Fermions in anisotropic harmonic trap

We study a few properties of fermions in an anisotropic harmonic trap in absence as well as in presence of an optical lattice. The density of states (DOS) and specific heat of the fermions are studied for different anisotropies. Analytical expressions for the DOS in a strongly anisotropic harmonic trap are derived. For a particular combined potential, where the fermions are hopping in a 3D lattice under a 2D harmonic potential, the Drude weight of the fermionic system is evaluated. The Drude weight is found to be flat in a wide range of fermion concentrations where it is almost temperature independent.     

On the thermodynamics of an ideal fermi gas on the lattice at finite density

We study the ideal gas of fermions on a lattice at finite density for both naive and Wilson fermions. Comparing the thermodynamical quantities thus calculated with the known results in the continuum theory, we are led to propose a modification of the naive form of the lattice action, which is same for both the naive and the Wilson fermions. The thermodynamical quantities, calculated by using this form, are shown to have the correct continuum limit.     

Poisson bracket scheme for vortex dynamics in superfluids and superconductors and the effect of the band structure of the crystal

Poisson brackets for the Hamiltonian dynamics of vortices are discussed for 3 regimes, in which the dissipation can be neglected and the vortex dynamics is reversible: (i) The superclean regime, in which the spectral flow is suppressed. (ii) The regime in which the fermions are pinned by the crystal lattice. This includes the regime of extreme spectral flow of fermions in the vortex core: these fermions are effectively pinned by the normal component. (iii) The case when the vortices are strongly pinned by the normal component. All these limits are described by the single parameter C ₀, the physical meaning of which is discussed for superconductors containing several bands of electrons and holes. The effect of the topology of the Fermi surface on the vortex dynamics is also discussed. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 11, 794–800 (10 December 1996) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Mixtures of correlated bosons and fermions: Dynamical mean‐field theory for normal and condensed phases

We derive a dynamical mean‐field theory for mixtures of interacting bosons and fermions on a lattice (BF‐DMFT). The BF‐DMFT is a comprehensive, thermodynamically consistent framework for the theoretical investigation of Bose‐Fermi mixtures and is applicable for arbitrary values of the coupling parameters and temperatures. It becomes exact in the limit of high spatial dimensions d or coordination number Z of the lattice. In particular, the BF‐DMFT treats normal and condensed bosons on equal footing and thus includes the effects caused by their dynamic coupling. Using the BF‐DMFT we investigate two different interaction models of correlated lattice bosons and fermions, one where all particles are spinless (model I) and one where fermions carry a spin one‐half (model II). In model I the local, repulsive interaction between bosons and fermions can give rise to an attractive effective interaction between the bosons. In model II it can also lead to an attraction between the fermions.     

Chiral symmetry and lattice QCD

Four lectures about chiral symmetry and dynamical fermions in QCD. 1) Chiral symmetry in continuum QCD with an eye toward lattice simulations. 2) Lattice fermions with exact chiral symmetry: staggered fermions, fermions in five dimensions, chiral fermions in four dimensions. 3) A typical lattice simulation from beginning to end: the simulation algorithm, designing observables to measure some desired quantity, analyzing the data. 4) Recent lattice results relevant to chiral symmetry: a mini-review.     

Saddle point mean field calculation in the Hubbard model

Using functional techniques, the Hubbard model consisting of self-coupled lattice fermions is transformed into a bosonic functional integral. In this form it is treated by a mean field approximation in its modern version as a systematic expansion around a saddle point. The method is generalized to the extended Hubbard model.     

Bose-Fermi mixtures in optical lattices

Using mean field theory, we have studied Bose-Fermi mixtures in a one-dimensional optical lattice in the case of an attractive boson-fermion interaction. We consider that the fermions are in the degenerate regime and that the laser intensities are such that quantum coherence across the condensate is ensured. We discuss the effect of the optical lattice on the critical rotational frequency for vortex line creation in the Bose-Einstein condensate, as well as how it affects the stability of the boson-fermion mixture. A reduction of the critical frequency for nucleating a vortex is observed as the strength of the applied laser is increased. The onset of instability of the mixture occurs for a sizably lower number of fermions in the presence of a deep optical lattice.     

