Scaling behavior of quantum critical relaxation dynamics in a heat bath

TL;DR

This paper investigates the universal scaling behavior of quantum relaxation dynamics near critical points, emphasizing the role of dissipation and confirming findings through the 1D transverse-field Ising model.

Contribution

It reveals how dissipation influences the universal scaling in quantum critical relaxation, extending understanding beyond purely Hamiltonian dynamics.

Findings

Universal scaling appears in both equilibrium and non-equilibrium stages.

Dissipation accelerates decay of high-energy levels, revealing low-lying mode behavior.

Dissipation rate introduces a new time scale affecting the scaling behavior.

Abstract

We study the scaling behavior of the relaxation dynamics to thermal equilibrium when a quantum system is near the quantum critical point. In particular, we investigate systems whose relaxation dynamics is described by a Lindblad master equation. We find that the universal scaling behavior not only exhibits in the equilibrium stage at the long-time limit, but also manifests itself in the non-equilibrium relaxation process. While the critical behavior is dictated by the low-lying energy levels of the Hamiltonian, the dissipative part in the Lindblad equation also plays important roles in two aspects: First, the dissipative part makes the high energy levels decay fast after which the universal behavior controlled by the low-lying modes emerges. Second, the dissipation rate gives rise to a time scale that affects the scaling behavior. We confirm our theory by solving the Lindblad equation for the one-dimensional transverse-field Ising model.