Replica symmetry breaking in random non-Hermitian systems

被引:16
|
作者
Garcia-Garcia, Antonio M. [1 ]
Jia, Yiyang [2 ]
Rosa, Dario [3 ,4 ]
Verbaarschot, Jacobus J. M. [5 ]
机构
[1] Shanghai Jiao Tong Univ, Sch Phys & Astron, Shanghai Ctr Complex Phys, Shanghai 200240, Peoples R China
[2] Weizmann Inst Sci, Dept Particle Phys & Astrophys, IL-7610001 Rehovot, Israel
[3] Inst Basic Sci IBS, Ctr Theoret Phys Complex Syst, Daejeon 34126, South Korea
[4] Korea Univ Sci & Technol UST, Basic Sci Program, Daejeon 34113, South Korea
[5] SUNY Stony Brook, Ctr Nucl Theory, Dept Phys & Astron, Stony Brook, NY 11794 USA
基金
以色列科学基金会; 中国国家自然科学基金; 国家重点研发计划;
关键词
RANDOM-MATRIX MODEL; DENSITY-OF-STATES; GRASSMANN INTEGRATION; PHASE-TRANSITION; LEVEL; REPRESENTATION; ENSEMBLES; SPECTRA; PHYSICS; QCD;
D O I
10.1103/PhysRevD.105.126027
中图分类号
P1 [天文学];
学科分类号
0704 ;
摘要
Recent studies have revealed intriguing similarities between the contribution of wormholes to the gravitational path integral and the phenomenon of replica symmetry breaking observed in spin glasses and other disordered systems. Interestingly, these configurations may also be important for the explanation of the information paradox of quantum black holes. Motivated by these developments, we investigate the thermodynamic properties of a PT-symmetric system composed of two random non-Hermitian Hamiltonians with no explicit coupling between them. After performing ensemble averaging, we identify numerically and analytically a robust first-order phase transition in the free energy of two models with quantum chaotic dynamics: the elliptic Ginibre ensemble of random matrices and a non-Hermitian Sachdev-Ye-Kitaev (SYK) model. The free energy of the Ginibre model is temperature independent in the low-temperature phase. The SYK model has similar behavior for sufficiently low temperature, and then it experiences a possible continuous phase transition to a phase with a temperature-dependent free energy before the first-order transition takes place at a higher temperature. We identify the order parameter of the first-order phase transition and obtain analytical expressions for the critical temperature. The mechanism behind the transition is the existence of replica symmetry breaking configurations coupling left and right replicas that control the low-temperature limit of the partition function. We speculate that quantum chaos may be necessary for the observed dominance of off-diagonal replica symmetry breaking configurations in the low-temperature limit.
引用
收藏
页数:32
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