Interaction versus dimerization in one-dimensional Fermi systems

In order to study the effect of interaction and lattice distortion on quantum coherence in one-dimensional Fermi systems, we calculate the ground state energy and the phase sensitivity of a ring of interacting spinless fermions on a dimerized lattice. Our numerical DMRG studies, in which we keep up to 1000 states for systems of about 100 sites, are supplemented by analytical considerations using bosonization techniques. We find a delocalized phase for an attractive interaction, which differs from that obtained for random lattice distortions. The extension of this delocalized phase depends strongly on the dimerization induced modification of the interaction. Taking into account the harmonic lattice energy, we find a dimerized ground state for a repulsive interaction only. The dimerization is suppressed at half filling, when the correlation gap becomes large. Received: 11 February 1998 / Revised: 1st April 1998 / Accepted: 30 April 1998     

Lattice fermions in euclidean space-time

A very short proof of a no-go theorem for putting fermions on a lattice is given using the Poincaré-Hopf theorem. The no-go theorem forbids the lattice formulation of theories with handed fermions without species doubling. Examples of such theories are chiral invariant QCD and the Weinberg-Salam-Glashow model. We give arguments why it could be possible to circumvent the no-go theorem by relaxing one of the assumptions, viz. bilinearity of the action in the fermion fields.     

QCD on the lattice and light hadron spectroscopy

Results in lattice Quantum Chromodynamics with fermions are reviewed. Estimates for the hadron spectrum on large lattices without and with light fermion polarization loops are discussed, and the results for different fermion regularizations are compared. The effects of the loops are found to be significant in lattice units, but to a greater part they can be reabsorbed in a redefinition of the overall scale. New estimates for the light quark masses with Wilson fermions are also presented. They differ substantially from previous estimates obtained by other methods in the continuum, and are much smaller. Finally it is argued that staggered fermions can lead to some anomalous results, which arise because of the doubling problem.     

The nuclear Yukawa model on a lattice

We present the results of the quantum field theory approach to the nuclear Yukawa model obtained by standard lattice techniques. We have considered the simplest case of two identical fermions interacting via a scalar meson exchange. Calculations have been performed using Wilson fermions in the quenched approximation. We found the existence of a critical coupling constant above which the model cannot be numerically solved. The range of the accessible coupling constants is below the threshold value for producing two-body bound states. Two-body scattering lengths have been obtained and compared to the non-relativistic results.     

A lattice Dirac operator for QCD with light dynamical quarks

In QCD chiral symmetry is explicitly broken by quark masses, the effect of which can be described reliably by chiral perturbation theory. Effects of explicit chiral symmetry breaking by the lattice regularisation of the Dirac operator, typically parametrised by the residual mass, should be negligible for almost all observables if the residual mass of the Dirac operator is much smaller than the quark mass. However, maintaining a small residual mass becomes increasingly expensive as the quark mass decreases towards the physical value and the continuum limit is approached. We investigate the feasibility of using a new approximately chiral Dirac operator with a small residual mass as an alternative to overlap and domain wall fermions for lattice simulations. Our Dirac operator is constructed from a Zolotarev rational approximation for the matrix sign function that is optimal for bulk modes of the hermitian kernel Dirac operator but not for the low-lying parts of its spectrum. We test our operator on various ³²³×64${32}^3\times 64$ lattices, comparing the residual mass and the performance of the Hybrid Monte Carlo algorithm at a similar lattice spacing and pion mass with a hyperbolic tangent operator as used by domain wall fermions. We find that our approximations have a significantly smaller residual mass than domain wall fermions at a similar computational cost, and still admit topological charge change.     

