Determination of the Nonequilibrium Steady State Emerging from a Defect

TL;DR

This paper investigates the non-equilibrium dynamics of a quantum system with a localized defect, identifying conditions for light-cone spreading and deriving a method to determine the resulting nonequilibrium steady state.

Contribution

It introduces a general procedure to obtain the (quasi-)stationary state after a local defect causes non-equilibrium evolution, demonstrated through an exact solution of the transverse-field Ising chain.

Findings

Light-cone spreads from the defect, creating regions with different properties.

The late-time state can be characterized using the proposed method.

Exact solution confirms the effectiveness of the approach.

Abstract

We consider the non-equilibrium time evolution of a translationally invariant state under a Hamiltonian with a localized defect. We discern the situations where a light-cone spreads out from the defect and separates the system into regions with macroscopically different properties. We identify the light-cone and propose a procedure to obtain a (quasi-)stationary state describing the late time dynamics of local observables. As an explicit example, we study the time evolution generated by the Hamiltonian of the transverse-field Ising chain with a local defect that cuts the interaction between two sites (a quench of the boundary conditions alongside a global quench). We solve the dynamics exactly and show that the late time properties can be obtained with the general method proposed.