Real-time dynamics of open quantum spin systems driven by dissipative processes

TL;DR

This paper investigates the real-time evolution of large open quantum spin systems driven solely by dissipative processes, revealing how different dissipative symmetries influence the approach to equilibrium and the role of conserved quantities.

Contribution

It introduces an efficient cluster algorithm to solve the Kossakowski-Lindblad equation for 2D quantum spin systems under dissipation, highlighting the impact of symmetry on equilibration times.

Findings

Symmetry of dissipation determines the timescales for reaching equilibrium.

Conservation of magnetization Fourier modes leads to slow, diffusion-like dynamics.

Dissipative processes can induce phase transitions from ordered to disordered states.

Abstract

We study the real-time evolution of large open quantum spin systems in two spatial dimensions, whose dynamics is entirely driven by a dissipative coupling to the environment. We consider different dissipative processes and investigate the real-time evolution from an ordered phase of the Heisenberg or XY-model towards a disordered phase at late times, disregarding unitary Hamiltonian dynamics. The corresponding Kossakowski-Lindblad equation is solved via an efficient cluster algorithm. We find that the symmetry of the dissipative process determines the time scales which govern the approach towards a new equilibrium phase at late times. Most notably, we find a slow equilibration if the dissipative process conserves any of the magnetization Fourier modes. In these cases, the dynamics can be interpreted as a diffusion process of the conserved quantity.