Quantum Phase Transitions in Bosonic Heteronuclear Pairing Hamiltonians

TL;DR

This paper investigates the phase diagram of two-component bosons with Feshbach resonant pairing in an optical lattice, confirming Ising quantum phase transitions and critical exponents through exact diagonalization and analytical comparisons.

Contribution

It extends previous studies by confirming Ising critical exponents and analyzing the low-energy spectrum and fluctuations in a one-dimensional bosonic Hamiltonian.

Findings

Confirmation of Ising critical exponents for magnetic susceptibilities

Good agreement between numerical results and exact Ising model solutions

Detailed analysis of low-energy spectrum and density fluctuations

Abstract

We explore the phase diagram of two-component bosons with Feshbach resonant pairing interactions in an optical lattice. It has been shown in previous work to exhibit a rich variety of phases and phase transitions, including a paradigmatic Ising quantum phase transition within the second Mott lobe. We discuss the evolution of the phase diagram with system parameters and relate this to the predictions of Landau theory. We extend our exact diagonalization studies of the one-dimensional bosonic Hamiltonian and confirm additional Ising critical exponents for the longitudinal and transverse magnetic susceptibilities within the second Mott lobe. The numerical results for the ground state energy and transverse magnetization are in good agreement with exact solutions of the Ising model in the thermodynamic limit. We also provide details of the low-energy spectrum, as well as density fluctuations and superfluid fractions in the grand canonical ensemble.