Uhlmann curvature in dissipative phase transitions

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.

Geometry of quantum evolution in a nonequilibrium environment

“…Combining Eqs. (24) with (26), it indicates that the frequency shift s(t) induced by the environmental nonequilibrium feature also has a significant impact on the correction to the effective geometric phase.…”

Uhlmann number in translational invariant systems

“…The recent success of the Uhlmann approach [27] in describing the topology of 1D Fermionic systems [18,19], remains in higher dimensions [20] not as straightforward [21]. Moreover, the importance of this approach and its relevance to directly observable physical quantities, still remains an interesting open question.In this letter, we propose to study 2D topological Fermionic systems, at finite temperature, by means of a new set of geometrical tools derived from the Uhlmann approach [27], the mean Uhlmann curvature (MUC) [28,29] . We study 2D-topological insulators (TIs) and 2Dtopological superconductors (TSCs), whose topological features are captured by the Chern number [15].…”

“…The mean Uhlmann curvature [28], defined as the Uhlmann phase per unit area for an infinitesimal loop, is given by…”

On quantumness in multi-parameter quantum estimation

“…(7) is known as compatibility condition [63]. In the context of quantum information geometry, and quantum holonomies of mixed states, U µν is known as mean Uhlmann curvature (MUC) [41,53,54,[64][65][66]. From a metrological point of view, U µν marks the incompatibility between λ µ and λ ν , where such an incompatibility arises from the inherent quantum nature of the underlying physical system.…”