Signatures of Quantum Criticality in the Complex Inverse Temperature Plane
Yang Liu, Songtai Lv, Yang Yang, and Haiyuan Zou*
Key Laboratory of Polar Materials and Devices (MOE), School of Physics and Electronic Science, East China Normal University, Shanghai 200241, China
Abstract ：Concepts of the complex partition functions and the Fisher zeros provide intrinsic statistical mechanisms for finite temperature and real time dynamical phase transitions. We extend the utility of these complexifications to quantum phase transitions. We exactly identify different Fisher zeros on lines or closed curves and elucidate their correspondence with domain-wall excitations or confined mesons for the one-dimensional transverse field Ising model. The crossover behavior of the Fisher zeros provides a fascinating picture for criticality near the quantum phase transition, where the excitation energy scales are quantitatively determined. We further confirm our results by tensor network calculations and demonstrate a clear signal of deconfined meson excitations from the disruption of the closed zero curves. Our results unambiguously show significant features of Fisher zeros for a quantum phase transition and open up a new route to explore quantum criticality.
收稿日期: 2023-02-07
出版日期: 2023-04-18
:
05.70.Jk
(Critical point phenomena)
05.10.Cc
(Renormalization group methods)
64.60.De
(Statistical mechanics of model systems (Ising model, Potts model, field-theory models, Monte Carlo techniques, etc.))
[1] Sachdev S 2011 Quantum Phase Transitions (Cambridge: Cambridge University Press) [2] Vojta M 2003 Rep. Prog. Phys. 66 2069 [3] Yang C N and Lee T D 1952 Phys. Rev. 87 404 [4] Lee T D and Yang C N 1952 Phys. Rev. 87 410 [5] Peng X H, Zhou H, Wei B B, Cui J, J D, and Liu R B 2015 Phys. Rev. Lett. 114 010601 [6] Brandner K, Maisi V F, Pekola J P, Garrahan J P, and Flindt C 2017 Phys. Rev. Lett. 118 180601 [7] Fisher M E 1965 Statistical Physics, Weak Interactions, Field Theory , Lectures in Theoretical Physics (Boulder: University of Colorado Press) vol VIIC [8] van Saarloos W and Kurtze D A 1984 J. Phys. A 17 1301 [9] Bena I, Droz M, and Lipowski A 2005 Int. J. Mod. Phys. B 19 4269 [10] Denbleyker A, Liu Y, Meurice Y, Qin M P, Xiang T, Xie Z Y, J F Y, and Zou H 2014 Phys. Rev. D 89 016008 [11] Denbleyker A, D D, Liu Y, Meurice Y, and Zou H 2010 Phys. Rev. Lett. 104 251601 [12] Meurice Y and Zou H 2011 Phys. Rev. D 83 056009 [13] Liu Y Z and Meurice Y 2011 Phys. Rev. D 83 096008 [14] Basu S, Arovas D P, Gopalakrishnan S, Hooley C A, and Oganesyan V 2022 Phys. Rev. Res. 4 013018 [15] Heyl M, Polkovnikov A, and Kehrein S 2013 Phys. Rev. Lett. 110 135704 [16] Andraschko F and Sirker J 2014 Phys. Rev. B 89 125120 [17] Zvyagin A 2016 Low Temp. Phys. 42 971 [18] Heyl M 2018 Rep. Prog. Phys. 81 054001 [19] Onsager L 1944 Phys. Rev. 65 117 [20] Kaufman B 1949 Phys. Rev. 76 1232 [21] Suzuki M 1976 Prog. Theor. Phys. 56 1454 [22] Pfeuty P 1970 Ann. Phys. 57 79 [23] Białończyk M, Gómez-Ruiz F, and Campo A D 2021 SciPost Phys. 11 013 [24] Jones G L 1966 J. Math. Phys. 7 2000 [25] Quan H T, Song Z, Liu X F, Zanardi P, and Sun C P 2006 Phys. Rev. Lett. 96 140604 [26] Banuls M C, Heller M P, Jansen K, Knaute J, and Svensson V 2022 arXiv:2206.10528 [hep-th] [27] Wu J D, Zhu L J, and Si Q M 2018 Phys. Rev. B 97 245127 [28] Coldea R, Tennant D, Wheeler E, Wawrzynska E, Prabhakaran D, Telling M, Habicht K, Smeibidl P, and Kiefer K 2010 Science 327 177 [29] Zamolodchikov A B 1989 Int. J. Mod. Phys. A 04 4235 [30] Zhang Z, Amelin K, Wang X, Zou H, Yang J, Nagel U, T R O O, Dey T, Nugroho A A, Lorenz T, Wu J, and Wang Z 2020 Phys. Rev. B 101 220411 [31] Zou H Y, Cui Y, Wang X et al. 2021 Phys. Rev. Lett. 127 077201 [32] Orús R 2014 Ann. Phys. 349 117 [33] Cirac J I, Pérez-García D, Schuch N, and Verstraete F 2021 Rev. Mod. Phys. 93 045003 [34] Meurice Y, Sakai R, and Unmuth-Yockey J 2022 Rev. Mod. Phys. 94 025005 [35] Xie Z Y, Chen J, Qin M P, Zhu J W, Yang L P, and Xiang T 2012 Phys. Rev. B 86 045139 [36] Amelin K, Engelmayer J, Viirok J et al. 2020 Phys. Rev. B 102 104431 [37] Liu X F, Fu Y F, Yu W Q, Yu J F, and Xie Z Y 2022 Chin. Phys. Lett. 39 067502 [38] Yang L P, Fu Y F, Xie Z Y, and Xiang T 2022 arXiv:2210.09896 [cond-mat.stat-mech] [39] Tong P Q and Liu X X 2006 Phys. Rev. Lett. 97 017201 [40] Chen X, Gu Z C, Liu Z X, and Wen X G 2013 Phys. Rev. B 87 155114 [41] Zou H Y, Zhao E H, Guan X W, and Liu W V 2019 Phys. Rev. Lett. 122 180401 [42] Zheng Q, Li X, and Zou H 2020 Phys. Rev. B 101 165131 [43] Michal V P, Aleiner I L, Altshuler B L, and Shlyapnikov G V 2016 Proc. Natl. Acad. Sci. USA 113 E4455 [44] Zhang K L and Song Z 2021 Phys. Rev. Lett. 126 116401 [45] Yang Y T and Luo H G 2023 Chin. Phys. Lett. 40 020502 [46] Senthil T, Vishwanath A, Balents L, Sachdev S, and Fisher M 2004 Science 303 1490 [47] Wei B B, Chen S W, Po H C, and Liu R B 2014 Sci. Rep. 4 5202
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.
[2]
.
[3]
.
[4]
.
[5]
.
[6]
.
[7]
.
[8]
.
[9]
.
[10]
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2023, Vol. 40 
