Unitary Fermions Research Articles

Spatially random disorder in unitary fermion system in (4 − ϵ)-dimensions and effective action at finite temperature

Non-relativistic conformal field theory is significant to understand various aspects of an ultra-cold system. In this paper, we study a non-relativistic system of two-component fermions interacting with a complex boson with Yukawa-like interactions near d = 4-spatial dimensions in the presence of a quenched disorder. The homogeneous theory flows to an interacting fixed point describing a unitary fermion system. In the presence of the disorder, we find that the system has an interesting phase structure in the space of the coupling constants and exhibits an interacting disorder fixed point in ϵ-expansion. The correlation function obeys Lifshitz scaling behaviour at the disorder fixed point with the anisotropic exponent being z = 2 + γE. We also study the disorder system at finite temperature and compute the leading contribution to the 1PI effective action.

Universal van der Waals Force between Heavy Polarons in Superfluids.

We investigate the long-range behavior of the induced Casimir interaction between two spinless heavy impurities, or polarons, in superfluid cold atomic gases. With the help of effective field theory (EFT) of a Galilean invariant superfluid, we show that the induced impurity-impurity potential at long distance universally shows a relativistic van der Waals-like attraction (∼1/r^{7}) resulting from the exchange of two superfluid phonons. We also clarify finite temperature effects from the same two-phonon exchange process. The temperature T introduces the additional length scale c_{s}/T with the speed of sound c_{s}. Leading corrections at finite temperature scale as T^{6}/r for distances r≪c_{s}/T smaller than the thermal length. For larger distances the potential shows a nonrelativistic van der Waals behavior (∼T/r^{6}) instead of the relativistic one. Our EFT formulation applies not only to weakly coupled Bose or Fermi superfluids but also to those composed of strongly correlated unitary fermions with a weakly coupled impurity. The sound velocity controls the magnitude of the van der Waals potential, which we evaluate for the fermionic superfluid in the BCS-BEC crossover.

Z2 topological invariants for mixed states of fermions in time-reversal invariant band structures

The topological classification of fermion systems in mixed states is a long standing quest. For Gaussian states, reminiscent of non-interacting unitary fermions, some progress has been made. While the topological quantization of certain observables such as the Hall conductivity is lost for mixed states, directly observable many-body correlators exist which preserve the quantized nature and naturally connect to known topological invariants in the ground state. For systems which break time-reversal (TR) symmetry, the ensemble geometric phase was identified as such an observable which can be used to define a Chern number in $(1+1)$ and $2$ dimensions. Here we propose a corresponding $\mathbb{Z}_2$ topological invariant for systems with TR symmetry. We show that this mixed-state invariant is identical to well-known $\mathbb{Z}_2$ invariants for the ground state of the so-called fictitious Hamiltonian, which for thermal states is just the ground state of the system Hamiltonian itself. We illustrate our findings for finite-temperature states of a paradigmatic $\mathbb{Z}_2$ topological insulator, the Kane-Mele model.

Tunneling Transport of Unitary Fermions across the Superfluid Transition.

We investigate the transport of a Fermi gas with unitarity-limited interactions across the superfluid phase transition, probing its response to a direct current (dc) drive through a tunnel junction. As the superfluid critical temperature is crossed from below, we observe the evolution from a highly nonlinear to an Ohmic conduction characteristic, associated with the critical breakdown of the Josephson dc current induced by pair condensate depletion. Moreover, we reveal a large and dominant anomalous contribution to resistive currents, which reaches its maximum at the lowest attained temperature, fostered by the tunnel coupling between the condensate and phononic Bogoliubov-Anderson excitations. Increasing the temperature, while the zeroing of supercurrents marks the transition to the normal phase, the conductance drops considerably but remains much larger than that of a normal, uncorrelated Fermi gas tunneling through the same junction. We attribute such enhanced transport to incoherent tunneling of sound modes, which remain weakly damped in the collisional hydrodynamic fluid of unpaired fermions at unitarity.

SU(1,1) Echoes for Breathers in Quantum Gases

Though the celebrated spin echoes have been widely used to reverse quantum dynamics, they are not applicable to systems whose constituents are beyond the control of the su(2) algebra. Here, we design echoes to reverse quantum dynamics of breathers in three-dimensional unitary fermions and two-dimensional bosons and fermions with contact interactions, which are governed by an underlying su(1,1) algebra. Geometrically, SU(1,1) echoes produce closed trajectories on a single or multiple Poincaré disks and thus could recover any initial states without changing the sign of the Hamiltonian. In particular, the initial shape of a breather determines the superposition of trajectories on multiple Poincaré disks and whether the revival time has period multiplication. Our work provides physicists with a recipe to tailor collective excitations of interacting many-body systems.

