Determination of dynamical quantum phase transitions in strongly correlated many-body systems using Loschmidt cumulants

Dynamical phase transitions extend the notion of criticality to non-stationary settings and are characterized by sudden changes in the macroscopic properties of time-evolving quantum systems. Investigations of dynamical phase transitions combine aspects of symmetry, topology, and non-equilibrium physics, however, progress has been hindered by the notorious difficulties of predicting the time evolution of large, interacting quantum systems. Here, we tackle this outstanding problem by determining the critical times of interacting many-body systems after a quench using Loschmidt cumulants. Specifically, we investigate dynamical topological phase transitions in the interacting Kitaev chain and in the spin-1 Heisenberg chain. To this end, we map out the thermodynamic lines of complex times, where the Loschmidt amplitude vanishes, and identify the intersections with the imaginary axis, which yield the real critical times after a quench. For the Kitaev chain, we can accurately predict how the critical behavior is affected by strong interactions, which gradually shift the time at which a dynamical phase transition occurs. Our work demonstrates that Loschmidt cumulants are a powerful tool to unravel the far-from-equilibrium dynamics of strongly correlated many-body systems, and our approach can immediately be applied in higher dimensions.

arXiv:2011.13612

Lee-Yang theory, high cumulants, and large-deviation statistics of the magnetization in the Ising model

Editors’ Suggestion: Phys. Rev. B 102, 174418 (2020)

We investigate the Ising model in one, two, and three dimensions using a cumulant method that allows us to determine the Lee-Yang zeros from the magnetization fluctuations in small lattices. By doing so with increasing system size, we are able to determine the convergence point of the Lee-Yang zeros in the thermodynamic limit and thereby predict the occurrence of a phase transition. The cumulant method is attractive from an experimental point of view since it uses fluctuations of measurable quantities, such as the magnetization in a spin lattice, and it can be applied to a variety of equilibrium and nonequilibrium problems. We show that the Lee-Yang zeros encode important information about the rare fluctuations of the magnetization. Specifically, by using a simple ansatz for the free energy, we express the large-deviation function of the magnetization in terms of Lee-Yang zeros. This result may hold for many systems that exhibit a first-order phase transition.

arXiv:2006.15125

Show BibTeX: @article{Deger2020b,
title = {{L}ee-{Y}ang theory, high cumulants, and large-deviation statistics of the magnetization in the {I}sing model},
author = {Deger, Aydin and Brange, Fredrik and Flindt, Christian},
journal = {Phys. Rev. B},
volume = {102},
issue = {17},
pages = {174418},
numpages = {12},
year = {2020},
month = {Nov},
publisher = {American Physical Society},
doi = {10.1103/PhysRevB.102.174418},
url = {https://link.aps.org/doi/10.1103/PhysRevB.102.174418}}