# Scaling behavior of the stationary states arising from dissipation at continuous quantum transitions

## TL;DR

This paper investigates the critical scaling behavior of steady states and nonequilibrium dynamics near quantum phase transitions under dissipation, using a Lindblad framework supported by numerical simulations of a 1D fermion system.

## Contribution

It introduces a general scaling framework for out-of-equilibrium and steady states near quantum critical points under dissipation, validated by numerical results.

## Key findings

- Derived universal scaling laws for dissipative quantum critical dynamics.
- Numerical validation using a 1D lattice fermion model with local dissipation.
- Identified the influence of dissipation on quantum phase transition behavior.

## Abstract

We study the critical behavior of the nonequilibrium dynamics and of the steady states emerging from the competition between coherent and dissipative dynamics close to quantum phase transitions. The latter is induced by the coupling of the system with a Markovian bath, such that the evolution of the system's density matrix can be effectively described by a Lindblad master equation. We devise general scaling behaviors for the out-of-equilibrium evolution and the stationary states emerging in the large-time limit for generic initial conditions, in terms of the parameters of the Hamiltonian providing the coherent driving and those associated with the dissipative interactions with the environment. Our framework is supported by numerical results for the dynamics of a one-dimensional lattice fermion gas undergoing a quantum Ising transition, in the presence of dissipative mechanisms which include local pumping and decay of particles.