A simple tensor network algorithm for two-dimensional steady states

Augustine Kshetrimayum,Hendrik Weimer,Román Orús

doi:10.1038/s41467-017-01511-6

Augustine Kshetrimayum, Hendrik Weimer + Show 1 more

Open Access

https://doi.org/10.1038/s41467-017-01511-6

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Abstract

Understanding dissipation in 2D quantum many-body systems is an open challenge which has proven remarkably difficult. Here we show how numerical simulations for this problem are possible by means of a tensor network algorithm that approximates steady states of 2D quantum lattice dissipative systems in the thermodynamic limit. Our method is based on the intuition that strong dissipation kills quantum entanglement before it gets too large to handle. We test its validity by simulating a dissipative quantum Ising model, relevant for dissipative systems of interacting Rydberg atoms, and benchmark our simulations with a variational algorithm based on product and correlated states. Our results support the existence of a first order transition in this model, with no bistable region. We also simulate a dissipative spin 1/2 XYZ model, showing that there is no re-entrance of the ferromagnetic phase. Our method enables the computation of steady states in 2D quantum lattice systems.

Highlights

Understanding dissipation in 2D quantum many-body systems is an open challenge which has proven remarkably difficult
In this paper we present a method to approximate such steady states for 2D quantum lattice systems of infinite size
The method that we propose here is based on tensor networks (TN)[14,15,16,17,18] and is, simple and efficient

Summary

Introduction

Understanding dissipation in 2D quantum many-body systems is an open challenge which has proven remarkably difficult. We show how numerical simulations for this problem are possible by means of a tensor network algorithm that approximates steady states of 2D quantum lattice dissipative systems in the thermodynamic limit. This process is important in several contexts, e.g., understanding the decoherence of complex wavefunctions[1], quantum thermodynamics[2], engineering of topological order through dissipation[3], and driven-dissipative universal quantum computation[4]. We simulate a dissipative spin 1/2 XYZ model, showing that there is no re-entrance of the ferromegnatic phase, compatible with recent cluster mean-field results[10]. Let us consider the special but quite common case in which the Liouvillian L can be decomposed as a sum of local operators. form L1⁄2ρ

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