In this paper we explore the transport properties of three-component Fermi gases confined to one spatial dimension, interacting via a three-body interaction, in the high temperature limit. At the classical level, the three-body interaction is scale invariant in one dimension. However, upon quantization, an anomaly appears which breaks the scale invariance. This is very similar to the physics of two-component fermions in two spatial dimensions, where the two-body interaction is also anomalous. Previous studies have already hinted that the physics of these two systems are intimately related. Here we expand upon those studies by examining the thermodynamic properties of this anomalous one-dimensional system in the high temperature limit. We show there is an exact mapping between the traditional two-body anomalous interaction in two dimensions, to that of three-body interaction in one dimension. This result is valid in the high temperature limit, where the thermodynamics can be understood in terms of few-body correlations.
In this paper we explore the transport properties of three-component Fermi gases confined to one spatial dimension, interacting via a three-body interaction, in the high temperature limit. At the classical level, the three-body interaction is scale invariant in one dimension. However, upon quantization, an anomaly appears which breaks the scale invariance. This is very similar to the physics of two-component fermions in two spatial dimensions, where the two-body interaction is also anomalous. Previous studies have already hinted that the physics of these two systems are intimately related. Here we expand upon those studies by examining the thermodynamic properties of this anomalous one-dimensional system in the high temperature limit. We show there is an exact mapping between the traditional two-body anomalous interaction in two dimensions, to that of three-body interaction in one dimension. This result is valid in the high temperature limit, where the thermodynamics can be understood in terms of few-body correlations.
In ultracold Fermi gases, the spatial dimension and the number of particles involved in interactions largely determine the behavior of the system. By exploiting harmonic trapping potentials and multiple hyperfine states, experiments wield a high degree of control over both of these parameters. In this work, we show that a nonrelativistic, one-dimensional, three-component Fermi system with three-body contact interactions exhibits a quantum anomaly, breaking the scale invariance that exists for this system classically. The exact solution of this three-body problem, wherein a bound trimer forms at arbitrarily small attractive couplings, features a correspondence to the two-dimensional, two-body Fermi system, through which we determine the first non-trivial virial coefficient. We further develop a numerical technique for solving the few-body problem for up to six particles and find that the effective interaction between two trimers is repulsive. To extend our analysis to the many-body problem, we apply the worm algorithm of quantum Monte Carlo and present results for various thermodynamic quantities. We find that for increasing attractive couplings, the system undergoes a Fermi-Fermi crossover from a set of three ideal Fermi gases to one weakly repulsive Fermi gas consisting of massive composite trimers. Finally, we adapt the three-body interaction to a two-dimensional lattice model, where we find strong evidence for a second-order phase transition with an associated reduction in a discrete global symmetry. While the exact experimental parameters we require have not yet been physically realized, our work provides a comprehensive first set of predictions for this model.
A system of three-species fermions in one spatial dimension (1D) with a contact three-body interaction is known to display a scale anomaly. This anomaly is identical to that of a two-dimensional (2D) system of two-species fermions. The exact relation between those two systems, however, is limited to the two-particle sector of the 2D case and the three-particle sector of the 1D case. Here, we implement a nonperturbative Monte Carlo approach, based on the worldline representation, to calculate the thermodynamics and static response of three-species fermions in 1D, thus tackling the many-body sector of the problem. We determine the energy, density, and pressure equations of state and the compressibility and magnetic susceptibility for a wide range of temperatures and coupling strengths. We compare our results with the third-order virial expansion and interpret the classical-quantum crossover as the onset of trimer degrees of freedom.
The study of strongly correlated quantum gases in two dimensions has important ramifications for understanding many intriguing phenomena in solid materials, such as high-Tc superconductivity and the fractional quantum-Hall effect. However, theoretical methods are plagued by the existence of significant quantum fluctuations. Here, we present two- and three-body exact solutions for both fermions and bosons trapped in a two-dimensional harmonic potential with an arbitrary s-wave scattering length. These few-particle solutions link in a natural way to the high-temperature properties of many-particle systems via a quantum virial expansion. As a concrete example, using the energy spectrum of few fermions, we calculate the second and third virial coefficients of a strongly interacting Fermi gas in two dimensions, and consequently investigate its high-temperature thermodynamics. Our thermodynamic results may be useful for ongoing experiments on two-dimensional Fermi gases. These exact results also provide an unbiased benchmark for quantum Monte Carlo simulations of two-dimensional Fermi gases at high temperatures.
