Coherent states for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" display="inline" overflow="scroll"><mml:mi>N</mml:mi></mml:math>-component fractional quantum Hall systems and their nonlinear sigma models

Calixto, M.; Peón-Nieto, Carlos; Pérez-Romero, E.

doi:10.1016/j.aop.2016.06.025

Cited by 6 publications

(16 citation statements)

References 58 publications

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“…The Hamiltonian that we shall eventually use is of the sigma model type (QH ferromagnet), written in terms of collective U (4) isospin operators (see [27] for the Ncomponent case). Let us see how to obtain it from H C .…”

Section: Model Hamiltonian and Semiclassical Analysismentioning

confidence: 99%

“…In the spin phase (ϑ + = 0 = θ b ) we have maximum spin S 2 = λ 2 [remember the identity (22)] and minimum ppin P 2 = 0, whereas in the ppin phase (ϑ + = −π/2 = θ b ) we have minimum spin S 2 = 0 and maximum ppin P 2 = λ 2 . In the canted phase, when inserting (25) into (27), we realize that both spin and ppin do not attain the maximum value, as can be appreciated in figure 3 and summarized in table I [the case λ = 1 was already depicted in figure 1]. Note that both (negative and positive) values of θ c a and ϑ c + in (25) give the same values of energy and squared spin and ppin in (27), even though the corresponding variational states |Z c − and |Z c + are different (quasi-orthogonal).…”

Section: Model Hamiltonian and Semiclassical Analysismentioning

confidence: 99%

“…In the canted phase, when inserting (25) into (27), we realize that both spin and ppin do not attain the maximum value, as can be appreciated in figure 3 and summarized in table I [the case λ = 1 was already depicted in figure 1]. Note that both (negative and positive) values of θ c a and ϑ c + in (25) give the same values of energy and squared spin and ppin in (27), even though the corresponding variational states |Z c − and |Z c + are different (quasi-orthogonal). This reflects a degeneracy problem that we shall analyze in the following section.…”

Section: Model Hamiltonian and Semiclassical Analysismentioning

confidence: 99%

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Hilbert space and ground-state structure of bilayer quantum Hall systems at ν=2/λ

2017

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We analyze the Hilbert space and ground state structure of bilayer quantum Hall (BLQH) systems at fractional filling factors ν = 2/λ (λ odd) and we also study the large SU (4) isospin-λ limit. The model Hamiltonian is an adaptation of the ν = 2 case [Z.F. Ezawa et al., Phys. Rev. B71 (2005) 125318] to the many-body situation (arbitrary λ flux quanta per electron). The semiclassical regime and quantum phase diagram (in terms of layer distance, Zeeeman, tunneling, etc, control parameters) is obtained by using previously introduced Grassmannian G 4 2 = U (4)/[U (2) × U (2)] coherent states as variational states. The existence of three quantum phases (spin, canted and ppin) is common to any λ, but the phase transition points depend on λ, and the instance λ = 1 is recovered as a particular case. We also analyze the quantum case through a numerical diagonalization of the Hamiltonian and compare with the mean-field results, which give a good approximation in the spin and ppin phases but not in the canted phase, where we detect exactly λ energy level crossings between the ground and first excited state for given values of the tunneling gap. An energy band structure at low and high interlayer tunneling (spin and ppin phases, respectively) also appears depending on angular momentum and layer population imbalance quantum numbers.

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Section: Model Hamiltonian and Semiclassical Analysismentioning

confidence: 99%

Section: Model Hamiltonian and Semiclassical Analysismentioning

confidence: 99%

Section: Model Hamiltonian and Semiclassical Analysismentioning

confidence: 99%

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Hilbert space and ground-state structure of bilayer quantum Hall systems at ν=2/λ

2017

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“…For zero tunneling ∆ t = 0, the Hamiltonian is diagonal in the orthonormal basis (16). Its eigenvalues can be straightforwardly obtained from (21) as…”

Section: B Numeric Diagonalization Resultsmentioning

confidence: 99%

“…and C j,m qa,q b = 0 for j = 0. Taking into account the matrix elements (21) and (48), we can calculate the Hamiltonian matrix elements J|H λ |J , where J = { j,m qa,q b } denotes a multi-index running from J = 1, . .…”

Section: B Numeric Diagonalization Resultsmentioning

confidence: 99%

Husimi function and phase-space analysis of bilayer quantum Hall systems at ν = 2/λ

Calixto¹,

Peón-Nieto²

2018

J. Stat. Mech.

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We propose localization measures in phase space of the ground state of bilayer quantum Hall (BLQH) systems at fractional filling factors ν = 2/λ, to characterize the three quantum phases (shortly denoted by spin, canted and ppin) for arbitrary U (4)-isospin λ. We use a coherent state (Bargmann) representation of quantum states, as holomorphic functions in the 8-dimensional Grassmannian phase-space G 4 2 = U (4)/[U (2)×U (2)] (a higher-dimensional generalization of the Haldane's 2-dimensional sphere S 2 = U (2)/[U (1) × U (1)]). We quantify the localization (inverse volume) of the ground state wave function in phase-space throughout the phase diagram (i.e., as a function of Zeeman, tunneling, layer distance, etc, control parameters) with the Husimi function second moment, a kind of inverse participation ratio that behaves as an order parameter. Then we visualize the different ground state structure in phase space of the three quantum phases, the canted phase displaying a much higher delocalization (a Schrödinger cat structure) than the spin and ppin phases, where the ground state is highly coherent. We find a good agreement between analytic (variational) and numeric diagonalization results.

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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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Coherent states for N-component fractional quantum Hall systems and their nonlinear sigma models

Cited by 6 publications

References 58 publications

Hilbert space and ground-state structure of bilayer quantum Hall systems at ν=2/λ

Hilbert space and ground-state structure of bilayer quantum Hall systems at ν=2/λ

Husimi function and phase-space analysis of bilayer quantum Hall systems at ν = 2/λ

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

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