Convergence of nuclear effective field theory with perturbative pions

The classic paper by Fleming, Mehen and Stewart cast doubts on the convergence of spin-triplet nucleon-nucleon partial wave scattering amplitudes when following the proposal of Kaplan, Savage and Wise to construct nuclear effective field theory around the unitary fermion limit with perturbative pion exchange. FMS identified the subclass of iterated one-pion exchange potential graphs as the cause of this poor convergence, which they showed persisted in the chiral limit. Theoretical tools are developed here to compute these Feynman graphs analytically to high order in all angular momentum channels simultaneously, examining the amplitudes computed to seven loops in the $L=J$ channels, and three loops in the coupled $L=J\pm1$ channels. One finds that there is nothing pathological about the perturbative expansion of a $1/r^3$ potential in general, and that the expansion converges satisfactorily in all partial waves except those with the lowest angular momentum, particularly the ${}^3P_0$ and the coupled ${}^3S_1-{}^3D_1$ channels. The results corroborate work by Birse, which suggests possible avenues to explore for improving the range of validity of the EFT expansion.

The spinful large charge sector of non-relativistic CFTs: from phonons to vortex crystals

We study operators in Schrödinger invariant field theories (non-relativistic conformal field theories or NRCFTs) with large charge (particle number) and spin. Via the state-operator correspondence for NRCFTs, such operators correspond to states of a superfluid in a harmonic trap with phonons or vortices. Using the effective field theory of the Goldstone mode, we compute the dimensions of operators to leading order in the angular momentum L and charge Q. We find a diverse set of scaling behaviors for NRCFTs in both d = 2 and d = 3 spatial dimensions. These results apply to theories with a superfluid phase, such as unitary fermions or critical anyon systems.

Universal Spin Transport and Quantum Bounds for Unitary Fermions

We review recent advances in experimental and theoretical understanding of spin transport in strongly interacting Fermi gases. The central new phenomenon is the observation of a lower bound on the (bare) spin diffusivity in the strongly interacting regime. Transport bounds are of broad interest for the condensed matter community, with a conceptual similarity to observed bounds in shear viscosity and charge conductivity. We discuss the formalism of spin hydrodynamics, how dynamics are parameterized by transport coefficients, the effect of confinement, the role of scale invariance, the quasiparticle picture, and quantum critical transport. We conclude by highlighting open questions, such as precise theoretical bounds, relevance to other phases of matter, and extensions to lattice systems.

Upper Bound on Diffusivity.

The linear growth of operators in local quantum systems leads to an effective light cone even if the system is nonrelativistic. We show that the consistency of diffusive transport with this light cone places an upper bound on the diffusivity: D≲v^{2}τ_{eq}. The operator growth velocity v defines the light cone, and τ_{eq} is the local equilibration time scale, beyond which the dynamics of conserved densities is diffusive. We verify that the bound is obeyed in various weakly and strongly interacting theories. In holographic models, this bound establishes a relation between the hydrodynamic and leading nonhydrodynamic quasinormal modes of planar black holes. Our bound relates transport data-including the electrical resistivity and the shear viscosity-to the local equilibration time, even in the absence of a quasiparticle description. In this way, the bound sheds light on the observed T-linear resistivity of many unconventional metals, the shear viscosity of the quark-gluon plasma, and the spin transport of unitary fermions.

Validating simple dynamical simulations of the unitary Fermi gas

We present a comparison between simulated dynamics of the unitary fermion gas using the superfluid local density approximation (SLDA) and a simplified bosonic model, the extended Thomas Fermi (ETF) with a unitary equation of state. Small amplitude fluctuations have similar dynamics in both theories for frequencies far below the pair breaking threshold and wave vectors much smaller than the Fermi momentum, and the low frequency linear responses match well for surprisingly large wave vectors, even up to the Fermi momentum. For non-linear dynamics such as vortex generation, the ETF provides a semi-quantitative description of SLDA dynamics as long as the fluctuations do not have significant power near the pair breaking threshold, otherwise the dynamics of the ETF cannot be trusted. Nonlinearities in the ETF tends to generate high-frequency fluctuations, and with no normal component to remove this energy from the superfluid, features like vortex lattices cannot relax and crystallize as they do in the SLDA. We present a heuristic diagnostic for validating the reliability of ETF dynamics by considering the approximate conservation of square of the gap: $\int|\Delta|^2$.

Predicting energies of small clusters from the inhomogeneous unitary Fermi gas

We investigate the inhomogeneous unitary Fermi gas and use the long-wavelength properties to predict the energies of small clusters of unitary fermions trapped in harmonic potentials. The large pairing gap and scale invariance place severe restrictions on the form of the density functional. We determine the relevant universal constants needed to constrain the functional from calculations of the bulk in oscillating external potentials. Comparing with exact Quantum Monte Carlo calculations, we find that the same functional correctly predicts the lack of shell closures for small clusters of fermions trapped in harmonic wells as well as their absolute energies. A rapid convergence to the bulk limit in three dimensions, where the surface to volume ratio is quite large, is demonstrated. The resulting functional can be tested experimentally, and is a key ingredient in predicting possible polarized superfluid phases and the properties of the unitary Fermi gas in optical lattices.

