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我国学者在一维自旋-电荷分离现象研究中取得进展

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发布时间：2021-08-25

来源：酯香香化学采购网

【化工仪器网科技前沿】

　　a：一维杨-高丁费米气体的电荷和自旋激发谱--黄色区是电荷自由度中的粒子-空穴连续激发谱，绿色区域是著名的双自旋子(spinon)的分数化激发谱。在小动量激发时，电荷与自旋激发都具有声子色散关系，但以不同的群速度传播，展现了电荷-自旋分离现象的本质。

　　b：该模型的比热临界相图--QC代表量子临界区，TLL代表朝永-拉亭戈液体，COR是非相干拉亭戈液体区(incoherent Luttinger liquid)，那里电荷自由度是相干的，自旋不再具有声速。

　　图：杨-高丁模型的低能激发与量子临界相图

　　在国家自然科学基金项目(批准号：11534014、11874393、1167420、11774390)等资助下，中国科学院精密测量科学与技术创新研究院管习文研究员团队、北京计算科学研究中心林海青院士团队、美国莱斯大学兰迪·休利特教授和浦晗教授团队合作，通过量子可积系统理论，得到了一维超冷费米气体独特的分数化准粒子和自旋-电荷分离现象的结果。相关研究成果以“一维排斥费米子中自旋电荷分离的演生与失效(Emergence and Disruption of Spin-Charge Separation in One-Dimensional Repulsive Fermions)”为题，于2020年11月2日发表在《物理评论快报》 (Physical Review Letters)杂志上。

　　粒子间复杂的相互作用和系统丰富的内部自由度通常给系统物理特性的描述带来巨大挑战。在一维量子多体物理中，朝永-拉亭戈液体理论以及多体的长程量子关联通常被用来描述一维多体系统的低能普适行为。一维相互作用费米子的低能激发通常会分裂成两支独立的朝永-拉亭戈液体，它们分别刻画携带自旋和电荷的准粒子，这种现象被称为自旋电荷分离。尽管这方面的研究有40多年的历史，然而对于这种现象至今仍缺乏令人信服的实验验证，一直是理论和实验研究难题。另一方面，一维自旋-1/2 接触相互作用的费米气体是典型的具有内部自由度的量子多体相互作用系统。杨振宁教授和高丁教授在1967年各自求解了该模型，即杨-高丁模型，成为量子统计物理中的典范。然而，该模型解所给出的方程极其复杂，发现其中所蕴含的物理规律一直是数学物理学科中的挑战性难题，从而阻碍了该模型在实际实验中的应用。

　　研究团队通过研究杨-高丁模型的精确解，发展相关的数学物理方法，首次计算了电荷自由度中的粒子-空穴集体激发谱和双自旋子(分数化准粒子)激发谱。通过求解该模型能谱的热力学方程，得到了相关热力学量的解析表达式，进而给出拉亭戈液体的普适规律及临界现象。研究团队进一步发现一旦激发涉及反向散射或在临界区受到热涨落的强烈干扰，电荷-自旋分离的朝永-拉亭戈液体特性就会失效，在临界区将会涌现出非相干的拉亭戈液体区(COR区)，表现出不同于临界区(QC)的自由费米临界标度关系。研究还证明了一维超冷费米原子体系的动力学结构因子不但可以用来观测自旋电荷分离的激发谱，而且可以用来验证朝永-拉亭戈液体动力学关联性质，并据此提出了实验验证自旋-电荷分离现象的具体方案。

　　以上研究结果提供了对分数化准粒子、自旋电荷分离、量子临界性和非相干拉亭戈液体的理解，给出了量子多体物理的一个范例，并为将来基于冷原子系统的实验观测奠定了理论基础。

