Quantum quench dynamics in the transverse-field Ising model: A numerical expansion in linked rectangular clusters

Abstract

We study quantum quenches in the transverse-field Ising model defined on different lattice geometries such as chains, two-and three-leg ladders, and twodimensional square lattices. Starting from fully polarized initial states, we consider the dynamics of the transverse and the longitudinal magnetization for quenches to weak, strong, and critical values of the transverse field. To this end, we rely on an efficient combination of numerical linked cluster expansions (NLCEs) and a forward propagation of pure states in real time. As a main result, we demonstrate that NLCEs comprising solely rectangular clusters provide a promising approach to study the real-time dynamics of two-dimensional quantum many-body systems directly in the thermodynamic limit. By comparing to existing data from the literature, we unveil that NLCEs yield converged results on time scales which are competitive to other state-of-the-art numerical methods.

Emergence of Hilbert Space Fragmentation in Ising Models with a Weak Transverse Field

“…It is particularly important for foundation of quantum statistical mechanics to elucidate dynamical properties of the model. Indeed, its quantum thermalization has recently been investigated in relatively large systems [14][15][16][17][18]. For example, ergodicity in the ordered phase is controversial in the twodimensional TFIM [14,15,19].…”

Numerical linked cluster expansions for inhomogeneous systems

“…Although Ref. [75] shares this feature with the present paper, it has a different focus. Our work focuses on inhomogeneity; while it uses a rectangle expansion, it relies on a basic cluster solver and does not study the expansion's particular features in depth.…”

“…After this paper was submitted, Ref. [75] presented NLCE calculations for dynamics with a rectangle expansion. Although Ref.…”

“…Ref. [75] focuses more on the rectangle expansion, combines it with a more advanced cluster solver, and presents extensive comparisons to other state-of-the-art numerical methods.…”

Variational classical networks for dynamics in interacting quantum matter

“…On the other hand, the description of quantum dynamics in higher dimensions is facing severe limitations. In spite of a few very recent efforts in two dimensions (2D) using tensor net-works [32][33][34][35][36][37][38][39][40][41] , artificial neural networks 30,42,43 , or numerical linked cluster expansion 44 , solving the quantum dynamics of 2D (and higher-dimensional) interacting systems remains one of the central challenges in computational quantum physics.…”