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Progress of Theoretical Physics

Phase Transition in Fermion Lattice Gas with Infinite-Ranged Interaction. I: Ground State Properties

Hikaru Kawamura

Published Sep 1, 1982• 5 citations
Publisher

Abstract

The gas-liquid transition of quantum lattice gas model with infinite-ranged attractive interaction is studied in the case of spinless (or completely p
DOI
10.1143/ptp.68.764

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Investigation of the gas-liquid transition in the spinless fermion lattice gas with infinite-ranged attractive interaction is continued. Equation of state and phase diagram are calculated exactly at finite temperatures. Quantum shift of the critical temperature is also calculated. In some cases, e.g., in the case of the linear chain with nearest neighbor hopping, the obtained isotherms have two separate horizontal parts on suitable conditions showing double phase transitions and there exist two critical points in the phase diagram. As far as the density of states has a single peak, on the other hand, the system has only one critical point.
In a recent letter [D. Poletti et al., EPL 93, 37008 (2011)] a model of attractive spinless fermions on the honeycomb lattice at half filling has been studied by mean-field theory, where distinct homogenous phases at rather large attraction strength V>3.36V>3.36V>3.36, separated by (topological) phase transitions, have been predicted. In this comment we argue that without additional interactions the ground states in these phases are not stable against phase separation. We determine the onset of phase separation at half filling Vps≈1.7V_{ps}\approx 1.7Vps​≈1.7 by means of infinite projected entangled-pair states (iPEPS) and exact diagonalization.
A translation invariant one-dimensional system of spinless fermions with a finite-range attraction experiences a quantum phase transition to a phase-separated state. While being a conventional Luttinger liquid for a small interaction strength, spinless fermions form a droplet with the size smaller than the available one-dimensional volume when the interaction strength exceeds some critical value. A particularly remarkable signature of the droplet formation is the change in the lower edge of the many-body excitation spectrum. In the homogeneous phase, it has a Luttinger-liquid shape of periodic arcs on top of the shallow parabolic dispersion of the center of mass. When the interaction strength is increased, the arcs disappear completely as soon as the droplet is formed. We perform an exact diagonalization study of this system with the focus on the signatures of the quantum phase transition and the droplet properties. The one-particle and density-density correlation functions, the pressure, the sound velocity, and the droplet density are examined. The value of the critical interaction strength obtained from numerical data reasonably agrees with a simple mean-field analytical estimate. Due to the boson-fermion correspondence valid in one dimension, our results also hold for hard-core bosons with a finite-range attraction.