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[ SQL ] SELECT `id`,`catname` FROM `yzn_goods_category` WHERE `pid` = 1 AND `status` = 1 ORDER BY `listorder` ASC,`id` DESC [ RunTime:0.000308s ]
[ SQL ] SELECT `id`,`catname` FROM `yzn_goods_category` WHERE `pid` = 2 AND `status` = 1 ORDER BY `listorder` ASC,`id` DESC [ RunTime:0.000282s ]
[ SQL ] SELECT `id`,`catname` FROM `yzn_goods_category` WHERE `pid` = 7 AND `status` = 1 ORDER BY `listorder` ASC,`id` DESC [ RunTime:0.000319s ]
[ SQL ] SELECT `id`,`catname` FROM `yzn_goods_category` WHERE `pid` = 16 AND `status` = 1 ORDER BY `listorder` ASC,`id` DESC [ RunTime:0.000272s ]
[ SQL ] SELECT `id`,`catname` FROM `yzn_goods_category` WHERE `pid` = 17 AND `status` = 1 ORDER BY `listorder` ASC,`id` DESC [ RunTime:0.000306s ]
[ SQL ] SELECT `id`,`catname` FROM `yzn_goods_category` WHERE `pid` IN (34,92) AND `status` = 1 ORDER BY `listorder` ASC,`id` DESC [ RunTime:0.000328s ]
[ SQL ] SELECT `id`,`catname` FROM `yzn_goods_category` WHERE `pid` IN (95,38) AND `status` = 1 ORDER BY `listorder` ASC,`id` DESC [ RunTime:0.000379s ]
[ SQL ] SELECT `id`,`catname` FROM `yzn_goods_category` WHERE `pid` = 1 AND `status` = 1 [ RunTime:0.000298s ]
[ SQL ] SELECT * FROM `yzn_goods_category` WHERE `status` = 1 AND `id` = 1 [ RunTime:0.000332s ]
[ SQL ] SELECT `id` FROM `yzn_goods_category` WHERE `status` = 1 AND ( arrparentid like '0,1,%' ) [ RunTime:0.000375s ]
[ SQL ] SHOW COLUMNS FROM `yzn_goods` [ RunTime:0.001027s ]
[ SQL ] SELECT `g`.`name`,p.id as p_id,`p`.`price`,`p`.`type`,`p`.`thumb`,`p`.`unit`,`p`.`is_where`,`p`.`goods_id`,`p`.`repeat_type` FROM `yzn_goods` `g` LEFT JOIN `yzn_goods_property` `p` ON `p`.`goods_id`=`g`.`id` WHERE `p`.`status` = 1 AND `p`.`is_del` = 0 AND `g`.`is_del` = 0 AND `p`.`is_where` LIKE '%1%' AND `g`.`cate_id` IN (25,26,29,30,48,1) AND `p`.`hot_sale` = '1' GROUP BY `p`.`repeat_type`,`p`.`goods_id` ORDER BY `p`.`sort` DESC,`p`.`id` DESC LIMIT 0,10 [ RunTime:0.001570s ]
[ SQL ] SELECT `id`,`catname` FROM `yzn_goods_category` WHERE `pid` = 2 AND `status` = 1 [ RunTime:0.000355s ]
[ SQL ] SELECT * FROM `yzn_goods_category` WHERE `status` = 1 AND `id` = 2 [ RunTime:0.000309s ]
[ SQL ] SELECT `id` FROM `yzn_goods_category` WHERE `status` = 1 AND ( arrparentid like '0,2,%' ) [ RunTime:0.000339s ]
[ SQL ] SELECT `g`.`name`,p.id as p_id,`p`.`price`,`p`.`type`,`p`.`thumb`,`p`.`unit`,`p`.`is_where`,`p`.`goods_id`,`p`.`repeat_type` FROM `yzn_goods` `g` LEFT JOIN `yzn_goods_property` `p` ON `p`.`goods_id`=`g`.`id` WHERE `p`.`status` = 1 AND `p`.`is_del` = 0 AND `g`.`is_del` = 0 AND `p`.`is_where` LIKE '%1%' AND `g`.`cate_id` IN (42,43,2) AND `p`.`hot_sale` = '1' GROUP BY `p`.`repeat_type`,`p`.`goods_id` ORDER BY `p`.`sort` DESC,`p`.`id` DESC LIMIT 0,10 [ RunTime:0.001499s ]
[ SQL ] SELECT `id`,`catname` FROM `yzn_goods_category` WHERE `pid` = 7 AND `status` = 1 [ RunTime:0.000321s ]
[ SQL ] SELECT * FROM `yzn_goods_category` WHERE `status` = 1 AND `id` = 7 [ RunTime:0.000295s ]
[ SQL ] SELECT `id` FROM `yzn_goods_category` WHERE `status` = 1 AND ( arrparentid like '0,7,%' ) [ RunTime:0.000300s ]
