ii)<\/strong>\u99ac\u7d04\u62c9\u7d0d\uff08<strong>Majorana<\/strong>\uff09\u8cbb\u7c73\u5b50\uff1a\u5728\u7c92\u5b50\u7269\u7406\u7684\u5b9a\u7fa9\u4e2d\uff0c\u99ac\u7d04\u62c9\u7d0d\u8cbb\u7c73\u5b50\u64c1\u6709\u81ea\u5df1\u662f\u81ea\u5df1\u7684\u53cd\u7c92\u5b50\u9019\u7a2e\u7279\u6b8a\u7684\u6027\u8cea\u3002\u5728\u51dd\u614b\u7269\u7406\u4e2d\uff0c\u7531\u65bc\u6578\u5b78\u4e0a\u5f62\u5f0f\u7684\u985e\u4f3c\uff0c\u666e\u904d\u8a8d\u70ba\u5728\u8d85\u5c0e\u9ad4\u4e2d\u7684\u535a\u683c\u67f3\u535a\u592b\uff08Bogoliubov\uff09\u7c92\u5b50\u5728\u67d0\u4e9b\u689d\u4ef6\u4e0b\u53ef\u4ee5\u662f\u99ac\u7d04\u62c9\u7d0d\u7c92\u5b50\u3002\u5176\u4e2d\u4e00\u500b\u5834\u5408\u5c31\u662f\u5728 <em>p<\/em> \u6ce2\u8d85\u5c0e\u9ad4\u7684\u300c\u6f29\u6e26\u300d<a href=\"#_ftn1\" name=\"_ftnref1\"><sup>[1]<\/sup><\/a>\u4e2d\uff0c\u4e00\u5982\u524d\u9762\u91cd\u8907\u95e1\u8ff0\u7684\uff0cPf \u614b\u662f\u4e00\u500b <em>p<\/em> \u6ce2\u8d85\u5c0e\u9ad4\u3002\u4e5f\u56e0\u6b64\u82e5\u4ed6\u771f\u7684\u63cf\u8ff0\u4e86v=5\/2\u614b\uff0c\u90a3\u9019\u500b\u970d\u723e\u7cfb\u7d71\u5c31\u4e5f\u8b8a\u6210\u641c\u5c0b\u99ac\u7d04\u62c9\u7d0d\u8cbb\u7c73\u5b50\u7684\u5e73\u81fa\u4e4b\u4e00\u3002<\/p>\n<p><strong>(iii) <\/strong>\u975e\u963f\u8c9d\u723e\u4efb\u610f\u5b50\uff08<strong>non-Abelian anyon<\/strong>\uff09\uff1a\u4efb\u610f\u5b50\uff08anyon\uff09\u662f\u5728 2+1 \u7dad\u7cfb\u7d71\u4e2d\u4e00\u500b\u7279\u6b8a\u7684\u6982\u5ff5\u3002\u51fa\u767c\u9ede\u662f\uff0c\u8003\u616e\u5728\u7a7a\u9593\u7684\u5169\u500b\u7c92\u5b50\uff0c\u6211\u5011\u8f38\u9001\u5176\u4e2d\u4e00\u500b\u7c92\u5b50\uff0c\u8b93\u5b83\u7e5e\u904e\u53e6\u5916\u4e00\u500b\u7c92\u5b50\uff0c\u7136\u5f8c\u6211\u5011\u554f\uff0c\u63cf\u8ff0\u9019\u5169\u500b\u7c92\u5b50\u7684\u6ce2\u51fd\u6578\u5728\u9019\u500b\u904e\u7a0b\u524d\u8ddf\u904e\u7a0b\u5f8c\u6709\u4ec0\u9ebc\u5dee\uff1f\u5728 3 \u7dad\u7a7a\u9593\u4e2d\uff0c\u5176\u5be6\u6c92\u6709\u8fa6\u6cd5\u771f\u7684\u53bb\u754c\u5b9a\u8aaa\u4e00\u500b\u7c92\u5b50\u771f\u7684\u300c\u7e5e\u904e\u300d\u4e86\u53e6\u4e00\u500b\u3002\u4f46\u5728 2 \u7dad\u7a7a\u9593\u662f\u6709\u8fa6\u6cd5\u7684\u3002\u6700\u4e00\u822c\u7684\u72c0\u6cc1\u662f\uff0c\u9019\u500b\u6ce2\u51fd\u6578\u6703\u88ab\u4e58\u4e0a\u4e00\u500b\u7d55\u5c0d\u503c\u70ba 1 \u7684\u8907\u6578\uff0c\u5f9e\u800c\u53ef\u4ee5\u63a8\u8ad6\uff0c\u7576\u6211\u5011\u4ea4\u63db\u5169\u500b\u7c92\u5b50\u7684\u4f4d\u7f6e\uff08\u7e5e\u534a\u5708\uff09\uff0c\u6ce2\u51fd\u6578\u4e5f\u6703\u88ab\u4e58\u4e0a\u4e00\u500b\u7d55\u5c0d\u503c\u70ba 1 \u7684\u8907\u6578\u3002\u7576\u9019\u500b\u6578\u4e0d\u662f +1\uff08\u73bb\u8272\u5b50\uff09\u6216 -1 \uff08\u8cbb\u7c73\u5b50\uff09\u6642\uff0c\u6211\u5011\u7a31\u5b83\u70ba\uff08\u963f\u8c9d\u723e\uff09\u4efb\u610f\u5b50\uff08(abelian) anyon\uff09\u3002\u5728\u9019\u908a abelian \u7684\u610f\u601d\u662f\u771f\u7684\u53ea\u6709\u4e58\u4e0a\u4e00\u500b\u8907\u6578\u3002Pf \u614b\u88e1\u9762\u5177\u6709\u7684\u662f\u66f4\u795e\u79d8\u7684 non-Abelian \u4efb\u610f\u5b50 [4]\u3002<\/p>\n<p>\u5b83\u7684\u610f\u7fa9\u662f\uff0c\u9996\u5148\uff0c\u7d66\u5b9a\u67d0\u500b\u80fd\u91cf\uff0c\u9019\u500b\u7cfb\u7d71\u5f97\u6709\u5f88\u591a\u7c21\u4f75\u614b\uff08degenerate states\uff09\uff0c\u4e5f\u5c31\u662f\u8aaa\u5f88\u591a\u5177\u5099\u4e0d\u540c\u91cf\u5b50\u6578\u7684\u72c0\u614b\u90fd\u5177\u5099\u9019\u500b\u80fd\u91cf\uff0c\u800c\u91cd\u8981\u7684\u9ede\uff0c\u662f\u9019\u4e9b\u7c21\u4f75\u614b\u4e0d\u80fd\u7d93\u7531\u5c40\u90e8\u7684\u64cd\u4f5c\uff08local operation\uff09\u5f9e\u4e00\u500b\u8dd1\u5230\u53e6\u5916\u4e00\u500b\u3002\u975e\u963f\u8c9d\u723e\u4efb\u610f\u5b50\u7684\u6982\u5ff5\u662f\uff0c\u7576\u6211\u5011\u7de8\u7e54\u9019\u4e9b\u4efb\u610f\u5b50\u7684\u6642\u7a7a\u8ecc\u8de1\u6642\uff0c\u7d50\u679c\u4e0d\u53ea\u662f\u5728\u6ce2\u51fd\u6578\u4e0a\u4e58\u4e0a\u4e00\u4e9b\u8907\u6578\uff0c\u800c\u8b93\u6211\u5011\u5f9e\u5176\u4e2d\u4e00\u500b\u7c21\u4f75\u614b\u8df3\u5230\u53e6\u5916\u4e00\u500b\u7c21\u4f75\u614b\u3002<\/p>\n<figure id=\"attachment_31602\" aria-describedby=\"caption-attachment-31602\" style=\"width: 650px\" class=\"wp-caption aligncenter\"><img decoding=\"async\" class=\"wp-image-31602\" src=\"http:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2018\/07\/pfaffian-fig2.png\" alt=\"\" width=\"650\" height=\"336\" data-wp-pid=\"31602\" srcset=\"https:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2018\/07\/pfaffian-fig2.png 905w, https:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2018\/07\/pfaffian-fig2-800x414.png 800w\" sizes=\"(max-width: 650px) 100vw, 650px\" \/><figcaption