Quantum Phase Transition Like Phenomenon in a Two-Qubit Yang-Baxter System

Wang, Gangcheng; Xue, Ke; Sun, Chunfang; Hu, Taotao; Zhou, Chengcheng; Du, Guijiao

doi:10.1007/s10773-010-0435-x

“…The idea that QPTs could be explored through the Berry phase properties was first proposed and applied in the prototypical XY spin-1/2 chain [31,32,37,39,40,57,65,76] and extended to many other many-body systems, such as the Dicke model [38,44], the Lipkin-Meshkov-Glick model [43,60,72], Yang-Baxter spin-1/2 model [49,58], quasi free-Fermion systems [47,53,56,85,102], interacting Fermion models [51,63,68,77,79,98,116], in ultracold atoms [73,74,91], in spin chains with long range interactions [70,81], in cluster models [106], in the spin-boson model [114], in the 1D compassmodel [59,96], and in connection to spin-crossover phenomena [55]. The critical properties of the geometric phase has also been studied in few-body systems interacting with critical chains [66,67,78,87,92,97,100], in non-Hermitian critical systems [...…”

Section: Introductionmentioning

confidence: 99%

Geometry of quantum phase transitions

Carollo

¹

,

Valenti

²

,

Spagnolo

³

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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“…The idea that QPTs could be explored through the Berry phase properties was first proposed and applied in the prototypical XY spin-1/2 chain [31,32,37,39,40,57,65,76] and extended to many other many-body systems, such as the Dicke model [38,44], the Lipkin-Meshkov-Glick model [43,60,72], Yang-Baxter spin-1/2 model [49,58], quasi free-Fermion systems [47,53,56,85,102], interacting Fermion models [51,63,68,77,79,98,116], in ultracold atoms [73,74,91], in spin chains with long range interactions [70,81], in cluster models [106], in the spin-boson model [114], in the 1D compassmodel [59,96], and in connection to spin-crossover phenomena [55]. The critical properties of the geometric phase has also been studied in few-body systems interacting with critical chains [66,67,78,87,92,97,100], in non-Hermitian critical systems [8...…”

Section: Introductionmentioning

confidence: 99%

Dissipation, Quantum Phase Transitions, and Measurement

Chakravarty¹

2010

Understanding Quantum Phase Transitions

0

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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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