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Physical review. B, Condensed matter

Exactly soluble model of two-dimensional interacting fermions in a uniform magnetic field

Erik C. Sowa, L. M. Falicov

Published Apr 15, 1984• 0 citations
Publisher

Abstract

The spectrum of a Hamiltonian for $N$ harmonically interacting two-dimensional particles in a constant perpendicular magnetic field is determined exactly by the transformation to normal coordinates. The energy of the ground state consistent with Fermi-Dirac statistics is calculated in the limit of a strong magnetic field. The Fermi energy is found to exhibit de Haas---van Alphen---like oscillations.

DOI
10.1103/physrevb.29.4364

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The spectrum of a Hamiltonian for NNN harmonically interacting two-dimensional particles in a constant perpendicular magnetic field is determined exactly by the transformation to normal coordinates. The energy of the ground state consistent with Fermi-Dirac statistics is calculated in the limit of a strong magnetic field. The Fermi energy is found to exhibit de Haas---van Alphen---like oscillations.
The normal-state energy spectrum of the two-dimensional ttt-JJJ model in a homogeneous perpendicular magnetic field is investigated. The density of states at the Fermi level as a function of the inverse magnetic field 1B\frac{1}{B}B1​ reveals oscillations in the range of hole concentrations $0.08
The normal-state energy spectrum of the two-dimensional t-J model in a homogeneous perpendicular magnetic eld B is investigated using the Mori projection operator technique.The density of states at the Fermi level as a function of 1/B reveals both high-and low-frequency oscillations.The high-frequency oscillations correspond to large Fermi surfaces, while the low-frequency components are related to van Hove singularities in the Landau subbands, which stem from their bending due to strong electron correlations.Frequencies of the low-frequency components are of the same order of magnitude as those observed in underdoped cuprates.These components become dominant if smoothing processes are involved.It is shown that despite increased distances between subbands the pseudogap aects only slightly the frequency of density of states oscillations.
The authors study a one dimensional model system of fermions which proves to be exactly soluble in the thermodynamic limit. It is shown that the thermodynamic functions for the model system are the same as for a system of noninteracting fermions in a harmonic oscillator well. As a special case of the model system, with a particular choice for the coupling constant, it reduces to a particular two-species system of fermions interacting via pairwise harmonic forces. For this case of the two-species system the free energy per particle, the pressure the specific heat at constant volume, and the isothermal compressibility are calculated in the canonical ensemble in closed form. It is shown that this system does not undergo a phase transition.
The isotropic oscillator in a uniform magnetic field is an exactly soluble quantum problem which can serve as a useful model of an atom in a magnetic field of arbitrary strength. The exact eigenvalue spectrum is derived, compared with perturbation theory for low field strengths, and shown to yield a quasi-Landau spectrum for high field strengths. The frequency, polarization, and relative intensity of the spectral lines of the Zeeman effect are determined as a function of the field strength. The effect of the field on atomic size and on the atomic wave functions is discussed; the three-dimensional system is shown to collapse into a needlelike one-dimensional system for a sufficiently intense field.
We derive the density functional for the ground-state energy of a two-dimensional, spin-polarized gas of neutral fermionic atoms with magnetic-dipole interaction, in the Thomas-Fermi-Dirac approximation. For many atoms in a harmonic trap, we give analytical solutions for the single-particle spatial density and the ground-state energy, in dependence on the interaction strength, and we discuss the weak-interaction limit that is relevant for experiments. We then lift the restriction of full spin polarization and account for a time-independent inhomogeneous external magnetic field. The field strength necessary to ensure full spin polarization is derived.