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arXiv:1912.06272 · Physical Review A

Dynamical structure factor of a fermionic supersolid on an optical lattice

Ettore Vitali, Patrick Kelly, Annette Lopez, Gianluca Bertaina, Davide Emilio Galli

Published Nov 30, 2020• 8 citations
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Abstract

Interfacing unbiased quantum Monte Carlo simulations with state-of-the-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 $\text{U}(1)$ 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 into 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.

DOI
10.1103/physreva.102.053324

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Interfacing unbiased quantum Monte Carlo simulations with state-of-the-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)\text{U}(1)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 into 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.
We leverage random phase approximation and unbiased auxiliary-field quantum Monte Carlo methods to compute dynamical correlations for a dilute homogeneous two-dimensional attractive Fermi gas. Our main purpose is to quantitatively study the collective excitations of the system to generate robust benchmark results and to shed light into fermionic superfluidity in the strongly correlated regime. In particular we are motivated by a recent paper suggesting that the Higgs mode can be detected in the spectrum of spin fluctuations. Despite the fact that we are somewhat limited by finite-size effects, our study indeed pinpoints a clear peak in the spin channel at low momentum, but a detailed analysis suggests that such a peak, though certainly interesting, does not correspond to the Higgs mode. We propose a different explanation for the shape of the spin structure factor. However, our results clearly show that the Higgs mode can be detected in the density channel at very small wave vectors, although very good resolution is necessary.
We study the attractive Hubbard model with mass imbalance to clarify low temperature properties of the fermionic mixtures in the optical lattice. By combining dynamical mean-field theory with the continuous-time quantum Monte Carlo simulation, we discuss the competition between the superfluid and density wave states at half filling. By calculating the energy and the order parameter for each state, we clarify that the coexisting (supersolid) state, where the density wave and superfluid states are degenerate, is realized in the system. We then determine the phase diagram at finite temperatures.
We study the superfluid phase of the one-band attractive Hubbard model of fermions as a prototype of a strongly correlated sss-wave fermion superfluid on a lattice. We show that the collective mode spectrum of this superfluid exhibits, in addition to the long wavelength sound mode, a sharp roton mode over a wide range of densities and interaction strengths. We compute the sound velocity and the roton gap within a generalized random phase approximation (GRPA) and show that the GRPA results are in good agreement, at strong coupling, with a spin-wave analysis of the appropriate strong-coupling pseudospin model. We also investigate, using this two-pronged approach, the breakdown of superfluidity in the presence of a supercurrent. We find that the superflow can break down at a critical flow momentum via several distinct mechanisms---depairing, Landau instabilities or dynamical instabilities---depending on the dimension, the interaction strength and the fermion density. The most interesting of these instabilities is a charge modulation dynamical instability which is distinct from previously studied dynamical instabilities of Bose superfluids. The charge order associated with this instability can be of two types: (i) a commensurate checkerboard modulation driven by softening of the roton mode at the Brillouin zone corner, or, (ii) an incommensurate density modulation arising from superflow-induced finite momentum pairing of Bogoliubov quasiparticles. We elucidate the dynamical phase diagram showing the critical flow momentum of the leading instability over a wide range of fermion densities and interaction strengths and point out implications of our results for experiments on cold atom fermion superfluids in an optical lattice.
The recent experimental realization of the half-filled three-color Fermi-Hubbard model on a square optical lattice provides a novel platform for exploring exotic states of matter beyond conventional SU(2) systems. In this Letter, we investigate the three-color Fermi-Hubbard model with color-dependent attractive interactions using determinant quantum Monte Carlo simulations. We find that, at quantum degenerate temperatures, a lattice Fermi supersolid state emerges from the interplay between a moderately-to-strongly interacting two-color subsystem and a weakly coupled third-color environment. This supersolid state, characterized by the coexistence of charge-density-wave and color-superfluid orders, is highly promising for experimental detection with current techniques. Our results demonstrate that the attractive three-color Fermi-Hubbard model on a square optical lattice offers an experimentally accessible system for exploring the supersolidity of ultracold lattice fermions, requiring only a simple lattice geometry and easily tunable onsite interactions.
Many-body physics poses one of the greatest challenges to science in the 21st century. Still more daunting is the problem of accurately calculating the properties of quantum many-body systems in the strongly correlated regime. Cold atomic gases provide an excellent test ground, for both experimentalists and theorists, to study the exotic and sometimes counterintuitive behavior of quantum many-body problems. Of particular interest is the appearance of collective excitations in these systems, such as the famous Goldstone mode and the elusive Higgs mode. It is particularly important to assess the robustness of theoretical and computational techniques to study such excitations. We build on the unprecedented opportunity provided by the fact that, in some cases, exact numerical predictions can be obtained through quantum Monte Carlo. We use these predictions to assess the accuracy of the Random Phase Approximation, which is widely considered to be a method of choice for the study of the collective excitations in a cold atomic Fermi gas modeled with a Fermi–Hubbard Hamiltonian. We found good agreement between the two methodologies for the dynamic properties, particularly for the position of the Goldstone mode. We also explored the possibility of using a renormalized, effective potential in place of the physical potential. We determined that using a renormalized potential is likely too simplistic a method for improving the accuracy of generalized Random Phase Approximation and that a more sophisticated approach is needed.
Abstract Based on random phase approximation, we numerically calculate dynamical structure factors of a balanced two-dimensional (2D) Fermi superfluid, and discuss their energy, momentum and interaction strength dependence in the 2D BEC–BCS crossover. At a small transferred momentum, a stable Higgs mode is observed in the unitary 2D Fermi superfluid gas where the particle–hole symmetry is not satisfied. Stronger interaction strength will make the visibility of the dispersion of Higgs mode harder to be observed. We also discuss the dimension effect and find that the signal of the Higgs mode in two dimension is more obvious than that in 3D case. At a large transferred momentum regime, stronger interaction strength will induce the weight of the molecules excitation increasing, while in verse the atomic one decreasing, which shows the pairing information of Fermi superfluid. The theoretical results qualitatively agree with the corresponding quantum Monte Carlo data.