arXiv subjects

Joaquín E. Drut

Publications and source records attributed to Joaquín E. Drut.

At least 19 recordsLinked to original sources

arXiv2024

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

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.

cond-mat.quant-gas↗

arXiv2023

A lattice pairing-field approach to ultracold Fermi gases

We develop a pairing-field formalism for ab initio studies of non-relativistic two-component fermions on a $(d\!+\!1)$-dimensional spacetime lattice. More specifically, we focus on theories where the interaction between the two components can be described by the exchange of a corresponding pairing field. The introduction of a pairing field may indeed be convenient for studies of, e.g., the finite-temperature phase structure and critical behavior of, e.g., ultracold atomic Fermi gases. Moreover, such a formalism allows to directly compute the momentum and frequency dependence of the pair propagator, from which the pair-correlation function can be extracted. For a first illustration of the application of our formalism, we compute the density equation of state and the superfluid order parameter for a gas of unpolarized fermions in $(0\!+\!1)$ dimensions by employing the complex Langevin approach to surmount the sign problem.

cond-mat.quant-gas↗

arXiv2023

Calculating and resumming the classical virial expansion using automated algebra

Using schematic model potentials, we calculate exactly the virial coefficients of a classical gas up to sixth order and use them to assess the convergence properties of the virial expansion of basic thermodynamic quantities such as pressure, density, and compressibility. At sufficiently strong couplings, as expected, the virial expansion fails to converge. However, at least for the interactions and parameter ranges we explored, we find that Padé-Borel resummation methods are extremely effective in improving the convergence of the expansion.

physics.comp-ph↗

arXiv2023

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.

cond-mat.quant-gas↗

arXiv2021

Pairing patterns in polarized unitary Fermi gases above the superfluid transition

We non-perturbatively 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.

cond-mat.quant-gas↗

arXiv2021

Ab initio nuclear thermodynamics from lattice effective field theory

We show that the {\it ab initio} calculations of nuclear thermodynamics can be performed efficiently using lattice effective field theory. The simulations use a new approach called the pinhole trace algorithm to calculate thermodynamic observables for a fixed number of protons and neutrons enclosed in a finite box. In this framework, we calculate the equation of state, the liquid-vapor coexistence line and the critical point of neutral symmetric nuclear matter with high precision. Since the algorithm uses a canonical ensemble with a fixed number of particles, it provides a sizable computational advantage over grand canonical ensemble simulations that can be a factor of several thousands to as much as several millions for large volume simulations.

nucl-th↗

arXiv2021

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.

cond-mat.quant-gas↗

arXiv2021

Quantum anomaly and thermodynamics of one-dimensional fermions with antisymmetric two-body interactions

A system of two-species, one-dimensional fermions, with an attractive two-body interaction of the derivative-delta type, features a scale anomaly. In contrast to the well-known two-dimensional case with contact interactions, and its one-dimensional cousin with three-body interactions (studied recently by some of us and others), the present case displays dimensional transmutation featuring a power-law rather than a logarithmic behavior. We use both the Schrödinger equation and quantum field theory to study bound and scattering states, showing consistency between both approaches. We show that the expressions for the reflection $(R)$ and the transmission $(T)$ coefficients of the renormalized, anomalous derivative-delta potential are identical to those of the regular delta potential. The second-order virial coefficient is calculated analytically using the Beth-Uhlenbeck formula, and we make comments about the proper $ε_B\rightarrow 0$ (where $ε_B$ is the bound-state energy) limit. We show the impact of the quantum anomaly (which appears as the binding energy of the two-body problem, or equivalently as Tan's contact) on the equation of state and on other universal relations. Our emphasis throughout is on the conceptual and structural aspects of this problem.

cond-mat.quant-gas↗

arXiv2020

Emergence of a pseudogap in the BCS-BEC crossover

Strongly correlated Fermi systems with pairing interactions become superfluid below a critical temperature $T_c$. The extent to which such pairing correlations alter the behavior of the liquid at temperatures $T > T_c$ is a subtle issue that remains an area of debate, in particular regarding the appearance of the so-called pseudogap in the BCS-BEC crossover of unpolarized spin-$1/2$ nonrelativistic matter. To shed light on this, we extract several quantities of crucial importance at and around the unitary limit, namely: the odd-even staggering of the total energy, the spin susceptibility, the pairing correlation function, the condensate fraction, and the critical temperature $T_c$, using a non-perturbative, constrained-ensemble quantum Monte Carlo algorithm.