Simulation and detection of dirac fermions with cold atoms in an optical lattice

We propose an experimental scheme to simulate and observe relativistic Dirac fermions with cold atoms in a hexagonal optical lattice. By controlling the lattice anisotropy, one can realize both massive and massless Dirac fermions and observe the phase transition between them. Through explicit calculations, we show that both the Bragg spectroscopy and the atomic density profile in a trap can be used to demonstrate the Dirac fermions and the associated phase transition.     

A chiral invariant decoupling of replica lattice fermions

A chiral invariant lattice fermion action which solves the species-doubling problem of Dirac fermions on a lattice for (even) dimensions of space-time less than eight is presented. The decoupling of replica fermions requires to give up rotational and gauge symmetry in the regularization procedure. The corresponding lattice Schwinger model reproduces all the results of the continuum theory.     

A strongly attractive Fermi gas in an optical lattice

We study strongly attractive fermions in an optical lattice superimposed by a trapping potential. We calculate the densities of fermions and condensed bound molecules at zero temperature. There is a competition between dissociated fermions and molecules leading to a reduction of the density of fermions at the trap center.     

Fermionic Representation of Two-Dimensional Dimer Models

Dimer models in two dimensions give rise to well-known statistical lattice problems, which can be exactly solved by the same combinatorial techniques associated with the Ising model and which have been used to account for the phase transitions in a number of physically interesting systems. More recently, dimer models have been regarded as classical limits of the quantum ground state of some antiferromagnetic systems. We then revisit an early transfer-matrix calculation for the dimer model on the simple square lattice. We write a spin representation for the transfer matrix associated with the canonical partition function of two paradigmatic dimers models, on the 4–8 lattice, with an Ising-type transition, and on the brick lattice, with a peculiar commensurate–incommensurate transition. Using standard techniques, the problem is reduced to the calculation of the eigenvalues of a system of free fermions.     

Negative-energy spinors and the Fock space of lattice fermions at finite chemical potential

Recently it was suggested that the problem of species doubling with Kogut-Susskind lattice fermions entails, at finite chemical potential, a confusion of particles with antiparticles. What happens instead is that the familiar correspondence of positive-energy spinors to particles, and of negative-energy spinors to antiparticles, ceases to hold for the Kogut-Susskind time derivative. To show this we highlight the role of the spinorial “energy” in the Osterwalder-Schrader reconstruction of the Fock space of non-interacting lattice fermions at zero temperature and nonzero chemical potential. We consider Kogut-Susskind fermions and, for comparison, fermions with an asymmetric one-step time derivative.     

Topological susceptibility in lattice QCD with unimproved Wilson fermions

We address a long standing problem regarding topology in lattice simulations of QCD with unimproved Wilson fermions. Earlier attempt with unimproved Wilson fermions at β=5.6 to verify the suppression of topological susceptibility with decreasing quark mass (mq) was unable to unambiguously confirm the suppression. We carry out systematic calculations for two degenerate flavours at two different lattice spacings (β=5.6 and 5.8). The effects of quark mass, lattice volume and the lattice spacing on the spanning of different topological sectors are presented. We unambiguously demonstrate the suppression of the topological susceptibility with decreasing quark mass, expected from chiral Ward identity and chiral perturbation theory.     

Bose-fermi mixtures in a three-dimensional optical lattice

We have studied mixtures of fermionic (40)K and bosonic (87)Rb quantum gases in a three-dimensional optical lattice. We observe that an increasing admixture of the fermionic species diminishes the phase coherence of the bosonic atoms as measured by studying both the visibility of the matter wave interference pattern and the coherence length of the bosons. Moreover, we find that the attractive interactions between bosons and fermions lead to an increase of the boson density in the lattice which we measure by studying three-body recombination in the lattice. In our data, we do not observe three-body loss of the fermionic atoms. An analysis of the thermodynamics of a noninteracting Bose-Fermi mixture in the lattice suggests a mechanism for sympathetic cooling of the fermions in the lattice.