id=\"caption-attachment-31602\" class=\"wp-caption-text\">Figure2. \u4e00\u500b\u7c21\u55ae\u7684\u60f3\u50cf\u975e\u963f\u8c9d\u723e\u6027\u4efb\u610f\u5b50\u7684\u793a\u610f\u5716\u3002\u5f62\u5f0f\u4e0a\u4e00\u500b\u99ac\u7d04\u62c9\u7d0d\u8cbb\u7c73\u5b50\u53ef\u4ee5\u8996\u70ba\u534a\u500b\u96fb\u5b50\u3002\u73fe\u5728\u6211\u5011\u8a2d\u60f3\u4e00\u500b\u6709\u56db\u500b\u99ac\u7d04\u62c9\u7d0d\u8cbb\u7c73\u5b50\u7684\u7269\u7406\u614b\uff08\u53ef\u4ee5\u88ab\u7406\u89e3\u6210\u6709\u5169\u500b\u300c\u96fb\u5b50\u300d\uff09\u7576\u6211\u5011\u5982\u5de6\u5716\u9019\u6a23\u4ea4\u63db\u5169\u500b\u99ac\u7d04\u62c9\u7d0d\u8cbb\u7c73\u5b50\uff0c\u6703\u56de\u5230\u539f\u4f86\u7684\u72c0\u614b\uff0c\u5247\u6ce2\u51fd\u6578\u6703\u4e58\u4e0a\u4e00\u500b\u7d55\u5c0d\u503c\u70ba 1 \u7684\u8907\u6578\u3002\u82e5\u6211\u5011\u5982\u5de6\u5716\u9019\u6a23\u4ea4\u63db\u539f\u672c\u5728\u4e0d\u540c\u300c\u96fb\u5b50\u300d\u5167\u7684\u99ac\u7d04\u62c9\u7d0d\u8cbb\u7c73\u5b50\uff0c\u5247\u6703\u9032\u5165\u53e6\u5916\u4e00\u500b\u7c21\u4f75\u614b\u3002\uff08photo credit: \u4f5c\u8005\u81ea\u7e6a\uff09<\/figcaption><\/figure>\n<p><span style=\"color: #008080;\"><strong>\u25cfPf or Not?<\/strong>\uff1a<\/span><\/p>\n<p>\u4ee5\u4e0a\u9019\u4e9b\u6027\u8cea\uff0c\u5728\u5b78\u7406\u4e0a\u53ef\u4ee5\u88ab\u61c9\u7528\u5728\u91cf\u5b50\u8a08\u7b97\uff0c\u53c8\u56e0\u70ba Pf \u614b\u662f\u547c\u8072\u6700\u9ad8\u7684v=5\/2\u5019\u9078\u4eba\u4e4b\u4e00\uff0c\u4e5f\u56e0\u6b64\u67d0\u4e9b\u5b78\u8005\u6703\u8a8d\u70ba\u9019\u500b\u970d\u723e\u614b\u4e5f\u6709\u6a5f\u6703\u8b8a\u6210\u5be6\u9a57\u91cf\u5b50\u8a08\u7b97\u7684\u5e73\u81fa\uff08\u4f46\u6211\u5011\u73fe\u5728\u77e5\u9053\u9019\u4e26\u4e0d\u662f\u4e00\u500b\u9818\u5148\u7684\u63d0\u8b70\u3002\uff09<\/p>\n<p>\u4f46\u7b46\u8005\u60f3\u8981\u5728\u4e0b\u7bc7\u63a5\u7e8c\u7684\u6545\u4e8b\u662f\uff0c\u5728 2007 \u5e74\u5de6\u53f3\uff0c\u6709\u5176\u4ed6\u5b78\u8005\u63d0\u51fa\u4e86\u8ddf Pf \u614b\u4e0d\u5206\u4f2f\u4ef2\u7684 anti-Pfaffian \u6ce2\u51fd\u6578\uff0c\u66f4\u751a\u8005\uff0c\u5728 2015 \u5e74\uff0c Son [2] \u63d0\u51fa PH-Pfaffian \u614b\uff0c\u7a76\u7adf\u9019\u4e9b\u4e0d\u540c\u7684 Pfaffian \u8ab0\u66f4\u53d7\u771f\u5be6\u4e16\u754c\u9752\u775e\uff1f\u4e14\u5f85\u4e0b\u56de\u5206\u89e3\u3002<\/p>\n<p>&nbsp;<\/p>\n<p><strong>\u53c3\u8003\u8cc7\u6599\uff1a<\/strong><br \/>\n[1] Md. Shafayat Hossain <em>et al<\/em>, Phys. Rev. Lett. <strong>120<\/strong>, 256601 (2018).