Quantum critical behaviors and decoherence of weakly coupled quantum Ising models within an isolated global system

TL;DR

This paper investigates how quantum critical correlations and decoherence in a subsystem of weakly coupled quantum Ising chains depend on the state of the environment, revealing different scaling behaviors under various environmental correlation regimes.

Contribution

It introduces a detailed analysis of quantum criticality and decoherence in a composite quantum Ising system, highlighting the influence of the environment's correlation structure on subsystem dynamics.

Findings

Decoherence susceptibility exhibits different power-law divergences depending on environmental correlations.

Quantum critical behavior in the subsystem depends on whether the environment has short-range, algebraic, or long-range correlations.

Scaling behaviors of quantum correlations are sensitive to the environment's quantum state.

Abstract

We discuss the quantum dynamics of an isolated composite system consisting of weakly interacting many-body subsystems. We focus on one of the subsystems, S, and study the dependence of its quantum correlations and decoherence rate on the state of the weakly-coupled complementary part E, which represents the environment. As a theoretical laboratory, we consider a composite system made of two stacked quantum Ising chains, locally and homogeneously weakly coupled. One of the chains is identified with the subsystem S under scrutiny, and the other one with the environment E. We investigate the behavior of S at equilibrium, when the global system is in its ground state, and under out-of-equilibrium conditions, when the global system evolves unitarily after a soft quench of the coupling between S and E. When S develops quantum critical correlations in the weak-coupling regime, the associated scaling behavior crucially depends on the quantum state of E whether it is characterized by short-range correlations (analogous to those characterizing disordered phases in closed systems), algebraically decaying correlations (typical of critical systems), or long-range correlations (typical of magnetized ordered phases). In particular, different scaling behaviors, depending on the state of E, are observed for the decoherence of the subsystem S, as demonstrated by the different power-law divergences of the decoherence susceptibility that quantifies the sensitivity of the coherence to the interaction with E.