Numerical study of unitary fermions in one spatial dimension

I perform lattice Monte Carlo studies of universal four-component fermion systems in one spatial dimension. Continuum few-body observables (i.e., ground-state energies and integrated contact densities) are determined for both unpolarized and polarized systems of up to eight fermions confined to a harmonic trap. Estimates of the continuum energies for four and five trapped fermions show agreement with exact analytic calculations to within approximately one percent statistical uncertainties. Continuum many-body observables are determined for unpolarized systems of up to 88 fermions confined to a finite box, and 56 fermions confined to a harmonic trap. Results are reported for universal quantities such as the Bertsch parameter, defined as the energy of the untrapped many-body system in units of the corresponding free-gas energy, and its subleading correction at large but finite scattering length. Two independent estimates of these quantities are obtained from thermodynamic limit extrapolations of continuum extrapolated observables. A third estimate of the Bertsch parameter is obtained by combining estimates of the untrapped and trapped integrated contact densities with additional theoretical input from a calculation based on Thomas-Fermi theory. All estimates of the Bertsch parameter and its subleading correction are found to be consistent to within approximately one percent statistical uncertainties. Finally, the continuum restoration of virial theorems is verified for both few- and many-body systems confined to a trap.

Lattice Monte Carlo calculations for unitary fermions in a finite box

We perform lattice Monte Carlo simulations for up to 66 unitary fermions in a finite box using a highly improved lattice action for nonrelativistic spin 1/2 fermions. We obtain a value of $0.366^{+0.016}_{-0.011}$ for the Bertsch parameter, defined as the energy of the unitary Fermi gas measured in units of the free gas energy in the thermodynamic limit. In addition, for up to four unitary fermions, we compute the spectrum of the lattice theory by exact diagonalization of the transfer matrix projected onto irreducible representations of the octahedral group for small to moderate size lattices, providing an independent check of our few-body simulation results. We compare our exact numerical and simulation results for the spectrum to benchmark studies of other research groups, as well as perform an extended analysis of our lattice action improvement scheme, including an analysis of the errors associated with higher partial waves and finite temporal discretization.

Lattice Monte Carlo calculations for unitary fermions in a finite box

Lattice Monte Carlo calculations for unitary fermions in a finite box

Nucleon scalar and tensor charges from lattice QCD with light Wilson quarks

We present 2+1 flavor Lattice QCD calculations of the nucleon scalar and tensor charges. Using the BMW clover-improved Wilson action with pion masses between 150 and 350 MeV and three source-sink separations between 0.9 and 1.4 fm, we achieve good control over excited-state contamination and extrapolation to the physical pion mass. As a consistency check, we also present results from calculations using unitary domain wall fermions with pion masses between 300 and 400 MeV, and using domain wall valence quarks and staggered sea quarks with pion masses between 300 and 600 MeV.

Adiabatic sound velocity and compressibility of a trapped d-dimensional ideal anyon gas

The adiabatic sound velocity and compressibility for harmonically trapped ideal anyons in arbitrary dimensions are calculated within Haldane fractional exclusion statistics. The corresponding low-temperature and high-temperature behaviors are studied in detail. To compare with the experimental result of unitary fermions, the sound velocity for anyons in the cigar-shaped trap is derived. The sound velocity for anyons in the disk-shaped trap is also calculated. With the parameter g=0.287, the sound velocity of cigar-shaped unitary fermions modeled by anyons is in good agreement with the experimental result, while that of disk-shaped unitary fermions is v0/vF=0.406 with Fermi velocity vF.

Noise, Sign Problems, and Statistics

We show how sign problems in simulations of many-body systems can manifest themselves in the form of heavy-tailed correlator distributions, similar to what is seen in electron propagation through disordered media. We propose an alternative statistical approach for extracting ground state energies in such systems, illustrating the method with a toy model and with lattice data for unitary fermions.

Lattice Monte Carlo calculations for unitary fermions in a harmonic trap

We present a new lattice Monte Carlo approach developed for studying large numbers of strongly interacting nonrelativistic fermions, and apply it to a dilute gas of unitary fermions confined to a harmonic trap. Our lattice action is highly improved, with sources of discretization and finite volume errors systematically removed; we are able to demonstrate the expected volume scaling of energy levels of two and three untrapped fermions, and to reproduce the high precision calculations published previously for the ground state energies for N = 3 unitary fermions in a box (to within our 0.3% uncertainty), and for N = 3, . . ., 6 unitary fermions in a harmonic trap (to within our ~ 1% uncertainty). We use this action to determine the ground state energies of up to 70 unpolarized fermions trapped in a harmonic potential on a lattice as large as 64^3 x 72; our approach avoids the use of importance sampling or calculation of a fermion determinant and employs a novel statistical method for estimating observables, allowing us to generate ensembles as large as 10^8 while requiring only relatively modest computational resources.

New Field-Theoretic Method for the Virial Expansion

We develop a graphical method for computing the virial expansion coefficients for a nonrelativistic quantum field theory. As an example we compute the third virial coefficient b3 for unitary fermions, a nonperturbative system. By calculating several graphs and performing an extrapolation, we arrive at b3=-0.2930, within 0.7% of a recent computation b3=-0.290 952 95 by Liu, Hu, and Drummond, which involved summing 10,000 energy levels for three unitary fermions in a harmonic trap.

Lattice Monte Carlo calculations for unitary fermions in a harmonic trap

Lattice Monte Carlo calculations for unitary fermions in a harmonic trap