Few-fermion systems in one dimension: Ground- and excited-state energies and contacts

Using the lattice Monte Carlo method, we compute the energy and Tan's contact in the ground state as well as the first excited state of few- to many-fermion systems in a one-dimensional periodic box. We focus on unpolarized systems of N=4,6,...,12 particles, with a zero-range interaction, and a wide range of attractive couplings. In addition, we provide extrapolations to the infinite-volume and thermodynamic limits.Comment: 8 pages, 12 figures; published versio

Pairing patterns in one-dimensional spin-and mass-imbalanced Fermi gases

We study spin- and mass-imbalanced mixtures of spin-1/2 fermions interacting via an attractive contact potential in one spatial dimension. Specifically, we address the influence of unequal particle masses on the pair formation by means of the complex Langevin method. By computing the pair-correlation function and the associated pair-momentum distribution we find that inhomogeneous pairing is present for all studied spin polarizations and mass imbalances. To further characterize the pairing behavior, we analyze the density-density correlations in momentum space, the so-called shot noise, which is experimentally accessible through time-of-flight imaging. At finite spin polarization, the latter is known to show distinct maxima at momentum configurations associated with the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) instability. Besides those maxima, we find that additional features emerge in the noise correlations when mass imbalance is increased, revealing the stability of FFLO-type correlations against mass imbalance and furnishing an experimentally accessible signature to probe this type of pairing

A complex Langevin approach to ultracold fermions

The theoretical treatment of Fermi systems consisting of particles with unequal masses is challenging. Even in one spatial dimension analytic solutions are limited to special configurations and numerical progress with Monte Carlo simulations is hindered by the sign-problem. To circumvent this issue, we exploit the Complex Langevin approach and study one-dimensional mass-imbalanced two-component Fermi gases with attractive and repulsive interactions. We find perfect agreement with results obtained by other methods in a range of parameter space. Promisingly, our approach is not limited to the specific model presented here and can easily be extended to finite spin polarization and, most notably, can also be applied in higher dimensions

Pairing and the spin susceptibility of the polarized unitary Fermi gas in the normal phase

We theoretically study the pairing behavior of the unitary Fermi gas in the normal phase. Our analysis is based on the static spin susceptibility, which characterizes the response to an external magnetic field. We obtain this quantity by means of the complex Langevin approach and compare our calculations to available literature data in the spin-balanced case. Furthermore, we present results for polarized systems, where we complement and expand our analysis at high temperature with high-order virial expansion results. The implications of our findings for the phase diagram of the spin-polarized unitary Fermi gas are discussed in the context of the state of the art

Pairing patterns in polarized unitary Fermi gases above the superfluid transition

We nonperturbatively study pairing in the high-temperature regime of polarized unitary two-component Fermi gases by extracting the pair-momentum distribution and shot-noise correlations. Whereas the pair-momentum distribution allows us to analyze the propagation of pairs composed of one spin-up and one spin-down fermion, shot-noise correlations provide us with a tomographic insight into pairing correlations around the Fermi surfaces associated with the two species. Assuming that the dominant pairing patterns right above the superfluid transition also govern the formation of condensates in the low-temperature regime, our analysis suggests that the superfluid ground state is homogeneous and of the Bardeen-Cooper-Schrieffer type over a wide range of polarizations

Finite-Temperature Equation of State of Polarized Fermions at Unitarity

We study in a nonperturbative fashion the thermodynamics of a unitary Fermi gas over a wide range of temperatures and spin polarizations. To this end, we use the complex Langevin method, a first principles approach for strongly coupled systems. Specifically, we show results for the density equation of state, the magnetization, and the magnetic susceptibility. At zero polarization, our results agree well with state-of-the-art results for the density equation of state and with experimental data. At finite polarization and low fugacity, our results are in excellent agreement with the third-order virial expansion. In the fully quantum mechanical regime close to the balanced limit, the critical temperature for superfluidity appears to depend only weakly on the spin polarization

Pairing patterns in polarized unitary Fermi gases above the superfluid transition

We nonperturbatively study pairing in the high-temperature regime of polarized unitary two-component Fermi gases by extracting the pair-momentum distribution and shot-noise correlations. Whereas the pair-momentum distribution allows us to analyze the propagation of pairs composed of one spin-up and one spin-down fermion, shot-noise correlations provide us with a tomographic insight into pairing correlations around the Fermi surfaces associated with the two species. Assuming that the dominant pairing patterns right above the superfluid transition also govern the formation of condensates in the low-temperature regime, our analysis suggests that the superfluid ground state is homogeneous and of the Bardeen-Cooper-Schrieffer type over a wide range of polarizations

Complex Langevin and other approaches to the sign problem in quantum many-body physics

We review the theory and applications of complex stochastic quantization to the quantum many-body problem. Along the way, we present a brief overview of a number of ideas that either ameliorate or in some cases altogether solve the sign problem, including the classic reweighting method, alternative Hubbard–Stratonovich transformations, dual variables (for bosons and fermions), Majorana fermions, density-of-states methods, imaginary asymmetry approaches, and Lefschetz thimbles. We discuss some aspects of the mathematical underpinnings of conventional stochastic quantization, provide a few pedagogical examples, and summarize open challenges and practical solutions for the complex case. Finally, we review the recent applications of complex Langevin to quantum field theory in relativistic and nonrelativistic quantum matter, with an emphasis on the nonrelativistic case

A complex Langevin approach to ultracold fermions

The theoretical treatment of Fermi systems consisting of particles with unequal masses is challenging. Even in one spatial dimension analytic solutions are limited to special configurations and numerical progress with Monte Carlo simulations is hindered by the sign-problem. To circumvent this issue, we exploit the Complex Langevin approach and study one-dimensional mass-imbalanced two-component Fermi gases with attractive and repulsive interactions. We find perfect agreement with results obtained by other methods in a range of parameter space. Promisingly, our approach is not limited to the specific model presented here and can easily be extended to finite spin polarization and, most notably, can also be applied in higher dimensions

Ground state of the two-dimensional attractive Fermi gas: Essential properties from few to many body

We calculate the ground-state properties of unpolarized two-dimensional attractive fermions in the range from few to many particles. Using first-principles lattice Monte Carlo methods, we determine the ground-state energy, Tan's contact, momentum distribution, and single-particle correlation function. We investigate those properties for systems of $N=4,8,...,40$ particles and for a wide range of attractive couplings. As the attractive coupling is increased, the thermodynamic limit is reached at progressively lower $N$ due to the dominance of the two-body sector. At large momenta $k$, the momentum distribution displays the expected $k^{-4}$ behavior, but its onset shifts from $k \simeq 1.8 k^{}_F$ at weak coupling towards higher $k$ at strong coupling.Comment: 7 pages, 4 figures, 3 table