[ SQL ] SELECT `g`.`name`,p.id as p_id,`p`.`price`,`p`.`type`,`p`.`thumb`,`p`.`unit`,`p`.`is_where`,`p`.`goods_id`,`p`.`repeat_type` FROM `yzn_goods` `g` LEFT JOIN `yzn_goods_property` `p` ON `p`.`goods_id`=`g`.`id` WHERE `p`.`status` = 1 AND `p`.`is_del` = 0 AND `g`.`is_del` = 0 AND `p`.`is_where` LIKE '%1%' AND `g`.`cate_id` IN (10,14,32,33,49,50,51,52,53,54,55,56,57,58,96,97,7) AND `p`.`hot_sale` = '1' GROUP BY `p`.`repeat_type`,`p`.`goods_id` ORDER BY `p`.`sort` DESC,`p`.`id` DESC LIMIT 0,10 [ RunTime:0.001544s ]
[ SQL ] SELECT `id`,`catname` FROM `yzn_goods_category` WHERE `pid` = 16 AND `status` = 1 [ RunTime:0.000312s ]
[ SQL ] SELECT * FROM `yzn_goods_category` WHERE `status` = 1 AND `id` = 16 [ RunTime:0.000426s ]
[ SQL ] SELECT `id` FROM `yzn_goods_category` WHERE `status` = 1 AND ( arrparentid like '0,16,%' ) [ RunTime:0.000299s ]
[ SQL ] SELECT `g`.`name`,p.id as p_id,`p`.`price`,`p`.`type`,`p`.`thumb`,`p`.`unit`,`p`.`is_where`,`p`.`goods_id`,`p`.`repeat_type` FROM `yzn_goods` `g` LEFT JOIN `yzn_goods_property` `p` ON `p`.`goods_id`=`g`.`id` WHERE `p`.`status` = 1 AND `p`.`is_del` = 0 AND `g`.`is_del` = 0 AND `p`.`is_where` LIKE '%1%' AND `g`.`cate_id` IN (59,60,61,62,63,16) AND `p`.`hot_sale` = '1' GROUP BY `p`.`repeat_type`,`p`.`goods_id` ORDER BY `p`.`sort` DESC,`p`.`id` DESC LIMIT 0,10 [ RunTime:0.001461s ]
[ SQL ] SELECT `id`,`catname` FROM `yzn_goods_category` WHERE `pid` = 17 AND `status` = 1 [ RunTime:0.000343s ]
[ SQL ] SELECT * FROM `yzn_goods_category` WHERE `status` = 1 AND `id` = 17 [ RunTime:0.000304s ]
[ SQL ] SELECT `id` FROM `yzn_goods_category` WHERE `status` = 1 AND ( arrparentid like '0,17,%' ) [ RunTime:0.002476s ]
[ SQL ] SELECT `g`.`name`,p.id as p_id,`p`.`price`,`p`.`type`,`p`.`thumb`,`p`.`unit`,`p`.`is_where`,`p`.`goods_id`,`p`.`repeat_type` FROM `yzn_goods` `g` LEFT JOIN `yzn_goods_property` `p` ON `p`.`goods_id`=`g`.`id` WHERE `p`.`status` = 1 AND `p`.`is_del` = 0 AND `g`.`is_del` = 0 AND `p`.`is_where` LIKE '%1%' AND `g`.`cate_id` IN (40,64,65,66,67,68,100,17) AND `p`.`hot_sale` = '1' GROUP BY `p`.`repeat_type`,`p`.`goods_id` ORDER BY `p`.`sort` DESC,`p`.`id` DESC LIMIT 0,10 [ RunTime:0.001523s ]
[ SQL ] SELECT `id`,`catname` FROM `yzn_goods_category` WHERE `pid` = 34 AND `status` = 1 [ RunTime:0.002957s ]
[ SQL ] SELECT `id`,`catname` FROM `yzn_goods_category` WHERE `pid` = 92 AND `status` = 1 [ RunTime:0.000264s ]
[ SQL ] SELECT * FROM `yzn_goods_category` WHERE `status` = 1 AND `id` IN (34,92) [ RunTime:0.000327s ]
[ SQL ] SELECT `id` FROM `yzn_goods_category` WHERE `status` = 1 AND ( arrparentid like '0,34,%' or arrparentid like '0,92,%' ) [ RunTime:0.000295s ]
[ SQL ] SELECT `g`.`name`,p.id as p_id,`p`.`price`,`p`.`type`,`p`.`thumb`,`p`.`unit`,`p`.`is_where`,`p`.`goods_id`,`p`.`repeat_type` FROM `yzn_goods` `g` LEFT JOIN `yzn_goods_property` `p` ON `p`.`goods_id`=`g`.`id` WHERE `p`.`status` = 1 AND `p`.`is_del` = 0 AND `g`.`is_del` = 0 AND `p`.`is_where` LIKE '%1%' AND `g`.`cate_id` IN (35,70,71,93,94,34,92) AND `p`.`hot_sale` = '1' GROUP BY `p`.`repeat_type`,`p`.`goods_id` ORDER BY `p`.`sort` DESC,`p`.`id` DESC LIMIT 0,10 [ RunTime:0.024431s ]
[ SQL ] SELECT `id`,`catname` FROM `yzn_goods_category` WHERE `pid` = 95 AND `status` = 1 [ RunTime:0.000662s ]
