Electronic structure of the Falicov-Kimball model with a magnetic field: Dynamical mean-field study

Tran, Minh-Tien

doi:10.1103/physrevb.81.115119

Cited by 3 publications

(8 citation statements)

References 38 publications

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“…1, we clearly observe a Hofstadter butterfly structure. Furthermore, we see that increasing interaction smears out the fine structure of the butterfly, consistent with DMFT calculations for the HH-Falicov-Kimball model [40]. These results clearly demonstrate the possibility to observe the Hofstadter butterfly in a Floquet system.…”

Section: Hofstadter Butterflysupporting

confidence: 86%

Spectral functions of a time-periodically driven Falicov-Kimball model: Real-space Floquet dynamical mean-field theory study

Qin

Hofstetter

2017

Phys. Rev. B

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We present a systematic study of the spectral functions of a time-periodically driven FalicovKimball Hamiltonian. In the high-frequency limit, this system can be effectively described as a Harper-Hofstadter-Falicov-Kimball model. Using real-space Floquet dynamical mean-field theory (DMFT), we take into account the interaction effects and contributions from higher Floquet bands in a non-perturbative way. Our calculations show a high degree of similarity between the interacting driven system and its effective static counterpart with respect to spectral properties. However, as also illustrated by our results, one should bear in mind that Floquet DMFT describes a nonequilibrium steady state, while an effective static Hamiltonian describes an equilibrium state. We further demonstrate the possibility of using real-space Floquet DMFT to study edge states on a cylinder geometry.

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Section: Hofstadter Butterflysupporting

confidence: 86%

Spectral functions of a time-periodically driven Falicov-Kimball model: Real-space Floquet dynamical mean-field theory study

Qin

Hofstetter

2017

Phys. Rev. B

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“…Although we give more results in this regime when we discuss scattering-rate below, we do not enter into the many details for this case since numerous studies have already tackled the interacting Hofstadter butterfly. [8][9][10][11][12][13][14] In the Landau regime, i.e. when the k y dependence of the eigenvalues in the Harper matrix Eq.…”

Section: (Color Online) Local Self-energy As a Function Ofmentioning

confidence: 99%

“…Although DMFT has been used to describe the effect of a uniform magnetic field with a single-impurity problem in the Falicov-Kimball model, 11 the general form of the DMFT self-consistency equation in a magnetic field has not been proven. In Sec.II, we derive the DMFT equations in the case where a uniform magnetic field is applied.…”

Section: Introductionmentioning

confidence: 99%

“…The effect of interactions on Hofstadter's butterfly has already been studied by various methods such as meanfield theory [8][9][10] , DMFT for the Falicov-Kimball model 11 or real-space DMFT [12][13][14] . The latter approach generalizes DMFT 15,16 to the case where the electromagnetic vector potential breaks translational invariance, by using a set of quantum impurities, one for each inequivalent site of the lattice.…”

Section: Introductionmentioning

confidence: 99%

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Orbital effect of the magnetic field in dynamical mean-field theory

2017

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The availability of large magnetic fields at international facilities and of simulated magnetic fields that can reach the flux-quantum-per-unit-area level in cold atoms, calls for systematic studies of orbital effects of the magnetic field on the self-energy of interacting systems. Here we demonstrate theoretically that orbital effects of magnetic fields can be treated within single-site dynamical meanfield theory with a translationally invariant quantum impurity problem. As an example, we study the one-band Hubbard model on the square lattice using iterated perturbation theory as an impurity solver. We recover the expected quantum oscillations in the scattering rate and we show that the magnetic fields allow the interaction-induced effective mass to be measured through the singleparticle density of states accessible in tunneling experiments. The orbital effect of magnetic fields on scattering becomes particularly important in the Hofstadter butterfly regime. II. THE DYNAMICAL MEAN-FIELD EQUATIONS WITH MAGNETIC FIELDHere we derive 17 the DMFT equations when the orbital effect of the magnetic field is taken into account in arXiv:1710.01396v1 [cond-mat.str-el]

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“…In addition, study of disorder and interaction are of genuine theoretical interest for the complexity they bring in to an otherwise non-interacting translationally invariant system. Studies of effect of disorder [7,8] and interaction [9] on Hofstadter butterfly have been carried out separately. Presence of disorder into such a system changes the scenario dramatically.…”

Section: Introductionmentioning

confidence: 99%

Interacting fermions in two dimension in simultaneous presence of disorder and magnetic field

Mandal¹,

Gupta²

2022

J. Phys.: Condens. Matter

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We study the revival of Hofstadter butterfly due to the competition between disorder and elec- tronic interaction using mean field approximation of unrestricted Hartree Fock method at zero tem- perature for two dimensional square and honeycomb lattices. Interplay of disorder and electronic correlation to nullify each other is corroborated by the fact that honeycomb lattice needs more strength of electronic correlation owing to its less co-ordination number which enhances the effect of disorder. The extent of revival of the butterfly is better in square lattice than honeycomb lattice due to higher coordination number. The effect of disorder and interaction is also investigated to study entanglement entropy and entanglement spectrum. We find that for honeycomb lattice area law of entanglement entropy is obeyed in all cases but for square lattice there is some departure from area law for larger subsystems. The entanglement spectrum have the reflection symmetry of the original butterfly of the Hofstadter spectrum. The interaction induces a gap in the entanglement spectrum as well conforming the correspondence between physical spectrum and entanglement spectrum. The effect of disorder closes the interaction induced gap in the entanglement spectrum establishing the nullification of interaction due to disorder and vice versa

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Electronic structure of the Falicov-Kimball model with a magnetic field: Dynamical mean-field study

Cited by 3 publications

References 38 publications

Spectral functions of a time-periodically driven Falicov-Kimball model: Real-space Floquet dynamical mean-field theory study

Spectral functions of a time-periodically driven Falicov-Kimball model: Real-space Floquet dynamical mean-field theory study

Orbital effect of the magnetic field in dynamical mean-field theory

Interacting fermions in two dimension in simultaneous presence of disorder and magnetic field

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