<br \/>\n[2] D. T. Son, Phys. Rev. X <strong>5<\/strong>, 031027 (2015).<br \/>\n[3] G. Moore, and N. Read, Nucl. Phys. <strong>B360<\/strong>, 362 (1991).<br \/>\n[4] D. A. Ivanov, Phys. Rev. Lett. <strong>86<\/strong>, 268 (2001).<\/p>\n<p><strong>\u8a3b\u89e3\uff1a<\/strong><br \/>\n<a href=\"#_ftnref1\" name=\"_ftn1\"><sup>[1]<\/sup><\/a> \u4e0d\u662f\u771f\u7684\u8996\u89ba\u4e0a\u7684\u6f29\u6e26\uff0c\u4f46\u8981\u89e3\u91cb\u9019\u500b\u6982\u5ff5\uff0c\u6703\u9700\u8981\u53e6\u5916\u4e00\u7bc7\u7368\u7acb\u7684\u6587\u7ae0\u3002<\/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 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\u524d\u6587\u4e2d\u6211\u5011\u8907\u7fd2\u4e86\u91cf\u5b50\u970d\u723e\u6548\u61c9\uff0c\u4e26\u5728\u6587\u7ae0\u7684\u4e0b\u534a\u6bb5\u4ecb\u7d39 v=5\/2 \u614b\uff0c\u4e26\u8aaa\u660e\u70ba\u4ec0\u9ebc\u4ed6\u662f\u500b\u6709\u8da3\u7684\u554f\u984c\uff0c\u4e26\u4e14\u7528\u4e00\u500b\u554f\u984c\u7d50\u5c3e \u2014\u2014 \u6211\u5011\u6709\u6c92\u6709\u4e00\u500b\u985e\u4f3c Laughlin \u6ce2\u51fd\u6578\u7684\u8a66\u9a57\u6ce2\u51fd\u6578\u4f86\u4ee3\u8868\u9019\u500b\u72c0\u614b\u3002\u800c\u5728\u672c\u6587\u4e2d\u6211\u5011\u5c07\u66f4\u6df1\u5165\u5730\u8a0e\u8ad6\u9019\u500b\u61f8\u554f\u3002<\/p>\n","protected":false},"author":20,"featured_media":31600,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3293,39],"tags":[2730,3944,2793,3942],"aioseo_notices":[],"jetpack_featured_media_url":"https:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2018\/07\/pfaffian2-fig0.png","_links":{"self":[{"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=\/wp\/v2\/posts\/31598"}],"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=31598"}],"version-history":[{"count":4,"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=\/wp\/v2\/posts\/31598\/revisions"}],"predecessor-version":[{"id":31616,"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=\/wp\/v2\/posts\/31598\/revisions\/31616"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=\/wp\/v2\/media\/31600"}],"wp:attachment":[{"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=31598"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=31598"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=31598"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}