[ SQL ] SELECT `id`,`catname` FROM `yzn_goods_category` WHERE `pid` = 38 AND `status` = 1 [ RunTime:0.000289s ]
[ SQL ] SELECT * FROM `yzn_goods_category` WHERE `status` = 1 AND `id` IN (95,38) [ RunTime:0.000406s ]
[ SQL ] SELECT `id` FROM `yzn_goods_category` WHERE `status` = 1 AND ( arrparentid like '0,38,%' or arrparentid like '0,95,%' ) [ RunTime:0.000307s ]
[ SQL ] SELECT `g`.`name`,p.id as p_id,`p`.`price`,`p`.`type`,`p`.`thumb`,`p`.`unit`,`p`.`is_where`,`p`.`goods_id`,`p`.`repeat_type` FROM `yzn_goods` `g` LEFT JOIN `yzn_goods_property` `p` ON `p`.`goods_id`=`g`.`id` WHERE `p`.`status` = 1 AND `p`.`is_del` = 0 AND `g`.`is_del` = 0 AND `p`.`is_where` LIKE '%1%' AND `g`.`cate_id` IN (47,74,75,76,77,78,79,80,81,82,83,99,95,38) AND `p`.`hot_sale` = '1' GROUP BY `p`.`repeat_type`,`p`.`goods_id` ORDER BY `p`.`sort` DESC,`p`.`id` DESC LIMIT 0,10 [ RunTime:0.001667s ]
[ SQL ] SHOW COLUMNS FROM `yzn_article` [ RunTime:0.000930s ]
[ SQL ] SELECT `A`.*,`AD`.*,`C`.`catname` FROM `yzn_article` `A` INNER JOIN `yzn_article_data` `AD` ON `A`.`id`=`AD`.`did` INNER JOIN `yzn_category` `C` ON `C`.`id`=`A`.`catid` WHERE `A`.`id` = 5596 AND `A`.`status` = 1 LIMIT 1 [ RunTime:0.000430s ]
[ SQL ] SHOW COLUMNS FROM `yzn_category` [ RunTime:0.000890s ]
[ SQL ] SELECT `id` FROM `yzn_category` WHERE `parentid` = 35 AND `status` = 1 [ RunTime:0.000263s ]
[ SQL ] SELECT `id` FROM `yzn_category` WHERE `parentid` IN (36,37,38,39,40,41,42) AND `status` = 1 [ RunTime:0.000251s ]
[ SQL ] SELECT `id` FROM `yzn_category` WHERE `parentid` = 43 AND `status` = 1 [ RunTime:0.000232s ]
[ SQL ] SELECT `id` FROM `yzn_category` WHERE `parentid` IN (44,45,46,47,48,49,50) AND `status` = 1 [ RunTime:0.000389s ]
[ SQL ] SELECT `id` FROM `yzn_category` WHERE `parentid` = 6 AND `status` = 1 [ RunTime:0.000219s ]
[ DB ] CONNECT:[ UseTime:0.013447s ] mysql:host=127.0.0.1;port=3306;dbname=yzncms;charset=utf8
[ SQL ] SELECT `A`.`id`,`A`.`title` FROM `yzn_article` `A` INNER JOIN `yzn_category` `C` ON `C`.`id`=`A`.`catid` WHERE `A`.`status` = 1 AND `A`.`catid` IN (35,36,37,38,39,40,41,42) ORDER BY `A`.`flag` DESC,`A`.`listorder` ASC,`A`.`updatetime` DESC [ RunTime:0.034881s ]
[ SQL ] UPDATE `yzn_article` SET `hits` = `hits` + 1 WHERE `id` = 5596 [ RunTime:0.000383s ]
[ SQL ] SELECT * FROM `yzn_poster` WHERE `cate_id` = 10 AND `p_c_id` = 41 ORDER BY `listorder` ASC LIMIT 4 [ RunTime:0.000548s ]
[ SQL ] SELECT COUNT(*) AS tp_count FROM `yzn_article` `a` INNER JOIN `yzn_category` `c` ON `a`.`catid`=`c`.`id` WHERE `catid` = 38 AND `a`.`status` = 1 [ RunTime:0.004155s ]
[ SQL ] SELECT `a`.*,`c`.`catname` FROM `yzn_article` `a` INNER JOIN `yzn_category` `c` ON `a`.`catid`=`c`.`id` WHERE `catid` = 38 AND `a`.`status` = 1 ORDER BY `flag` DESC,`listorder` ASC,`updatetime` DESC LIMIT 0,6 [ RunTime:0.008549s ]
[ SQL ] SELECT COUNT(*) AS tp_count FROM `yzn_article` `a` INNER JOIN `yzn_category` `c` ON `a`.`catid`=`c`.`id` WHERE `catid` = 37 AND `a`.`status` = 1 [ RunTime:0.005121s ]
[ SQL ] SELECT `a`.*,`c`.`catname` FROM `yzn_article` `a` INNER JOIN `yzn_category` `c` ON `a`.`catid`=`c`.`id` WHERE `catid` = 37 AND `a`.`status` = 1 ORDER BY `flag` DESC,`listorder` ASC,`updatetime` DESC LIMIT 0,6 [ RunTime:0.007686s ]