Ground-state properties of strongly interacting Fermi gases in two dimensions

Abstract

Exact calculations are performed on the two-dimensional strongly interacting, unpolarized, uniform Fermi gas with a zero-range attractive interaction. Two auxiliary-field approaches are employed which accelerate the sampling of imaginary-time paths using BCS trial wave functions and a force bias technique. Their combination enables calculations on large enough lattices to reliably compute ground-state properties in the thermodynamic limit. A new equation of state is obtained, with a parametrization provided, which can serve as a benchmark and allow accurate comparisons with experiments. The pressure, contact parameter, and condensate fraction are determined systematically vs. kF a. The momentum distribution, pairing correlation, and the structure of the pair wave function are computed. The use of force bias to accelerate the Metropolis sampling of auxiliary-fields in determinantal approaches is discussed. Exact results on fundamental models are uncommon, especially for strongly interacting fermion systems. In the rare cases where they exist (for example in onedimensional models by Bethe ansatz or density matrix renormalization group [1, 2]), they have invariably played an integral role in bringing about physical insights, advancing our understanding, and serving as benchmarks for the development of new theoretical and computational approaches.The Fermi gas with a zero-range attractive interactions is a model for strongly interacting fermions which has generated a great deal of research activities [3,4]. The model is of interest in both condensed matter and nuclear physics. As a model it is rather unique in that, thanks to advances in experimental techniques using ultracold atoms, it can be realized in a laboratory with great precision and control [4,5].In three-dimensions (3D) the interplay between experiment, theory and computation has lead to rapid advances [6][7][8][9]. An example is seen in the evolution [10] of the determination of the so-called Bertsch parameter at unitarity. Quantitative comparisons have allowed validation of our understanding and provided an impetus for developments of both experimental and theoretical techniques. The remarkable level of agreement achieved recently between calculation [8] and experiment [7] demonstrates the tremendous progress towards precise understanding and control of strongly correlated quantum matter.The two-dimensional (2D) Fermi gas has attracted considerable recent interest [11][12][13][14][15][16][17][18][19], especially with its experimental realization using highly anisotropic trapping potentials [20]. In 2D a bound state always exists, and the BCS-BEC cross-over offers rich possibilities between the interplay of inter-particle spacing (density) and interaction strength, where effects beyond the mean-field description will be more pronounced than in 3D. Interest in this model is further enhanced by the 2D nature of many of the most interesting and complex materials, including high-T c cuprate superconductors and topological superconductors [21].In this paper, ...

Fermions in Two Dimensions: Scattering and Many-Body Properties

“…(26), which contains parameters that are optimized for each η independently. We have compared our results to previous ab-initio work, finding significantly lower energies than prior ground-state DMC results [42] in the crossover regime and excellent agreement with AFQMC [43]. More recently another QMC study has emerged [48] that finds DMC results in agreement with ours.…”

“…As in 3D, the 2D regime is not well described by the twodimensional BCS theory in the crossover region. As a result, the determination of ground-state properties of strongly interacting Fermi gases has been attempted with Quantum Monte Carlo methods starting with a pioneering calculation using DMC [42], which was later updated using Auxiliary-Field Quantum Monte Carlo (AFQMC) [43], as well as DMC using a more sophisticated wave function that included several variational parameters [44]. These previous works focused on the determination of the contact parameter and ground state energies throughout the crossover.…”

Response Functions for the Two-Dimensional Ultracold Fermi Gas: Dynamical BCS Theory and Beyond

“…In particular, for the spin-balanced cold Fermi gas there is no fermion sign problem in the auxiliary-field Quantum Monte Carlo (AFQMC) method [27,28,29,30]. The AFQMC method is able to provide unbiased, numerically exact results for any observable on the ground state of the cold Fermi gas [17,25]. We have recently showed [23,18] that it is possible to reach beyond static properties and compute imaginary-time correlation functions such as…”

“…The calculation is sign-problem free, allowing us to obtain exact results. We use a Metropolis sampling of the paths, exploiting a force bias [17,27] that allows high acceptance ratio in the updates. The infinite variance problem is eliminated with a bridge link approach [31].…”

“…Exact calculations have been recently achieved using auxiliary-field quantum Monte Carlo (AFQMC) methodologies both for ground state properties [17] and excited states [18].…”