Geometrical properties of the ground state manifold in the spin boson model

Henriet, Loïc

doi:10.1103/physrevb.97.195138

Cited by 2 publications

(3 citation statements)

References 32 publications

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“…[13] In this line of work, it would be also interesting to analyze, from the point of view of the parameter space in the classical setting, the effect of a quantum dissipative environment on a fermionic system. [55] Furthermore, in the context of many-body systems, the quantum metric tensor can be related to the mean-square fluctuation of the macroscopic bulk polarization in insulators. [56] In this line of work, it would be interesting to extend our classical metric to many-body fermionic systems using Grassmann variables and see whether it can predict similar results to those of the quantum case.…”

Section: Discussionmentioning

confidence: 99%

“…In this sense, it will be very interesting to apply our approach to other more realistic systems such as those of condensed matter physics where the Berry curvature and the quantum metric tensor play an important role, in particular, toward understanding the existence of tensor monopoles in the parameter space [13]. In this line of work, it would be also interesting to analyze, from the point of view of the parameter space in the classical setting, the effect of a quantum dissipative environment on a fermionic system [55]. Furthermore, in the context of many-body systems, the quantum metric tensor can be related to the mean-square fluctuation of the macroscopic bulk polarization in insulators [56].…”

Section: Discussionmentioning

confidence: 99%

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Geometry of the Parameter Space of a Quantum System: Classical Point of View

Alvarez‐Jimenez¹,

González²,

Gutiérrez‐Ruiz³

et al. 2019

Annalen der Physik

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The local geometry of the parameter space of a quantum system is described by the quantum metric tensor and the Berry curvature, which are two fundamental objects that play a crucial role in understanding geometrical aspects of condensed matter physics. Classical integrable systems are considered and a new approach is reported to obtain the classical analogs of the quantum metric tensor and the Berry curvature. An advantage of this approach is that it can be applied to a wide variety of classical systems corresponding to quantum systems with bosonic and fermionic degrees of freedom. The approach used arises from the semiclassical approximation of the Berry curvature and the quantum metric tensor in the Lagrangian formalism. This semiclassical approximation is exploited to establish, for the first time, the relation between the quantum metric tensor and its classical counterpart. The approach described is illustrated and validated by applying it to five systems: the generalized harmonic oscillator, the symmetric and linearly coupled harmonic oscillators, the singular Euclidean oscillator, and a spin‐half particle in a magnetic field. Finally, some potential applications of this approach and possible generalizations that can be of interest in the field of condensed matter physics are mentioned.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Geometry of the Parameter Space of a Quantum System: Classical Point of View

Alvarez‐Jimenez¹,

González²,

Gutiérrez‐Ruiz³

et al. 2019

Annalen der Physik

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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 [...…”

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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Geometrical properties of the ground state manifold in the spin boson model

Cited by 2 publications

References 32 publications

Geometry of the Parameter Space of a Quantum System: Classical Point of View

Geometry of the Parameter Space of a Quantum System: Classical Point of View

Geometry of quantum phase transitions

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