Monopoles in gluodynamics and blocking from continuum to lattice

We review the method of blocking of topological defects from continuum to lattice as a nonperturbative tool to construct effective actions for these defects. The actions are formulated in the continuum limit, while the couplings of these actions can be derived from simple observables calculated numerically on lattices with a finite lattice spacing. We demonstrate the success of the method in deriving the effective actions for Abelian monopoles in the pure SU(2) gauge models in an Abelian gauge. In particular, we discuss the gluodynamics in three and four spacetime dimensions at zero and nonzero temperatures. Besides the action, the quantities of our interest are the monopole density, the magnetic Debye mass, and the monopole condensate.     

Vortex-antivortex lattice in ultracold fermionic gases

We discuss ultracold Fermi gases in two dimensions, which could be realized in a strongly confining one-dimensional optical lattice. We obtain the temperature versus effective interaction phase diagram for an s-wave superfluid and show that, below a certain critical temperature Tc, spontaneous vortex-antivortex pairs appear for all coupling strengths. In addition, we show that the evolution from weak-to-strong coupling is smooth, and that the system forms a square vortex-antivortex lattice at a lower critical temperature TM.     

Novel probe of the vacuum of the lattice gluodynamics

We introduce the notion of a minimal number of negative links on the lattice for a given original configuration of SU(2) fields. Negative links correspond to a large potential, not necessarily to large action. The idea is that the minimal number of negative links is a gauge invariant notion. To verify this hypothesis, we measure the correlator of two negative links, averaged over all the directions, as a function of the distance between the links. The inverse correlation length coincides within the error bars with the lightest glueball mass.     

Symmetry properties of fermionic bilinears in lattice QCD

The 256 fermionic bilinears $\text{ψ}\text{γTψ}$ appearing in the Kogut-Susskind/Kähler-Dirac theory are classified into representations of the hypercubic rotation reflection group; charge conjugation and U(1)_A are also considered. Applications to the study of the normalization of lattice currents are suggested.     

Molecules of fermionic atoms in an optical lattice

We create molecules from fermionic atoms in a three-dimensional optical lattice using a Feshbach resonance. In the limit of low tunneling, the individual wells can be regarded as independent three-dimensional harmonic oscillators. The measured binding energies for varying scattering length agree excellently with the theoretical prediction for two interacting atoms in a harmonic oscillator. We demonstrate that the formation of molecules can be used to measure the occupancy of the lattice and perform thermometry.     

Topological superfluid in a fermionic bilayer optical lattice

In this paper, a topological superfluid phase with Chern number ?? = ±1, possessing gapless edge states and non-Abelian anyonsis designed in a ?? = ±1 topological insulator proximity to ans-wave superfluid on an optical lattice with the effective gauge fieldand layer-dependent Zeeman field coupled to ultracold fermionic atoms’ pseudo spin. Wealso study its topological properties and calculate the phase stiffness by using therandom-phase-approximation approach. Finally we derive the temperature of theKosterlitz-Thouless transition by means of renormalized group theory. Owning to theexistence of non-Abelian anyons, this ?? = ±1 topological superfluid may be a possible candidate fortopological quantum computation.     

Distribution for fermionic discrete lattice gas within the canonical ensemble

The distinct deviations from the Fermi-Dirac statistics ascertained recently at low temperatures for a one-dimensional, spinless fermionic discrete lattice gas with conserved number of noninteracting particles hopping on the non-degenerated, well-separated single-particle energy levels are studied in numerical and theoretical terms. The generalized distribution is derived in the formn(h)={Y _h exp [(_h–)]+1{su–1 valid even in the thermodynamic limit, when the discreteness of the energy levels is kept. This distribution demonstrates good agreement with the data obtained numerically both by the canonical partition function technique and by Monte Carlo simulation.     

Dissipation-induced d-wave pairing of fermionic atoms in an optical lattice

We show how dissipative dynamics can give rise to pairing for two-component fermions on a lattice. In particular, we construct a parent Liouvillian operator so that a BCS-type state of a given symmetry, e.g., a d-wave state, is reached for arbitrary initial states in the absence of conservative forces. The system-bath couplings describe single-particle, number-conserving and quasilocal processes. The pairing mechanism crucially relies on Fermi statistics. We show how such Liouvillians can be realized via reservoir engineering with cold atoms representing a driven dissipative dynamics.     

