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arXiv:2404.18743

An unconventional deformation of the nonrelativistic spin-1/2 Fermi gas

Vimal Palanivelrajan, Joaquín E. Drut

Published Apr 29, 2024• 0 citations
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Abstract

We explore a generalization of nonrelativistic fermionic statistics that interpolates between bosons and fermions, in which up to $K$ particles may occupy a single-particle state. We show that it can be mapped exactly to $K$ flavors of fermions with imaginary polarization. In particular, for $K\!=\!2$, we use such a mapping to derive the virial coefficients and relate them to those of conventional spin-1/2 fermions in an exact fashion. We also use the mapping to derive next-to-leading-order perturbative results for the pressure equation of state. Our results indicate that the $K\!=\!2$ particles are more strongly coupled than conventional spin-$1/2$ fermions, as measured by the interaction effects on the virial expansion and on the pressure equation of state. In the regime set by the unitary limit, the proposed $K\!=\!2$ deformation represents a universal many-body system whose properties remain largely unknown. In particular, the system can be expected to become superfluid at a critical temperature $T_c$ higher than that of the unitary limit. We suggest it may be possible to realize this system experimentally by engineering a polarized coupling to an electrostatic potential. Finally, we show that the $K\!=\!2$ system does not display a sign problem for determinantal Monte Carlo calculations, which indicates that $T_c$ can at least in principle be calculated with conventional methods.

DOI
10.48550/arxiv.2404.18743

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We explore a generalization of nonrelativistic fermionic statistics that interpolates between bosons and fermions, in which up to KKK particles may occupy a single-particle state. We show that it can be mapped exactly to KKK flavors of fermions with imaginary polarization. In particular, for K ⁣= ⁣2K\!=\!2K=2, we use such a mapping to derive the virial coefficients and relate them to those of conventional spin-1/2 fermions in an exact fashion. We also use the mapping to derive next-to-leading-order perturbative results for the pressure equation of state. Our results indicate that the K ⁣= ⁣2K\!=\!2K=2 particles are more strongly coupled than conventional spin-1/21/21/2 fermions, as measured by the interaction effects on the virial expansion and on the pressure equation of state. In the regime set by the unitary limit, the proposed K ⁣= ⁣2K\!=\!2K=2 deformation represents a universal many-body system whose properties remain largely unknown. In particular, the system can be expected to become superfluid at a critical temperature TcT_cTc​ higher than that of the unitary limit. We suggest it may be possible to realize this system experimentally by engineering a polarized coupling to an electrostatic potential. Finally, we show that the K ⁣= ⁣2K\!=\!2K=2 system does not display a sign problem for determinantal Monte Carlo calculations, which indicates that TcT_cTc​ can at least in principle be calculated with conventional methods.
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.
We present a nonperturbative computation of the equation of state of polarized, attractively interacting, nonrelativistic fermions in one spatial dimension at finite temperature. We show results for the density, spin magnetization, magnetic susceptibility, and Tan's contact. We compare with the second-order virial expansion, a next-to-leading-order lattice perturbation theory calculation, and interpret our results in terms of pairing correlations. Our lattice Monte Carlo calculations implement an imaginary chemical potential difference to avoid the sign problem. The thermodynamic results on the imaginary side are analytically continued to obtain results on the real axis. We focus on an intermediate- to strong-coupling regime, and cover a wide range of temperatures and spin imbalances.
An outstanding idea originally introduced by Greenberg is to investigate whether there is equivalence between intermediate statistics, which may be different from anyonic statistics, and q-deformed particle algebra. Also, a model to be studied for addressing such an idea could possibly provide us some new consequences about the interactions of particles as well as their internal structures. Motivated mainly by this idea, in this work, we consider a q-deformed Fermi gas model whose statistical properties enable us to effectively study interpolating statistics. Starting with a generalized Fermi-Dirac distribution function, we derive several thermostatistical functions of a gas of these deformed fermions in the thermodynamical limit. We study the high-temperature behavior of the system by analyzing the effects of q deformation on the most important thermostatistical characteristics of the system such as the entropy, specific heat, and equation of state. It is shown that such a deformed fermion model in two and three spatial dimensions exhibits the interpolating statistics in a specific interval of the model deformation parameter 0 < q < 1. In particular, for two and three spatial dimensions, it is found from the behavior of the third virial coefficient of the model that the deformation parameter q interpolates completely between attractive and repulsive systems, including the free boson and fermion cases. From the results obtained in this work, we conclude that such a model could provide much physical insight into some interacting theories of fermions, and could be useful to further study the particle systems with intermediate statistics.
From ultracold atoms to quantum chromodynamics, reliable ab initio studies of strongly interacting fermions require numerical methods, typically in some form of quantum Monte Carlo calculation. Unfortunately, (non)relativistic systems at finite density (spin polarization) generally have a sign problem, such that those ab initio calculations are impractical. It is well-known, however, that in the relativistic case imaginary chemical potentials solve this problem, assuming the data can be analytically continued to the real axis. Is this feasible for nonrelativistic systems? Are the interesting features of the phase diagram accessible in this manner? By introducing complex chemical potentials, for real total particle number and imaginary polarization, the sign problem is avoided in the nonrelativistic case. To give a first answer to the above questions, we perform a mean-field study of the finite-temperature phase diagram of spin-1/2 fermions with imaginary polarization.
We study the high-temperature behavior of an intermediate-statistics fermionic gas model whose quantum statistical properties enable us to effectively deduce the details about both the interaction among deformed (quasi)particles and their anyonic behavior. Starting with a deformed fermionic grand partition function, we calculate, in the thermodynamical limit, several thermostatistical functions of the model such as the internal energy and the entropy by means of a formalism of the fermionic q calculus. For high temperatures, a virial expansion of the equation of state for the system is obtained in two and three dimensions and the first five virial coefficients are derived in terms of the model deformation parameter q. From the results obtained by the effect of fermionic deformation, it is found that the model parameter q interpolates completely between bosonlike and fermionic systems via the behaviors of the third and fifth virial coefficients in both two and three spatial dimensions and in addition it characterizes effectively the interaction among quasifermions. Our results reveal that the present deformed (quasi)fermion model could be very efficient and effective in accounting for the nonlinear behaviors in interacting composite particle systems.
We present finite-temperature, lattice Monte Carlo calculations of the particle number density, compressibility, pressure, and Tan's contact of an unpolarized system of short-range, attractively interacting spin-1/2 fermions in one spatial dimension, i.e., the Gaudin-Yang model. In addition, we compute the second-order virial coefficients for the pressure and the contact, both of which are in excellent agreement with the lattice results in the low-fugacity regime. Our calculations yield universal predictions for ultracold atomic systems with broad resonances in highly constrained traps. We cover a wide range of couplings and temperatures and find results that support the existence of a strong-coupling regime in which the thermodynamics of the system is markedly different from the noninteracting case. We compare and contrast our results with identical systems in higher dimensions.