Exotic Ising dynamics in a Bose-Hubbard model

TL;DR

This paper investigates the dynamical behavior of a two-species Bose-Hubbard model, revealing Ising-like excitations, E8 spectrum near criticality, and proposing experimental detection methods.

Contribution

It demonstrates the emergence of Ising dynamics and E8 spectrum in a Bose-Hubbard model with Feshbach resonance, using numerical simulations and linking to experimental observables.

Findings

Observation of excitation continuum and bound states in ferromagnetic phase

Detection of E8 mass spectrum near the Ising critical point

Proposals for experimental measurement of excitations in optical lattices

Abstract

We explore the dynamical properties of a one-dimensional Bose-Hubbard model, where two bosonic species interact via Feshbach resonance. We focus on the region in the phase diagram which is described by an effective, low-energy ferromagnetic Ising model in both transverse and longitudinal fields. In this regime, we numerically calculate the dynamical structure factor of the Bose-Hubbard model using the time-evolving block decimation method. In the ferromagnetic phase, we observe both the continuum of excitations and the bound states in the presence of a longitudinal field. Near the Ising critical point, we observe the celebrated E8 mass spectrum in the excited states. We also point out possible measurements which could be used to detect these excitations in an optical lattice experiment.