Geometry of quantum phase transitions

Davide Valenti, Angelo Carollo, Bernardo Spagnolo, Angelo Carollo, Bernardo Spagnolo

Research output: Contribution to journalArticlepeer-review

16 Citations (Scopus)


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.
Original languageEnglish
Pages (from-to)1-72
Number of pages72
JournalPhysics Reports
Publication statusPublished - 2020

All Science Journal Classification (ASJC) codes

  • General Physics and Astronomy


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