Geometry of quantum phase transitions
arXiv:1911.10196 · doi:10.1016/j.physrep.2019.11.002
Abstract
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.
94 pages, 15 figures, 399 references, To appear in: Physics Reports (2019). arXiv admin note: text overlap with arXiv:1305.4527, arXiv:quant-ph/0701061 by other authors
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- Comparing metrics for mixed quantum states: Sjoqvist and Bures
- Phase space formulation of the Abelian and non-Abelian quantum geometric tensor
- Generalization of Rayleigh's Criterion on Parameter Estimation with Incoherent Sources
- Greenberger-Horne-Zeilinger state generation in qubit-chains via a single -pulse
- Classical description of the parameter space geometry in the Dicke and Lipkin-Meshkov-Glick models
- The Quantum Geometric Tensor in a Parameter Dependent Curved Space
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