A little bit of self-correction

TL;DR

This paper explores how stable, decoherence-free subspaces can emerge in the thermal dynamics of finite quantum spin chains at low temperatures, revealing new insights into quantum self-correction and metastability.

Contribution

It demonstrates the existence of effective decoherence-free subspaces arising from symmetry relations, independent of ground state entanglement, and discusses their stability and practical limitations.

Findings

Stable subspaces persist for exponential times in inverse temperature

Metastable subspaces are linked to symmetry in excited states

Practical realization is limited by symmetry-breaking perturbations

Abstract

We investigate the emergence of stable subspaces in the low-temperature quantum thermal dynamics of finite spin chains. Our analysis reveals the existence of effective decoherence-free qudit subspaces, persisting for timescales exponential in $\beta$. Surprisingly, the appearance of metastable subspaces is not directly related to the entanglement structure of the ground state(s). Rather, they arise from symmetry relations in low-lying excited states. Despite their stability within a 'phase', practical realization of stable qubits is hindered by susceptibility to symmetry-breaking perturbations. This work highlights that there can be non-trivial quantum behavior in the thermal dynamics of noncommuting many body models, and opens the door to more extensive studies of self-correction in such systems.