Simulating Lindbladian evolution with non-abelian symmetries: Ballistic front propagation in the $SU(2)$ Hubbard model with a localized loss

TL;DR

This paper introduces a non-Abelian TEBD method to simulate Lindbladian dynamics in open quantum systems, demonstrating ballistic front propagation and quantum Zeno effects in an $SU(2)$ Hubbard model with localized loss.

Contribution

The paper develops a novel non-Abelian TEBD approach for Lindbladian systems, enabling the study of symmetries and open system dynamics with new insights into front propagation and quantum Zeno effects.

Findings

Ballistic front propagation with renormalized velocity observed.

Suppression of particle current at high loss rates due to quantum Zeno effect.

Operator entanglement propagates faster than particle depletion.

Abstract

We develop a non-Abelian time evolving block decimation (NA-TEBD) approach to study of open systems governed by Lindbladian time evolution, while exploiting an arbitrary number of abelian or non-abelian symmetries. We illustrate this method in a one-dimensional fermionic $SU(2)$ Hubbard model on a semi-infinite lattice with localized particle loss at one end. We observe a ballistic front propagation with strongly renormalized front velocity, and a hydrodynamic current density profile. For large loss rates, a suppression of the particle current is observed, as a result of the quantum Zeno effect. Operator entanglement is found to propagate faster than the depletion profile, preceding the latter.