Abstract
We study the quantum relaxation of the two-dimensional transverse-field Ising model after global quenches with a real-time variational Monte Carlo method and address the question whether this non-integrable, two-dimensional system thermalizes or not. We consider both interaction quenches in the paramagnetic phase and field quenches in the ferromagnetic phase and compare the time-averaged probability distributions of non-conserved quantities like magnetization and correlation functions to the thermal distributions according to the canonical Gibbs ensemble obtained with quantum Monte Carlo simulations at temperatures defined by the excess energy in the system. We find that the occurrence of thermalization crucially depends on the quench parameters: While after the interaction quenches in the paramagnetic phase thermalization can be observed, our results for the field quenches in the ferromagnetic phase show clear deviations from the thermal system. These deviations increase with the quench strength and become especially clear comparing the shape of the thermal and the time-averaged distributions, the latter ones indicating that the system does not completely lose the memory of its initial state even for strong quenches. We discuss our results with respect to a recently formulated theorem on generalized thermalization in quantum systems.
Highlights
Before we apply the real-time variational Monte Carlo (rt-VMC) algorithm to large system sizes, we consider a system of size 4 × 4, whose time evolution can be computed with numerical integration of the Schrödinger equation, and compare the rt-VMC
We have studied the quantum relaxation of the 2D-TFIM after global interaction quenches in the paramagnetic phase and global field quenches in the ferromagnetic phase using a newly developed rt-VMC method which allowed us to explore system sizes and time scales that have not been accessible before
In order to answer the question whether this two-dimensional, non-integrable system thermalizes or not we compared time-averaged results after the quenches to results for the system in thermal equilibrium at a temperature defined by the excess energy after the quench
Summary
For the interaction quenches the expectation values of the observables and their distributions are computed in the course of the single spin flip quantum Monte Carlo algorithm for the coefficients of the equations of motion at each time step, while for the field quenches there is a direct functional relationship to the variational parameters. The time averages of the observables are compared to the thermal expectation values of the system in equilibrium at the effective temperature Teff attributed to the quench, which are given by
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