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arXiv:1911.03466 · Journal of Physics Condensed Matter

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

Saptarshi Mandal, Sanjay Gupta

Published Mar 14, 2022• 1 citation
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Abstract

We study the revival of Hofstadter butterfly due to the competition between disorder and electronic interaction using mean field approximation of unrestricted Hartree Fock method at zero temperature 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.

DOI
10.1088/1361-648x/ac5d8a

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We study thermodynamic properties of the two-dimensional (2D) Falicov-Kimball model in the presence of external magnetic field perpendicular to the lattice.The field is taken into account by the Peierls substitution in the hopping term.We show how the Hofstadter butterfly is affected by electronic correlations.In the non-interacting case the field dependent energy spectrum forms the famous Hofstadter butterfly.Our results indicate that for arbitrary nonzero interaction strength and arbitrary magnetic field there is a gap in the energy spectrum at sufficiently low temperature.The gap vanishes with increase of temperature for weak coupling, however, it persists at high temperatures if the coupling is strong enough.Numerical results have been obtained with the help of Monte Carlo technique based on a modified Metropolis algorithm.
We investigate a finite two-dimensional system in the presence of an external magnetic field. We discuss how the energy spectrum depends on the system size, boundary conditions, and Coulomb repulsion. On one hand, using these results, we present the field dependence of the transport properties of a nanosystem. In particular, we demonstrate that these properties depend on whether the system consists of an even or an odd number of sites. On the other hand, on the basis of exact results obtained for a finite system, we investigate whether the Hofstadter butterfly is robust against strong electronic correlations. We show that for sufficiently strong Coulomb repulsion, the Hubbard gap decreases when the magnetic field increases.
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