1
|
Carollo A, Spagnolo B, Valenti D. Uhlmann curvature in dissipative phase transitions. Sci Rep 2018; 8:9852. [PMID: 29959332 PMCID: PMC6026214 DOI: 10.1038/s41598-018-27362-9] [Citation(s) in RCA: 92] [Impact Index Per Article: 15.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/15/2018] [Accepted: 05/10/2018] [Indexed: 11/09/2022] Open
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.
Collapse
Affiliation(s)
- Angelo Carollo
- Department of Physics and Chemistry, Group of Interdisciplinary Theoretical Physics, University of Palermo, Viale delle Scienze, Ed. 18, I-90128, Palermo, Italy. .,Radiophysics Department, Lobachevsky State University of Nizhni Novgorod, 23 Gagarin Avenue, Nizhni, Novgorod, 603950, Russia.
| | - Bernardo Spagnolo
- Department of Physics and Chemistry, Group of Interdisciplinary Theoretical Physics, University of Palermo, Viale delle Scienze, Ed. 18, I-90128, Palermo, Italy.,Radiophysics Department, Lobachevsky State University of Nizhni Novgorod, 23 Gagarin Avenue, Nizhni, Novgorod, 603950, Russia.,Istituto Nazionale di Fisica Nucleare, Sezione di Catania, Via S. Sofia 64, I-90123, Catania, Italy
| | - Davide Valenti
- Department of Physics and Chemistry, Group of Interdisciplinary Theoretical Physics, University of Palermo, Viale delle Scienze, Ed. 18, I-90128, Palermo, Italy.,Istituto di Biomedicina ed Immunologia Molecolare (IBIM) "Alberto Monroy", CNR, Via Ugo La Malfa 153, I-90146, Palermo, Italy
| |
Collapse
|
2
|
Mera B, Vlachou C, Paunković N, Vieira VR. Uhlmann Connection in Fermionic Systems Undergoing Phase Transitions. PHYSICAL REVIEW LETTERS 2017; 119:015702. [PMID: 28731730 DOI: 10.1103/physrevlett.119.015702] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/23/2017] [Indexed: 05/05/2023]
Abstract
We study the behavior of the Uhlmann connection in systems of fermions undergoing phase transitions. In particular, we analyze some of the paradigmatic cases of topological insulators and superconductors in one dimension, as well as the BCS theory of superconductivity in three dimensions. We show that the Uhlmann connection signals phase transitions in which the eigenbasis of the state of the system changes. Moreover, using the established fidelity approach and the study of the edge states, we show the absence of thermally driven phase transitions in the case of topological insulators and superconductors. We clarify what is the relevant parameter space associated with the Uhlmann connection so that it signals the existence of order in mixed states. In addition, the study of Majorana modes at finite temperature opens the possibility of applications in realistic stable quantum memories. Finally, the analysis of the different behavior of the BCS model and the Kitaev chain, with respect to the Uhlmann connection, suggested that in realistic scenarios the gap of topological superconductors could also, generically, be temperature dependent.
Collapse
Affiliation(s)
- Bruno Mera
- CeFEMA, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1049-001 Lisboa, Portugal
- Departamento de Física, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1049-001 Lisboa, Portugal
- Instituto de Telecomunicações, 1049-001 Lisbon, Portugal
| | - Chrysoula Vlachou
- Instituto de Telecomunicações, 1049-001 Lisbon, Portugal
- Departamento de Matemática, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1049-001 Lisboa, Portugal
| | - Nikola Paunković
- Instituto de Telecomunicações, 1049-001 Lisbon, Portugal
- Departamento de Matemática, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1049-001 Lisboa, Portugal
| | - Vítor R Vieira
- CeFEMA, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1049-001 Lisboa, Portugal
- Departamento de Física, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1049-001 Lisboa, Portugal
| |
Collapse
|
3
|
Paunković N, Rocha Vieira V. Macroscopic distinguishability between quantum states defining different phases of matter: fidelity and the Uhlmann geometric phase. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 77:011129. [PMID: 18351840 DOI: 10.1103/physreve.77.011129] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/31/2007] [Indexed: 05/26/2023]
Abstract
We study the fidelity approach to quantum phase transitions (QPTs) and apply it to general thermal phase transitions (PTs). We analyze two particular cases: The Stoner-Hubbard itinerant electron model of magnetism and the BCS theory of superconductivity. In both cases we show that the sudden drop of the mixed state fidelity marks the line of the phase transition. We conduct a detailed analysis of the general case of systems given by mutually commuting Hamiltonians, where the nonanalyticity of the fidelity is directly related to the nonanalyticity of the relevant response functions (susceptibility and heat capacity), for the case of symmetry-breaking transitions. Further, on the case of BCS theory of superconductivity, given by mutually noncommuting Hamiltonians, we analyze the structure of the system's eigenvectors in the vicinity of the line of the phase transition showing that their sudden change is quantified by the emergence of a generically nontrivial Uhlmann mixed state geometric phase.
Collapse
Affiliation(s)
- Nikola Paunković
- SQIG-Instituto de Telecomunicações, IST, Lisbon, P-1049-001 Lisbon, Portugal
| | | |
Collapse
|