Uhlmann number in translational invariant systems

Leonforte, Luca; Valenti, Davide; Spagnolo, Bernardo; Carollo, Angelo

doi:10.1038/s41598-019-45546-9

Cited by 22 publications

(28 citation statements)

References 52 publications

(79 reference statements)

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“…Finally, one of the relevant features of these geometrical approaches is the potential experimental accessibility of many of their related quantities. Fidelity susceptibility [166,231,232], Fisher information [127,159], geometric phases [186][187][188] and geometric curvature [118,119,233] can be probed through experimentally viable procedures.…”

Section: Introductionmentioning

confidence: 99%

Geometry of quantum phase transitions

2020

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In this article we provide a review of geometrical methods employed in the analysis of quantum phase transitions and non-equilibrium dissipative phase transitions. After a pedagogical introduction to geometric phases and geometric information in the characterisation of quantum phase transitions, we describe recent developments of geometrical approaches based on mixed-state generalisation of the Berry-phase, i.e. the Uhlmann geometric phase, 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, whereas in NESS-QPTs this distinction may fade off. The approach described in this review, among other things, can quantitatively assess the quantum character of such critical phenomena. This framework is applied 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 geometric phase curvature, the divergence of the correlation length, the character of the criticality and the gap-either Hamiltonian or dissipative-are reviewed.

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Section: Introductionmentioning

confidence: 99%

Geometry of quantum phase transitions

2020

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“…(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.…”

Section: Introductionmentioning

confidence: 99%

On quantumness in multi-parameter quantum estimation

et al. 2019

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In this article we derive a measure of quantumness in quantum multiparameter estimation problems. We can show that the ratio between the mean Uhlmann Curvature and the Fisher Information provides a figure of merit which estimates the amount of incompatibility arising from the quantum nature of the underlying physical system. This ratio accounts for the discrepancy between the attainable precision in the simultaneous estimation of multiple parameters and the precision predicted by the Cramér-Rao bound. As a testbed for this concept, we consider a quantum many-body system in thermal equilibrium, and explore the quantum compatibility of the model across its phase diagram.

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“…Hence, it provides a way to probe criticalities in a physically appealing way. Moreover, such a non-local character can also be useful to probe critical phenomena such as topological phase transitions [15], which are undetectable by local order parameters [16,17].…”

Section: Phase Transition In Dissipative Quantum Many Body Systemsmentioning

confidence: 99%

Non-Equilibrium Phenomena in Quantum Systems, Criticality and Metastability

Carollo

Spagnolo

Valenti

2019

11th Italian Quantum Information Science Conference (IQIS2018)

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We summarise here some relevant results related to non-equilibrium quantum systems. We characterise quantum phase transitions (QPT) in out-of-equilibrium quantum systems through a novel approach based on geometrical and topological properties of mixed quantum systems. We briefly describe results related to non-perturbative studies of the bistable dynamics of a quantum particle coupled to an environment. Finally, we shortly summarise recent studies on the generation of solitons in current-biased long Josephson junctions.

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Uhlmann number in translational invariant systems

Cited by 22 publications

References 52 publications

Geometry of quantum phase transitions

Geometry of quantum phase transitions

On quantumness in multi-parameter quantum estimation

Non-Equilibrium Phenomena in Quantum Systems, Criticality and Metastability

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