Test of quantum thermalization in the two-dimensional transverse-field Ising model

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.

Quantum dynamics in transverse-field Ising models from classical networks

“…⊗ |s N of a many-body Hilbert space, where the s l label the local basis, the coefficients of the wave function |ψ are expressed as ψ( s) = s|ψ = e H ( s) (1) where H ( s) is an effective Hamilton function defining the classical network. Wave functions of this form were used in combination with Monte Carlo algorithms for variational ground state searches [14][15][16] and time evolution [17][18][19][20][21][22][23]. Recently, it was suggested that the wave function (1) can generally be encoded in an artificial neural network (ANN) trained to resemble the desired state [23].…”

Eigenstate thermalization hypothesis in quantum dimer models

“…Our study of the 2D QDM combines a number of features that have proven to be of interest in other recent work on ETH [14][15][16][17][18]: First, it continues the progress of ETH studies from the familiar territory of 1D systems [19][20][21][22] into higher dimensions. Questions about ETH in systems in two or more dimensions, such as the transverse-field Ising model on the square lattice [14][15][16], are of great interest but challenging due to the rapid increase of the Hilbert-space dimension with system size.…”

“…Questions about ETH in systems in two or more dimensions, such as the transverse-field Ising model on the square lattice [14][15][16], are of great interest but challenging due to the rapid increase of the Hilbert-space dimension with system size. Second, the Hilbert space of the QDM is spanned by dimer configurations subject to strong local constraints.…”

Probing the Quench Dynamics of Antiferromagnetic Correlations in a 2D Quantum Ising Spin System

“…We achieve many-body states with longer-range antiferromagnetic correlations by implementing a near-adiabatic quench of the longitudinal field and study the buildup of correlations as we vary the rate with which we change the field. Lattice quantum spin models serve as a paradigm for exploring a range of many-body phenomena, including quantum phase transitions [1,2], equilibration and thermalization [3,4], and quench dynamics [5][6][7][8][9][10]. While there exists a variety of well-developed theoretical techniques to study the equilibrium properties of quantum spin systems [11][12][13][14][15][16][17], the toolkit for simulating real-time dynamics of these systems is rather limited and can only capture the evolution accurately for short times, especially for systems in more than one dimension [11,[18][19][20].…”