Improved lattice operators for nonrelativistic fermions

In this work I apply a recently proposed improvement procedure, originally conceived to reduce finite lattice-spacing effects in transfer matrices for dilute Fermi systems, to tuning operators for the calculation of observables. I construct, in particular, highly improved representations for the energy and the contact as a first step in an improvement program for finite-temperature calculations. I illustrate the effects of improvement on those quantities with a ground-state lattice calculation at unitarity

Advances in non-relativistic matter via complex Langevin approaches

The recent progress in understanding the mathematics of complex stochastic quantization, as well as its application to quantum chromodynamics in situations that have a complex phase problem (e.g. finite quark density, real time), has opened up an intriguing possibility for non-relativistic many-body physics which has so far remained largely unexplored. In this brief contribution, I review a few specific examples of advances in the characterization of the thermodynamics of non-relativistic matter in a variety of one-dimensional cases affected by the sign problem: repulsive interactions, finite polarization, finite mass imbalance, and projection to finite systems to obtain virial coefficients

Strongly coupled Graphene on the Lattice

The two-dimensional carbon allotrope graphene has recently attracted a lot of attention from researchers in the disciplines of Lattice Field Theory, Lattice QCD and Monte Carlo calculations. This interest has been prompted by several remarkable properties of the conduction electrons in graphene. For instance, the conical band structure of graphene at low energies is strongly reminiscent of relativistic Dirac fermions. Also, due the low Fermi velocity of vF ≃ c/300, where c is the speed of light in vacuum, the physics of the conduction electrons in graphene is qualitatively similar to Quantum Electrodynamics in a strongly coupled regime. In turn, this opens up the prospect of the experimental realization of gapped, strongly correlated states in the electronic phase diagram of graphene. Here, we review the experimental and theoretical motivations for Lattice Field Theory studies of graphene, and describe the directions that such research is likely to progress in during the next few years. We also give a brief overview of the two main lattice theories of graphene, the hexagonal Hubbard theory and the low-energy Dirac theory. Finally, we describe the prospect of extracting response functions, such as the electric conductivity, using Lattice Field Theory calculations

Interacting bosons at finite angular momentum via complex langevin

Quantum field theories with a complex action suffer from a sign problem in stochastic nonpertur-bative treatments, making many systems of great interest – such as polarized or mass-imbalanced fermions and QCD at finite baryon density – extremely challenging to treat numerically. Another such system is that of bosons at finite angular momentum; experimentalists have successfully achieved vortex formation in ultracold bosonic atoms, and have measured quantities of interest such as density profiles and the moment of inertia. However, the treatment of superfluids requires the use of complex bosons, making the usual numerical methods unusable. In this work, we apply complex Langevin, a method that has gained much attention in lattice QCD, to the calculation of basic properties of interacting bosons at finite angular momentum. We show preliminary results for the angular momentum and moment of inertia and benchmark calculations in the noninteracting limit

Exact-exchange density functional theory for neutron drops

We compute the ground-state properties of finite systems of neutrons in an external harmonic trap, interacting via the Minnesota potential, using the "exact-exchange" form of orbital-dependent density functional theory. We compare our results with Hartree-Fock calculations and find very close agreement. Within the context of the interaction studied, we conclude that this simple orbital-dependent functional brings conventional nuclear density functional theory to the level of Hartree-Fock in an ab initio fashion. Our work is a first step toward higher order ab initio nuclear functionals based on realistic nucleon-nucleon interactions

Critical exponents of the semimetal-insulator transition in graphene: A Monte Carlo study

The low-energy theory of graphene exhibits spontaneous chiral symmetry breaking due to pairing of quasiparticles and holes, corresponding to a semimetal-insulator transition at strong Coulomb coupling. We report a lattice Monte Carlo study of the critical exponents of this transition as a function of the number of Dirac flavors Nf, finding δ=1.25±0.05 for Nf =0, δ=2.26±0.06 for Nf =2 and δ=2.62±0.11 for Nf =4, with γ1 throughout. We compare our results with recent analytical work for graphene and closely related systems and discuss scenarios for the fate of the chiral transition at finite temperature and carrier density, an issue of relevance for upcoming experiments with suspended graphene samples

Exact-exchange density functional theory for neutron drops

We compute the ground-state properties of finite systems of neutrons in an external harmonic trap, interacting via the Minnesota potential, using the "exact-exchange" form of orbital-dependent density functional theory. We compare our results with Hartree-Fock calculations and find very close agreement. Within the context of the interaction studied, we conclude that this simple orbital-dependent functional brings conventional nuclear density functional theory to the level of Hartree-Fock in an ab initio fashion. Our work is a first step toward higher order ab initio nuclear functionals based on realistic nucleon-nucleon interactions

Fermi-Fermi crossover in the ground state of one-dimensional few-body systems with anomalous three-body interactions

In one spatial dimension, quantum systems with an attractive three-body contact interaction exhibit a scale anomaly. In this work, we examine the few-body sector for up to six particles. We study those systems with a self-consistent, nonperturbative, iterative method in the subspace of zero total momentum. Exploiting the structure of the contact interaction, the method reduces the complexity of obtaining the wave function by three powers of the dimension of the Hilbert space. We present results on the energy, momentum, and spatial structure, as well as Tan's contact. We find a Fermi-Fermi crossover interpolating between large, weakly bound trimers and compact, deeply bound trimers: at weak coupling, the behavior is captured by degenerate perturbation theory; at strong coupling, the system is governed by an effective theory of heavy trimers (plus free particles in the case of asymmetric systems). Additionally, we find that there is no trimer-trimer attraction and therefore no six-body bound state

Fourth- And Fifth-Order Virial Coefficients from Weak Coupling to Unitarity

In the current era of precision quantum many-body physics, one of the most scrutinized systems is the unitary limit of the nonrelativistic spin-1/2 Fermi gas, due to its simplicity and relevance for atomic, condensed matter, and nuclear physics. The thermodynamics of this strongly correlated system is determined by universal functions which, at high temperatures, are governed by universal virial coefficients bn that capture the effects of the n-body system on the many-body dynamics. Currently, b2 and b3 are well understood, but the situation is less clear for b4, and no predictions have been made for b5. To answer these open questions, we implement a nonperturbative analytic approach based on the Trotter-Suzuki factorization of the imaginary-time evolution operator, using progressively finer temporal lattice spacings. By means of these factorizations and automated algebra codes, we obtain the interaction-induced change Δbn from weak coupling to unitarity. At unitarity, we find that Δb3=-0.356(4) in agreement with previous results, Δb4=0.062(2), which is in agreement with all previous theoretical estimates but at odds with experimental determinations, and Δb5=0.078(6), which is a prediction. We show the impact of those answers on the density equation of state and Tan contact, and trace their origin back to their polarized and unpolarized components

Renormalization group flow of quartic perturbations in graphene: Strong coupling and large- N limits

We explore the renormalization group flow of quartic perturbations in the low-enegy theory of graphene, in the strong Coulomb coupling and large- N limits, where N is the number of fermion flavors. We compute the anomalous dimensions of the quartic couplings u up to leading order in 1 N and find both relevant and irrelevant directions in the space of quartic couplings. We discuss possible phase diagrams and relevance for the physics of graphene