Dynamics of two-dimensional open quantum lattice models with tensor networks

TL;DR

This paper introduces a tensor network method using iPEPO for simulating the dynamics and steady-states of large two-dimensional open quantum lattice models, effectively capturing entanglement in dissipative systems.

Contribution

The authors develop a novel iPEPO-based tensor network approach optimized for open quantum systems in the thermodynamic limit, surpassing existing techniques in accuracy and applicability.

Findings

Successfully simulates dissipative quantum Ising and boson models

Accurately captures entanglement in dissipative regimes

Demonstrates method's effectiveness against exact calculations

Abstract

Being able to describe accurately the dynamics and steady-states of driven and/or dissipative but quantum correlated lattice models is of fundamental importance in many areas of science: from quantum information to biology. An efficient numerical simulation of large open systems in two spatial dimensions is a challenge. In this work, we develop a tensor network method, based on an infinite Projected Entangled Pair Operator (iPEPO) ansatz, applicable directly in the thermodynamic limit. We incorporate techniques of finding optimal truncations of enlarged network bonds by optimising an objective function appropriate for open systems. Comparisons with numerically exact calculations, both for the dynamics and the steady-state, demonstrate the power of the method. In particular, we consider dissipative transverse quantum Ising and driven-dissipative hard core boson models in non-mean field limits, proving able to capture substantial entanglement in the presence of dissipation. Our method enables to study regimes which are accessible to current experiments but lie well beyond the applicability of existing techniques.