We show that a system of three species of one-dimensional fermions, with an attractive three-body contact interaction, features a scale anomaly directly related to the anomaly of two-dimensional fermions with two-body contact forces. We show, furthermore, that those two cases (and their multispecies generalizations) are the only nonrelativistic systems with contact interactions that display a scale anomaly. While the two-dimensional case is well known and has been under study both experimentally and theoretically for years, the one-dimensional case presented here has remained unexplored. For the latter, we calculate the impact of the anomaly on the equation of state, which appears through the generalization of Tan's contact for three-body forces, and determine the pressure at finite temperature. In addition, we show that the third-order virial coefficient is proportional to the second-order coefficient of the two-dimensional two-body case.
The virial expansion characterizes the high-temperature approach to the quantum-classical crossover in any quantum many-body system. Here, we calculate the virial coefficients up to the fifth order of Fermi gases in one, two, and three dimensions, with attractive contact interactions, as relevant for a variety of applications in atomic and nuclear physics. To that end, we discretize the imaginary-time direction and calculate the relevant canonical partition functions. In coarse discretizations, we obtain analytic results featuring relationships between the interaction-induced changes $\mathrm{\ensuremath{\Delta}}{b}_{3}, \mathrm{\ensuremath{\Delta}}{b}_{4}$, and $\mathrm{\ensuremath{\Delta}}{b}_{5}$ as functions of $\mathrm{\ensuremath{\Delta}}{b}_{2}$, the latter being exactly known in many cases by virtue of the Beth-Uhlenbeck formula. Using automated-algebra methods, we push our calculations to progressively finer discretizations and extrapolate to the continuous-time limit. We find excellent agreement for $\mathrm{\ensuremath{\Delta}}{b}_{3}$ with previous calculations in all dimensions and we formulate predictions for $\mathrm{\ensuremath{\Delta}}{b}_{4}$ and $\mathrm{\ensuremath{\Delta}}{b}_{5}$ in one and two dimensions. We also provide, for a range of couplings, the subspace contributions $\mathrm{\ensuremath{\Delta}}{b}_{31}, \mathrm{\ensuremath{\Delta}}{b}_{22}, \mathrm{\ensuremath{\Delta}}{b}_{41}$, and $\mathrm{\ensuremath{\Delta}}{b}_{32}$, which determine the equation of state and static response of polarized systems at high temperature. As a performance check, we compare the density equation of state and Tan contact with quantum Monte Carlo calculations, diagrammatic approaches, and experimental data where available. Finally, we apply Pad\'e and Pad\'e-Borel resummation methods to extend the usefulness of the virial coefficients to approach and in some cases go beyond the unit-fugacity point.
We elucidate universal many-body properties of a one-dimensional, two-component ultracold Fermi gas near the p-wave Feshbach resonance. The low-energy scattering in this system can be characterized by two parameters, that is, p-wave scattering length and effective range. At the unitarity limit where the p-wave scattering length diverges and the effective range is reduced to zero without conflicting with the causality bound, the system obeys universal thermodynamics as observed in a unitary Fermi gas with contact s-wave interaction in three dimensions. It is in contrast to a Fermi gas with the p-wave resonance in three dimensions in which the effective range is inevitably finite. We present the universal equation of state in this unitary p-wave Fermi gas within the many-body T-matrix approach as well as the virial expansion method. Moreover, we examine the single-particle spectral function in the high-density regime where the virial expansion is no longer valid. On the basis of the Hartree-like self-energy shift at the divergent scattering length, we conjecture that the equivalence of the Bertsch parameter across spatial dimensions holds even for a one-dimensional unitary p-wave Fermi gas.