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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 two-dimensional 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.
Highlights
We have studied the nonequilibrium dynamics of the transverse and the longitudinal magnetization resulting from quantum quenches with fully polarized initial states in the transverse-field Ising model defined on different lattice geometries
Depending on the geometry and the parameter regime under consideration, the quench dynamics has been found to display a variety of different behaviors ranging from quick equilibration, over slower monotonous relaxation, to persistent oscillations
We have demonstrated that numerical linked cluster expansions (NLCEs) comprising solely rectangular clusters provide a promising approach to study the dynamics of two-dimensional quantum many-body systems directly in the thermodynamic limit
Summary
Understanding the dynamics of isolated quantum many-body systems out of equilibrium is an active area of research of modern theoretical and experimental physics [1,2,3]. We scrutinize the nonequilibrium dynamics for quantum quenches in the Ising model with transverse magnetic field While this model is exactly solvable in the case of a chain and has been studied in numerous instances, our main focus is on nonintegrable geometries such as two- and three-leg ladders and, in particular, two-dimensional square lattices. Given the states |↑〉 and |→〉, we study the nonequilibrium dynamics resulting from quantum quenches to weak (g < gc), strong (g > gc), or critical values (g = gc) of the transverse field, i.e., depending on the initial state these are quenches either within the same equilibrium phase, or to or across the critical point.
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