Identifying the order of a quantum phase transition by means of Wehrl entropy in phase space

Castaños, Octavio; Calixto, M.; Pérez‐Bernal, F.; Romera, E.

doi:10.1103/physreve.92.052106

Cited by 21 publications

(36 citation statements)

References 74 publications

(129 reference statements)

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“…Even considering moderate values of space dimension, the approach provides solutions reflecting the main salient features of the system, a situation very useful when the solution cannot be obtained by conventional methods. Hence, this approach may be useful in catastrophe theory where a small change in the original stable potential changes the topology of the problem [57], as well as in the study of quantum phase transitions [58], but also provides new ways to obtain Franck-Condon factors between different potentials since in our approach a common basis of harmonic oscillators are used [59].…”

Section: Discussionmentioning

confidence: 99%

Algebraic DVR Approaches Applied to Describe the Stark Effect

et al. 2020

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Two algebraic approaches based on a discrete variable representation are introduced and applied to describe the Stark effect in the non-relativistic Hydrogen atom. One approach consists of considering an algebraic representation of a cutoff 3D harmonic oscillator where the matrix representation of the operators r2 and p2 are diagonalized to define useful bases to obtain the matrix representation of the Hamiltonian in a simple form in terms of diagonal matrices. The second approach is based on the U(4) dynamical algebra which consists of the addition of a scalar boson to the 3D harmonic oscillator space keeping constant the total number of bosons. This allows the kets associated with the different subgroup chains to be linked to energy, coordinate and momentum representations, whose involved branching rules define the discrete variable representation. Both methods, although originating from the harmonic oscillator basis, provide different convergence tests due to the fact that the associated discrete bases turn out to be different. These approaches provide powerful tools to obtain the matrix representation of 3D general Hamiltonians in a simple form. In particular, the Hydrogen atom interacting with a static electric field is described. To accomplish this task, the diagonalization of the exact matrix representation of the Hamiltonian is carried out. Particular attention is paid to the subspaces associated with the quantum numbers n=2,3 with m=0.

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Section: Discussionmentioning

confidence: 99%

Algebraic DVR Approaches Applied to Describe the Stark Effect

et al. 2020

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“…[19]. It has also been applied in different contexts, like entanglement theory [42], uncertainty relations [43], and quantum phase transitions [44], just to name a few. In the context of thermodynamics, our interest here, a theory of entropy production for spin systems was put forth in Ref.…”

Section: Entropic Dynamics In Quantum Phase Spacementioning

confidence: 99%

Wehrl entropy production rate across a dynamical quantum phase transition

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Landi

Solano

et al. 2020

Phys. Rev. Research

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The quench dynamics of many-body quantum systems may exhibit nonanalyticities in the Loschmidt echo, a phenomenon known as dynamical phase transition (DPT). Despite considerable research into the underlying mechanisms behind this phenomenon, several open questions still remain. Motivated by this, we put forth a detailed study of DPTs from the perspective of quantum phase space and entropy production, a key concept in thermodynamics. We focus on the Lipkin-Meshkov-Glick model and use spin-coherent states to construct the corresponding Husimi-Q quasiprobability distribution. The entropy of the Q function, known as Wehrl entropy, provides a measure of the coarse-grained dynamics of the system and, therefore, evolves nontrivially even for closed systems. We show that critical quenches lead to a quasimonotonic growth of the Wehrl entropy in time, combined with small oscillations. The former reflects the information scrambling characteristic of these transitions and serves as a measure of entropy production. On the other hand, the small oscillations imply negative entropy production rates and therefore signal the recurrences of the Loschmidt echo. Finally, we also study a Gaussification of the model based on a modified Holstein-Primakoff approximation. This allows us to identify the relative contribution of the low-energy sector to the emergence of DPTs. The results presented in this article are relevant not only from the dynamical quantum phase transition perspective but also for the field of quantum thermodynamics, since they point out that the Wehrl entropy can be used as a viable measure of entropy production.

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“…[ 34,36 ] In fact, delocalization and entanglement in phase space turns out to also be a common feature of QPTs. [ 32 ] In fact, in the next section, we analyze the phase‐space structure of normal and superradiant phases of two paradigmatic spin‐boson systems (Rabi‐Dicke and Jaynes‐Cummings), comparing them with band and topological insulator phases of phosphorene and silicene, respectively.…”

Section: Information‐theoretic Analysis and Bi‐ti Topological Transitionmentioning

confidence: 99%

“…Actually, localization, entropy, and entanglement measures of Hamiltonian eigenstates have proven to be good markers of the QPT for the Dike model of matter‐radiation interaction, [ 17–20 ] vibron model of molecules, [ 21–23 ] the ubiquitous Lipkin‐Meshkov‐Glick, [ 24–27 ] Bose‐Einstein condensates, [ 28 ] bilayer quantum Hall effect, [ 29–31 ] etc. As shown in, [ 32 ] these entropic measures are even capable of identifying the order of the corresponding QPT. Inverse participation ratio and several kinds of entropies have also turned out to be useful to visualize the TI‐BI transition in phosphorene [ 33 ] and silicene, [ 34–37 ] where entropy‐based Chern‐like numbers distinguishing TI and BI phases have been defined.…”

Section: Introductionmentioning

confidence: 99%

Analogies between the topological insulator phase of 2D Dirac materials and the superradiant phase of atom‐field systems

Calixto

Romera

Castaños

2020

Int J of Quantum Chemistry

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A semiclassical phase‐space perspective of band‐ and topological‐insulator regimes of 2D Dirac materials and normal‐ and superradiant phases of atom‐field interacting models is given in terms of delocalization, entropies, and quantum correlation measures. From this point of view, the low‐energy limit of tight‐binding models describing the electronic band structure of topological 2D Dirac materials such as phosphorene and silicene with tunable band gaps share similarities with Rabi‐Dicke and Jaynes‐Cummings atom‐field interaction models, respectively. In particular, the edge state of the 2D Dirac materials in the topological insulator phase exhibits a Schrödinger's cat structure similar to the ground state of two‐level atoms in a cavity interacting with a one‐mode radiation field in the superradiant phase. Delocalization seems to be a common feature of topological insulator and superradiant phases.

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Identifying the order of a quantum phase transition by means of Wehrl entropy in phase space

Cited by 21 publications

References 74 publications

Algebraic DVR Approaches Applied to Describe the Stark Effect

Algebraic DVR Approaches Applied to Describe the Stark Effect

Wehrl entropy production rate across a dynamical quantum phase transition

Analogies between the topological insulator phase of 2D Dirac materials and the superradiant phase of atom‐field systems

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