cond-mat.quant-gas↗

arXiv2020

Ab initio nuclear thermodynamics

We propose a new Monte Carlo method called the pinhole trace algorithm for {\it ab initio} calculations of the thermodynamics of nuclear systems. For typical simulations of interest, the computational speedup relative to conventional grand-canonical ensemble calculations can be as large as a factor of one thousand. Using a leading-order effective interaction that reproduces the properties of many atomic nuclei and neutron matter to a few percent accuracy, we determine the location of the critical point and the liquid-vapor coexistence line for symmetric nuclear matter with equal numbers of protons and neutrons. We also present the first {\it ab initio} study of the density and temperature dependence of nuclear clustering.

nucl-th↗

arXiv2020

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

We study spin- and mass-imbalanced mixtures of spin-$\tfrac{1}{2}$ 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.

cond-mat.quant-gas↗

arXiv2019

Thermodynamics of spin-orbit coupled bosons in two dimensions from complex Langevin

We investigate the thermal properties of interacting spin-orbit coupled bosons with contact interactions in two spatial dimensions. To that end, we implement the complex Langevin method, motivated by the appearance of a sign problem, on a square lattice with periodic boundary conditions. We calculate the density equation of state non-perturbatively in a range of spin-orbit couplings and chemical potentials. Our results show that mean-field solutions tend to underestimate the average density, especially for stronger values of the spin-orbit coupling. Additionally, the finite nature of the simulation volume induces the formation of pseudo-condensates. These have been observed to be destroyed by the spin-orbit interactions.

cond-mat.quant-gas↗

arXiv2019

A Quantum Field-Theoretical Perspective on Scale Anomalies in 1D systems with Three-Body Interactions

We analyze, from a canonical quantum field theory perspective, the problem of one-dimensional particles with three-body attractive interactions, which was recently shown to exhibit a scale anomaly identical to that observed in two-dimensional systems with two-body interactions. We study in detail the properties of the scattering amplitude including both bound and scattering states, using cutoff and dimensional regularization, and clarify the connection between the scale anomaly derived from thermodynamics to the non-vanishing nonrelativistic trace of the energy-momentum tensor.

hep-th↗

arXiv2019

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.

cond-mat.quant-gas↗

arXiv2018

Surmounting the sign problem in non-relativistic calculations: a case study with mass-imbalanced fermions

The calculation of the ground state and thermodynamics of mass-imbalanced Fermi systems is a challenging many-body problem. Even in one spatial dimension, analytic solutions are limited to special configurations and numerical progress with standard Monte Carlo approaches is hindered by the sign problem. The focus of the present work is on the further development of methods to study imbalanced systems in a fully non-perturbative fashion. We report our calculations of the ground-state energy of mass-imbalanced fermions using two different approaches which are also very popular in the context of the theory of the strong interaction (Quantum Chromodynamics, QCD): (a) the hybrid Monte Carlo algorithm with imaginary mass imbalance, followed by an analytic continuation to the real axis; and (b) the Complex Langevin algorithm. We cover a range of on-site interaction strengths that includes strongly attractive as well as strongly repulsive cases which we verify with non-perturbative renormalization group methods and perturbation theory. Our findings indicate that, for strong repulsive couplings, the energy starts to flatten out, implying interesting consequences for short-range and high-frequency correlation functions. Overall, our results clearly indicate that the Complex Langevin approach is very versatile and works very well for imbalanced Fermi gases with both attractive and repulsive interactions.

cond-mat.quant-gas↗

arXiv2018

Polarized fermions in one dimension: density and polarization from complex Langevin calculations, perturbation theory, and the virial expansion

We calculate the finite-temperature density and polarization equations of state of one-dimensional fermions with a zero-range interaction, considering both attractive and repulsive regimes. In the path-integral formulation of the grand-canonical ensemble, a finite chemical potential asymmetry makes these systems intractable for standard Monte Carlo approaches due to the sign problem. Although the latter can be removed in one spatial dimension, we consider the one-dimensional situation in the present work to provide an efficient test for studies of the higher-dimensional counterparts. To overcome the sign problem, we use the complex Langevin approach, which we compare here with other approaches: imaginary-polarization studies, third-order perturbation theory, and the third-order virial expansion. We find very good qualitative and quantitative agreement across all methods in the regimes studied, which supports their validity.

cond-mat.quant-gas↗

arXiv2018

Virial expansion for the Tan contact and Beth-Uhlenbeck formula from 2D SO(2,1) anomalies

The relationship between 2D $SO(2,1)$ conformal anomalies in nonrelativistic systems and the virial expansion is explored using recently developed path-integral methods. In the process, the Beth-Uhlenbeck formula for the shift of the second virial coefficient $δb_2$ is obtained, as well as a virial expansion for the Tan contact. A possible extension of these techniques for higher orders in the virial expansion is discussed.

cond-mat.quant-gas↗

arXiv2018

Quantum anomaly and thermodynamics of one-dimensional fermions with three-body interactions

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 forces. We show, furthermore, that those two cases (and their multi species generalizations) are the only non-relativistic 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.

cond-mat.quant-gas↗