arXiv subjects

Joaquín E. Drut

Publications and source records attributed to Joaquín E. Drut.

51 records · Page 3Linked to original sources

arXiv2012

Shear Viscosity of a Unitary Fermi Gas

We present the first ab initio determination of the shear viscosity eta of the Unitary Fermi Gas, based on finite temperature quantum Monte Carlo calculations and the Kubo linear-response formalism. We determine the temperature dependence of the shear viscosity to entropy density ratio eta/s. The minimum of eta/s appears to be located above the critical temperature for the superfluid-to-normal phase transition with the most probable value being eta/s approx 0.2 hbar/kB, which almost saturates the Kovtun-Son-Starinets universal value hbar/(4 pi kB).

cond-mat.quant-gas↗

arXiv2012

Improved lattice operators for non-relativistic 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.

cond-mat.stat-mech↗

arXiv2012

The Equation of State of the Unitary Fermi Gas: An Update on Lattice Calculations

The thermodynamic properties of the unitary Fermi gas (UFG) have recently been measured to unprecedented accuracy at the MIT. In particular, these measurements provide an improved understanding of the regime below T/eF ~ 0.20, where a transition into a superfluid phase occurs. In light of this development, we present an overview of state-of-the-art auxiliary field quantum Monte Carlo (AFQMC) results for the UFG at finite temperature and compare them with the MIT data for the energy, chemical potential, and density. These AFQMC results have been obtained using methods based on the hybrid Monte Carlo (HMC) algorithm, which was first introduced within the context of lattice QCD.

cond-mat.quant-gas↗

arXiv2011

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 v_F = 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.

hep-lat↗

arXiv2011

The unitary Fermi gas at finite temperature: momentum distribution and contact

The Unitary Fermi Gas (UFG) is one of the most strongly interacting systems known to date, as it saturates the unitarity bound on the quantum mechanical scattering cross section. The UFG corresponds to a two-component Fermi gas in the limit of short interaction range and large scattering length, and is currently realized in ultracold-atom experiments via Feshbach resonances. While easy to define, the UFG poses a challenging quantum many-body problem, as it lacks any characteristic scale other than the density. As a consequence, accurate quantitative predictions of the thermodynamic properties of the UFG require Monte Carlo calculations. However, significant progress has also been made with purely analytical methods. Notably, in 2005 Tan derived a set of exact thermodynamic relations in which a universal quantity known as the "contact" C plays a crucial role. Recently, C has also been found to determine the prefactor of the high- frequency power-law decay of correlators as well as the right-hand-sides of shear- and bulk viscosity sum rules. The contact is therefore a central piece of information on the UFG in equilibrium as well as away from equilibrium. In this talk we describe some of the known aspects of Fermi gases at and around unitarity, show our latest Monte Carlo results for the contact at finite temperature, and summarize the open questions in the field, some of which we are starting to answer using large-scale Monte Carlo calculations by adapting methods from Lattice QCD.

hep-lat↗

arXiv2011

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 towards higher-order ab initio nuclear functionals based on realistic nucleon-nucleon interactions.

nucl-th↗

arXiv2011

Momentum Distribution and Contact of the Unitary Fermi gas

We calculate the momentum distribution n(k) of the Unitary Fermi Gas using Quantum Monte Carlo calculations at finite temperature T/ε_F as well as in the ground state. At large momenta k/k_F, we find that n(k) falls off as C/k^4, in agreement with the Tan relations. From the asymptotics of n(k), we determine the contact C as a function of T/ε_F and present a comparison with theory. At low T/ε_F, we find that C increases with temperature, and we tentatively identify a maximum around T/ε_F \simeq 0.4. Our calculations are performed on lattices of spatial extent up to N_x = 14 with a particle number per unit volume of \simeq 0.03 - 0.07.

cond-mat.stat-mech↗

arXiv2010

Graphene: from materials science to particle physics

Since its discovery in 2004, graphene, a two-dimensional hexagonal carbon allotrope, has generated great interest and spurred research activity from materials science to particle physics and vice versa. In particular, graphene has been found to exhibit outstanding electronic and mechanical properties, as well as an unusual low-energy spectrum of Dirac quasiparticles giving rise to a fractional quantum Hall effect when freely suspended and immersed in a magnetic field. One of the most intriguing puzzles of graphene involves the low-temperature conductivity at zero density, a central issue in the design of graphene-based nanoelectronic components. While suspended graphene experiments have shown a trend reminiscent of semiconductors, with rising resistivity at low temperatures, most theories predict a constant or even decreasing resistivity. However, lattice field theory calculations have revealed that suspended graphene is at or near the critical coupling for excitonic gap formation due to strong Coulomb interactions, which suggests a simple and straightforward explanation for the experimental data. In this contribution we review the current status of the field with emphasis on the issue of gap formation, and outline recent progress and future points of contact between condensed matter physics and Lattice QCD.

