Long-range Order in One-dimensional Spinless Fermi Gas with Attractive Dipole-Dipole Interaction

TL;DR

This paper explores the phase transition in a one-dimensional spinless Fermi gas with attractive dipole interactions, revealing a transition from a TL liquid to a phase with true long-range order and potential topological quantum computing applications.

Contribution

It demonstrates the emergence of long-range order in a 1D dipolar Fermi system, challenging the traditional TL liquid paradigm and linking to the Kitaev model.

Findings

Weak interaction: linear spectrum, power-law decay of correlations

Critical interaction: nonlinear spectrum, finite superconducting correlations

Potential for topological quantum computation

Abstract

One-dimensional spinless Fermi gas 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.