Quantum Criticality in Open Quantum Spin Chains with Nonreciprocity

TL;DR

This paper explores how nonreciprocity affects quantum critical behavior in open spin chains, revealing a universal scaling regime unaffected by the Liouvillian skin effect and identifying conditions where edge effects dominate.

Contribution

It demonstrates the existence of a universal critical scaling regime in nonreciprocal open quantum spin chains, unaffected by the Liouvillian skin effect, using tensor network methods.

Findings

Universal scaling collapse observed regardless of reciprocity

Critical exponents differ from free fermions

Liouvillian skin effect relevant only when healing length exceeds system size

Abstract

We investigate the impact of nonreciprocity on universality and critical phenomena in open quantum interacting many-body systems. Nonreciprocal open quantum systems often have an exotic spectral sensitivity to boundary conditions, known as the Liouvillian skin effect (LSE). By considering an open quantum XXZ spin chain that exhibits LSE, we demonstrate the existence of a universal scaling regime that is not affected by the presence of the LSE. We resolve the critical exponents, which differ from those of free fermions, via tensor network methods and demonstrate that observables exhibit a universal scaling collapse, irrespective of the reciprocity. We find that the LSE only becomes relevant when a healing length scale $\xi_{\rm heal}$ at the system's edge (which is different to the localization length of the eigenstate of the Liouvillian) exceeds the system size, allowing edge properties to dominate the physics. We expect this result to be a generic feature of nonreciprocal models in the vicinity of a critical point. The driven-dissipative quantum criticality we observe has no classical analogue and stems from the existence of multiple dark states.