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arXiv:1712.03842 · Physical review. B./Physical review. B

Droplet formation in a one-dimensional system of attractive spinless fermions

Vera V. Vyborova, Oleg Valentinovich Lychkovskiy, Alexey N. Rubtsov

Published Dec 5, 2018• 4 citations

Abstract

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.

DOI: 10.1103/physrevb.98.235407

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We study the finite-energy density phase diagram of spinless fermions with attractive interactions in one dimension in the presence of uncorrelated diagonal disorder. Unlike the case of repulsive interactions, a delocalized Luttinger-liquid phase persists at weak disorder in the ground state, which is a well-known result. We revisit the ground-state phase diagram and show that the recently introduced occupation-spectrum discontinuity computed from the eigenspectrum of the one-particle density matrix is noticeably smaller in the Luttinger liquid compared to the localized regions. Moreover, we use the functional renormalization group scheme to study the finite-size dependence of the conductance, which also resolves the existence of the Luttinger liquid and is computationally cheap. Our main results concern the finite-energy density case. Using exact diagonalization and by computing various established measures of the many-body localization-delocalization transition, we argue that the zero-temperature Luttinger liquid smoothly evolves into a finite-energy density ergodic phase without any intermediate phase transition.

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One-dimensional gas of spinless fermions with attractive dipole-dipole interaction is investigated. Results obtained show when the interaction is weak, the excitation spectrum is linear and the superconducting correlation function decays as power law, indicating the validity of the Tomonaga-Luttinger (TL) liquid picture. However, when the interaction reaches a critical value, the excitation spectrum is nonlinear and the superconducting correlation function keeps finite for infinity separation, indicating real long-range order established and the breakdown of the TL liquid picture. We prove that the existence of long-range order is not in contradiction with the Hohenberg theorem and show that this system is related to the Kitaev toy model, therefore, it has potential applications for the future topological quantum computation.