Dynamical structure factor of a fermionic supersolid on an optical lattice

TL;DR

This paper presents exact numerical results for the dynamical structure factor of a fermionic supersolid in an optical lattice, providing benchmarks and new insights into collective modes in strongly correlated Fermi systems.

Contribution

The study combines quantum Monte Carlo simulations with analytic continuation to accurately compute dynamical correlations in a fermionic supersolid, benchmarking and challenging existing approximation methods.

Findings

Agreement on low-energy Nambu-Goldstone mode between methods

Identification of a high-energy spin mode

Differences in higher energy structures between approaches

Abstract

Interfacing unbiased quantum Monte Carlo simulations with state-of-art analytic continuation techniques, we obtain exact numerical results for dynamical density and spin correlations in the attractive Hubbard model, describing a spin-balanced two-dimensional cold Fermi gas on an optical lattice. We focus on half-filling, where on average one fermion occupies each lattice site, and the system displays an intriguing supersolid phase: a superfluid with a checkerboard density modulation. The coexistence of $U(1)$ broken symmetry and the density modulations makes this regime very challenging and interesting for the calculation of dynamical properties. We compare our unbiased results with state-of-the-art Generalized Random Phase Approximation calculations: both approaches agree on a well-defined low-energy Nambu-Goldstone collective mode in the density correlations, while the higher energy structures appear to differ significantly. We also observe an interesting high-energy spin mode. We argue that our results provide a robust benchmark for Generalized Random Phase Approximation techniques, which are widely considered to be the method of choice for dynamical correlations in Fermi gases. Also, our calculations yield new physical insight in the high-energy behavior of the dynamical structure factor of the attractive Hubbard model, which is a well known prototype lattice model for superconductors and is a fertile field to target the observation of collective modes in strongly correlated systems.