hep-lat↗

arXiv2010

Preconditioning the non-relativistic many-fermion problem

Preconditioning is at the core of modern many-fermion Monte Carlo algorithms, such as Hybrid Monte Carlo, where the repeated solution of a linear problem involving an ill-conditioned matrix is needed. We report on a performance comparison of three preconditioning strategies, namely Chebyshev polynomials, strong-coupling approximation and weak-coupling expansion. We use conjugate gradient (CG) on the normal equations as well as stabilized biconjugate gradient (BiCGStab) as solvers and focus on the fermion matrix of the unitary Fermi gas. Our results indicate that BiCGStab is by far the most efficient strategy, both in terms of the number of iterations and matrix-vector operations.

hep-lat↗

arXiv2010

Toward large-scale Hybrid Monte Carlo simulations of the Hubbard model on graphics processing units

The performance of the Hybrid Monte Carlo algorithm is determined by the speed of sparse matrix-vector multiplication within the context of preconditioned conjugate gradient iteration. We study these operations as implemented for the fermion matrix of the Hubbard model in d+1 space-time dimensions, and report a performance comparison between a 2.66 GHz Intel Xeon E5430 CPU and an NVIDIA Tesla C1060 GPU using double-precision arithmetic. We find speedup factors ranging between 30-350 for d = 1, and in excess of 40 for d = 3. We argue that such speedups are of considerable impact for large-scale simulational studies of quantum many-body systems.

cond-mat.stat-mech↗

arXiv2010

Signatures of a gap in the conductivity of graphene

The electrical conductivity of suspended graphene has recently been measured for the first time, and found to behave as σ~ \sqrt{|n|} as expected for Dirac quasiparticles at large carrier density. The charge inhomogeneity is strongly reduced in suspended samples, which revealed an unexpected insulating trend in σ(T). Above a transitional density n*, the temperature dependence was found to revert to metallic. We show that these features of the DC conductivity are consistent with a simple model of gapped Dirac quasiparticles, with specific signatures of a gap in the vicinity of the charge-neutrality point. Our findings are reminiscent of the conductivity profile in semiconducting materials, exhibiting a thermal activation for T \geq \tilde T and a weakly T-dependent background for T \leq \tilde T, where \tilde T is given by the saturation density \tilde n associated with the residual charge inhomogeneity. We discuss possible origins of a bandgap in graphene as well as alternative scenarios.

cond-mat.str-el↗

arXiv2010

First-order chiral transition in the compact lattice theory of graphene and the case for improved actions

A comparison of the compact and non-compact lattice versions of the low-energy theory of graphene is presented. The compact theory is found to exhibit a chiral phase transition which appears to be of first order, at a critical coupling of beta_c = 0.42 +/- 0.01. We confirm that the non-compact theory exhibits a second-order transition at beta_c = 0.072 +/- 0.003, and determine the effects of UV-divergent tadpole contributions in both cases. Upon tadpole improvement of the non-compact theory we find beta_c^{TI} = 0.163 +/- 0.002, which strengthens the case for a semimetal-insulator transition in graphene at strong Coulomb coupling. Finally, we highlight the need for systematic studies using improved lattice actions.

cond-mat.str-el↗

arXiv2009

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 $N_f^{}$, finding $δ= 1.25 \pm 0.05$ for $N_f^{} = 0$, $δ= 2.26 \pm 0.06$ for $N_f^{} = 2$ and $δ= 2.62 \pm 0.11$ for $N_f^{} = 4$, with $γ\simeq 1$ 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.

cond-mat.str-el↗

arXiv2009

Lattice field theory simulations of graphene

We discuss the Monte Carlo method of simulating lattice field theories as a means of studying the low-energy effective theory of graphene. We also report on simulational results obtained using the Metropolis and Hybrid Monte Carlo methods for the chiral condensate, which is the order parameter for the semimetal-insulator transition in graphene, induced by the Coulomb interaction between the massless electronic quasiparticles. The critical coupling and the associated exponents of this transition are determined by means of the logarithmic derivative of the chiral condensate and an equation-of-state analysis. A thorough discussion of finite-size effects is given, along with several tests of our calculational framework. These results strengthen the case for an insulating phase in suspended graphene, and indicate that the semimetal-insulator transition is likely to be of second order, though exhibiting neither classical critical exponents, nor the predicted phenomenon of Miransky scaling.

cond-mat.str-el↗

arXiv2009

Is graphene in vacuum an insulator?

We present evidence, from Lattice Monte Carlo simulations of the phase diagram of graphene as a function of the Coulomb coupling between quasiparticles, that graphene in vacuum is likely to be an insulator. We find a semimetal-insulator transition at $α_g^\text{crit} = 1.11 \pm 0.06$, where $α_g^{} \simeq 2.16$ in vacuum, and $α_g^{} \simeq 0.79$ on a SiO$_2^{}$ substrate. Our analysis uses the logarithmic derivative of the order parameter, supplemented by an equation of state. The insulating phase disappears above a critical number of four-component fermion flavors $4 < N_f^{\text{crit}} < 6$. Our data are consistent with a second-order transition.

cond-mat.str-el↗