Geometry effect of dynamical quantum phase transitions at finite temperatures

Jia-Chen Tang, Xu-Yang Hou, Hao Guo

Dynamical quantum phase transitions (DQPTs) probe the nonequilibrium evolution of quantum systems, unveiling their geometric and topological characteristics. In this study, we introduce the concepts of parallel quench and dynamic geometrical order parameter (DGOP) for nonband models without momentum-space structure, where these quantities capture the geometric shifts associated with DQPTs. At zero temperature, the DGOP corresponds to the Pancharatnam geometric phase, while at finite temperatures, it extends to the interferometric geometric phase. We further generalize the dynamic topological order parameter (DTOP) to finite-temperature band models, examining its behavior in the Su-Schrieffer-Heeger model. Our analysis shows that thermal fluctuations and boundary effects at finite temperatures disrupt the quantization of the DTOP, yet it retains signatures of topological transitions. These findings deepen the understanding of geometric and topological properties in quantum dynamics, illuminating DQPTs across both nonband and band frameworks.

Angelo C. M. Carollo, Davide Valenti, Bernardo Spagnolo

David J. Dean

Debashish Mondal, Tanay Nag

We investigate the interplay between non-Hermiticity and finite temperature in the context of a mixed-state dynamical quantum phase transition (MSDQPT). We consider a $p$-wave superconductor model, encompassing complex hopping and non-Hermiticity, that can lead to gapless phases in addition to gapped phases, to examine the MSDQPT and winding number via the intraphase quench. We find that the MSDQPT is always present irrespective of the gap structure of the underlying phase; however, the profile of Fisher zeros changes between the above phases. Such occurrences of MSDQPT are in contrast to the zero-temperature case in which a DQPT does not take place for the gapped phase. Surprisingly, the half-integer jumps in winding number at zero temperature are washed away for finite temperature in the gapless phase. We study the evolution of the minimum time required by the system to experience MSDQPT with the inverse temperature such that gapped and gapless phases can be differentiated. Our study indicates that the minimum time shows monotonic (nonmonotonic) behavior for the gapped (gapless) phase.

Protyush Nandi, Sirshendu Bhattacharyya, Subinay Dasgupta

The signature of quantum phase transition is generally wiped out at finite temperature. A few quantities that have been observed to carry this signature through a nonanalytic behavior are also limited to low temperatures only. With an aim to identify a suitable dynamical quantity at a high temperature, we have recently constructed a function from quantum fidelity, which has the potential to bear a nonanalytic signature at the quantum critical point beyond low-temperature regime. In this paper, we elaborate our earlier paper and demonstrate the behavior of the corresponding rate function and the robustness of the nonanalyticity for a number of many-body Hamiltonians in different dimensions. We have also shown that our rate function reduces to that used in the demonstration of the dynamical quantum phase transition (DQPT) at zero temperature. It has been further observed that, unlike DQPT, the long-time limit of the rate function can faithfully detect the equilibrium quantum phase transition as well.

Ralf Schützhold