Uhlmann curvature in dissipative phase transitions

Angelo Carollo,Davide Valenti,Bernardo Spagnolo

doi:10.1038/s41598-018-27362-9

Abstract

A novel approach based on the Uhlmann curvature is introduced for the investigation of non-equilibrium steady-state quantum phase transitions (NESS-QPTs). Equilibrium phase transitions fall invariably into two markedly non-overlapping categories: classical phase transitions and quantum phase transitions. NESS-QPTs offer a unique arena where such a distinction fades off. We propose a method to reveal and quantitatively assess the quantum character of such critical phenomena. We apply this tool to a paradigmatic class of lattice fermion systems with local reservoirs, characterised by Gaussian non-equilibrium steady states. The relations between the behaviour of the Uhlmann curvature, the divergence of the correlation length, the character of the criticality and the dissipative gap are demonstrated. We argue that this tool can shade light upon the nature of non equilibrium steady state criticality in particular with regard to the role played by quantum vs classical fluctuations.

Highlights

A novel approach based on the Uhlmann curvature is introduced for the investigation of non-equilibrium steady-state quantum phase transitions (NESS-QPTs)
We propose the use of the geometric phase (GP)11,12, and in particular its mixed state generalisation, the Uhlmann GP13, to investigate non-equilibrium steady states (NESSs)-QPT
We have introduced an entirely novel approach to quantitatively assess the “quantum-ness” of critical phenomena

Summary

Introduction

A novel approach based on the Uhlmann curvature is introduced for the investigation of non-equilibrium steady-state quantum phase transitions (NESS-QPTs). The relations between the behaviour of the Uhlmann curvature, the divergence of the correlation length, the character of the criticality and the dissipative gap are demonstrated We argue that this tool can shade light upon the nature of non equilibrium steady state criticality in particular with regard to the role played by quantum vs classical fluctuations. A comprehensive picture and characterisation of dissipative NESS-QPTs is lacking, partly due to their nature lying in a blurred domain, where features typical of zero temperature QPTs coexists with properties typical of thermal phase transitions Such a coexistence between quantum and classical fluctuations are to some extent reminiscent of quantum to classical crossovers in equilibrium QPTs, with a major striking difference: the remarkably sharp character of a truly critical phenomenon. The MUC, defined as the Uhlmann GP per unit area of a density matrix evolving along an infinitesimal loop, has a fundamental interpretation in multiparameter quantum metrology: it www.nature.com/scientificreports/

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