Chiral magnetic effect in SU(2) lattice gluodynamics at zero temperature

The chiral magnetic effect is the appearance of a quark electric current along a magnetic-field direction in topologically nontrivial gauge fields. There is evidence that this effect is observed in collisions between heavy ions at the RHIC collider. The features of the chiral magnetic effect in SU(2) lattice gluodynamics at zero temperature have been investigated. It has been found that the electric current increases in the magnetic-field direction owing to quantum fluctuations of gluon fields. Fluctuations of the local charge density and chirality also increase with the magnetic field strength, which is a signature of the chiral magnetic effect.     

Effective monopole potential for SU(2) lattice gluodynamics in the spatial maximal Abelian gauge

We investigate the dual superconductor hypothesis in finite-temperature SU(2) lattice gluodynamics in the spatial maximal Abelian gauge. This gauge is more physical than the ordinary maximal Abelian gauge due to absence of nonlocalities in the temporal direction. We show numerically that in the spatial maximal Abelian gauge the probability distribution of the Abelian monopole field is consistent with the dual superconductor mechanism of confinement: the Abelian condensate vanishes in the deconfinement phase and is nonzero in the confinement phase. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 3, 166–170 (10 February 1999) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Calculation of the viscosity of SU(2) gluodynamics with the lattice simulation

The viscosity of SU(2) gluodynamics within the simulation of the lattice quantum chromodynamics at a temperature of T/T _c = 1.2 has been calculated with the Kubo formula relating the viscosity to the spectral function of the correlation function of the energy-momentum tensor. The correlation function of the energy-momentum tensor has been calculated using the numerical simulation of the lattice SU(2) gluodynamics on supercomputers.     

Evidence for diquarks in lattice QCD

Diquarks may play an important role in hadron spectroscopy, baryon decays, and color superconductivity. We investigate the existence of diquark correlations in lattice QCD by considering systematically all the lowest energy diquark channels in a color gauge-invariant setup. We measure mass differences between the various channels and show that the positive parity scalar diquark is the lightest. Quark-quark correlations inside the diquark are clearly seen in this channel, and yield a diquark size of O(1) fm.     

Quantum phase transitions of fermionic atoms in an anisotropic triangular optical lattice

The effect of anisotropy caused by a confining potential on the properties of fermionic cold atoms in a triangular optical lattice is systematically investigated by using the dynamical cluster approximation combined with the continuous time quantum Monte–Carlo algorithm.The quantum phase diagrams which reflect the temperature–interaction relation and the competition between the anisotropic parameter and the interaction are presented with full consideration of the anisotropy of the system.Our results show that the system undergoes a transition from Fermi liquid to Mott insulator when the repulsive interaction reaches a critical value.The Kondo effect also can be observed in this system and the pseudogap is suppressed at low temperatures due to the Kondo effect.A feasible experiment protocol to observe these phenomena in an anisotropic triangular optical lattice with cold atoms is proposed,in which the hopping terms are closely related to the lattice confining potential and the atomic interaction can be adjusted via the Feshbach resonance.     

Majorana modes and topological superfluids for ultracold fermionic atoms in anisotropic square optical lattices

Motivated by the recent experimental realization of two-dimensional spin-orbit couplingthrough optical Raman lattice scheme, we study attractive interacting ultracold gases withspin-orbit interaction in anisotropic square optical lattices, and find that richs-wavetopological superfluids can be realized, including Z₂ topological superfluids beyondthe characterization of “tenfold way” in addition to chiral topological superfluids. Thetopological defects-superfluid vortex and edge dislocations-may host Majorana modes insome topological superfluids, which are helpful for realizing topological quantumcomputation and Majorana fermionic quantum computation. In addition, we also discuss theBerezinsky-Kosterlitz-Thouless phase transitions for different topologicalsuperfluids.     

Localization of bosonic atoms by fermionic impurities in a three-dimensional optical lattice

We observe a localized phase of ultracold bosonic quantum gases in a 3-dimensional optical lattice induced by a small contribution of fermionic atoms acting as impurities in a Fermi-Bose quantum gas mixture. In particular, we study the dependence of this transition on the fermionic (40)K impurity concentration by a comparison to the corresponding superfluid to Mott-insulator transition in a pure bosonic (87)Rb gas and find a significant shift in the transition parameter. The observed shift is larger than expected based on a simple mean-field argument, which indicates that disorder-related effects play a significant role.     

Multiloop modular invariance of the covariant lattice construction of fermionic strings

A simple proof of multiloop modular invariance is given for all ten- and lower-dimensional string theories that can be obtained with the covariant lattice construction.