Competing Orders in One-Dimensional Half-Integer Fermionic Cold Atoms: A Conformal Field Theory Approach

TL;DR

This paper uses conformal field theory to analyze the phases and phase transitions of half-integer spin fermionic cold atoms in one-dimensional optical lattices, revealing competing superfluid and charge-density wave orders.

Contribution

It introduces a conformal field theory framework to study the phase diagram and quantum phase transitions of half-integer spin fermionic cold atoms, identifying universality classes and Mott phases.

Findings

Two superfluid phases emerge for F ≥ 3/2: BCS and molecular superfluid.

Quantum phase transitions belong to Ising and three-state Potts universality classes.

Mott transition and insulating phases are characterized at one atom per site.

Abstract

The physical properties of arbitrary half-integer spins F = N - 1/2 fermionic cold atoms loaded into a one-dimensional optical lattice are investigated by means of a conformal field theory approach. We show that for attractive interactions two different superfluid phases emerge for F \ge 3/2: A BCS pairing phase, and a molecular superfluid phase which is formed from bound-states made of 2N fermions. In the low-energy approach, the competition between these instabilities and charge-density waves is described in terms of Z_N parafermionic degrees of freedom. The quantum phase transition for F=3/2,5/2 is universal and shown to belong to the Ising and three-state Potts universality classes respectively. For a filling of one atom per site, a Mott transition occurs and the nature of the possible Mott-insulating phases are determined.