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Chinese Physics Letters

Finite Size Corrections for One Dimensional Interacting Fermions

Liu Yimin, Pu Fuque, Su Hang

Published Aug 1, 1992• 0 citations
Publisher

Abstract

Using the method based on the Euler-Maclaurin formula, we calculate the finite size correction to the energy of the ground state and the excited state for the delta interacting fermion gas in the periodic boundary condition with N - 1 of the N fermions having the same spin and one having the opposite spin. In the thermodynamic limit, we obtain the conformal anomaly, operator dimension and the correlation functions.

DOI
10.1088/0256-307x/9/8/001

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Using the method based on the Euler-Maclaurin formula, we calculate the finite size correction to the energy of the ground state and the excited state for the delta interacting fermion gas in the periodic boundary condition with N - 1 of the N fermions having the same spin and one having the opposite spin. In the thermodynamic limit, we obtain the conformal anomaly, operator dimension and the correlation functions.
The exact energies and wavefunctions for a system of (N − 1) one-dimensional fermions all of the same spin and one fermion of the opposite spin are calculated in the large volume, finite density limit, when the particles interact via an attractive delta function potential. It is found that the attractive potential gives rise to a bound state, but, in spite of the presence of this bound state, all of the physical properties which are calculated (ground-state energy, effective mass of a certain class of excitations, etc.) are analytic continuations in the coupling constant of the corresponding results in the repulsive case. In addition, it is possible to have eigenstates which do not have the bound state present. These excited states are also discussed and are found to exhibit a negative effective mass and to modify the particle density at very large distances from the different particle.
By using the Euler–MacLaurin formula, this paper studies the thermodynamic properties of an ideal Fermi gas confined in a D -dimensional rectangular container. The general expressions of the thermodynamic quantities with the finite-size corrections are given explicitly and the effects of the size and shape of the container on the properties of the system are discussed. It is shown that the corrections of the thermodynamic quantities due to the finite-size effects are significant to be considered for the case of strong degeneracy but negligible for the case of weak degeneracy or non-degeneracy. It is important to find that some familiar conclusions under the thermodynamic limit are no longer valid for the finite-size systems and there are some novel characteristics resulting from the finite-size effects, such as the nonextensivity of the system, the anisotropy of the pressure, and so on.