Isotropic majority-vote model on a square lattice

The stationary critical properties of the isotropic majority vote model on a square lattice are calculated by Monte Carlo simulations and finite size analysis. The critical exponents, , and are found to be the same as those of the Ising model and the critical noise parameter is found to beq _c =0.075±0.001.     

Phonon softening and dispersion in the 1D Holstein model of spinless fermions

We investigate the effect of electron-phonon interaction on the phononic properties in the one-dimensional half-filled Holstein model of spinless fermions. By means of determinantal Quantum Monte Carlo simulation we show that the behavior of the phonon dynamics gives a clear signal of the transition to a charge-ordered phase, and the phase diagram obtained in this way is in excellent agreement with previous DMRG results. By analyzing the phonon propagator we extract the renormalized phonon frequency, and study how it first softens as the transition is approached and then subsequently hardens in the charge-ordered phase. We then show how anharmonic features develop in the phonon propagator, and how the interaction induces a sizable dispersion of the dressed phonon in the non-adiabatic regime.     

Finite clusters of fast-rotating spinless bosons in a harmonic trap

Rapidly rotating two-dimensional ultracold Bose–Einstein condensates of spinless bosons in a harmonic trap have attracted considerable interest during the recent years. It is expected that, in the fast-rotation limit, the system of bosons will exhibit collective behavior similar to that of two-dimensional electrons in the fractional quantum Hall effect regime. It is predicted that the most robust correlated bosonic state in this regime will be the Bose Laughlin state at a half filling factor. An exact treatment of such a state is generally a formidable task due to the inherent many-particle nature of the wave function. We report in this work that a transformation to Jacobi coordinates allows one to obtain much desirable exact analytic closed-form expressions for various quantities of interest corresponding to a Bose Laughlin wave function for various finite systems of particles.     

On the chiral limit in lattice gauge theories with Wilson fermions

The chiral limit κ ? κ _c (β) in lattice gauge theories with Wilson fermions and problems related to near-to-zero (’exceptional’) eigenvalues of the fermionic matrix are studied. For this purpose we employ compact lattice QED in the confinement phase. A new estimator $\tilde m_\pi$ for the calculation of the pseudoscalar mass m _π is proposed which does not suffer from ’divergent’ contributions at κ ? κ _c (β)We conclude that the main contribution to the pion mass comes from larger modes, and ’exceptional’ eigenvalues play no physical role. The behaviour of the subtracted chiral condensate $\left\langle {\bar \psi \psi } \right\rangle _{subt}$ near κ _c (β) is determined. We observe a comparatively large value of $\left\langle {\bar \psi \psi } \right\rangle _{subt} \cdot Z_P^{ - 1}$ , which could be interpreted as a possible effect of the quenched approximation.     

Unified treatment of fermions and bosons

Dirac's matrices can be interpreted as an 8-rank covariant antisymmetric tensor field on an 11-dimensional manifold (space-time ×S ⁷) enforcing a linkage between the Lorentz transformation and rotations ofS ⁷, conferring spinorial properties on any quantity having an index in the inner spaceS ⁷.     

Three-state majority-vote model on square lattice

Here, a non-equilibrium model with two states (−1,+1) and a noise q on simple square lattices proposed for M.J. Oliveira (1992) following the conjecture of up-down symmetry of Grinstein and colleagues (1985) is studied and generalized. This model is well-known, today, as the majority-vote model. They showed, through Monte Carlo simulations, that their obtained results fall into the universality class of the equilibrium Ising model on a square lattice. In this work, we generalize the majority-vote model for a version with three states, now including the zero state, (−1,0,+1) in two dimensions. Using Monte Carlo simulations, we showed that our model falls into the universality class of the spin-1 (−1,0,+1) and spin-1/2 Ising model and also agree with majority-vote model proposed for M.J. Oliveira (1992). The exponent ratio obtained for our model was γ/ν=1.77(3), β/ν=0.121(5), and 1/ν=1.03(5). The critical noise obtained and the fourth-order cumulant were q_c=0.106(5) and U^∗=0.62(3).     

Correlated fermions on a checkerboard lattice

A model of strongly correlated spinless fermions on a checkerboard lattice is mapped onto a quantum fully packed loop model. We identify a large number of fluctuationless states specific to the fermionic case. We also show that for a class of fluctuating states the fermionic sign problem can be gauged away. This claim is supported by numerical evaluation of the low-lying states. Furthermore, we analyze excitations at the Rokhsar-Kivelson point of this model using the relation to the height model and the single-mode approximation.     

Susskind fermions on a euclidean lattice

A version of euclidean lattice QCD obtained by introducing the fermions using Susskind's method is described and certain properties discussed. A U(1) axial current having the correct axial anomaly in the continuum limit is identified. We find $\text{Λ}{}_{\mathrm{<mtext>min</mtext>}}\text{Λ}{}_{\mathrm{<mtext>L,Suss</mtext>}}\text{= 28.78}$ for SU(3) with 4 flavors.     

Interacting fermions on a random lattice

We extend previous work on the properties of the Dirac lagrangian on two-dimensional random lattices to the case where interaction terms are included. Although for free fermions the chiral symmetry of the doubles is spontaneously broken by their interaction with the lattice and they decouple from long-distance physics, our results in this paper show that all is undone by quantum corrections in an interacting field theory and that the end result is very similar to what is found with Wilson fermions. Two field-theoretical models with interacting fermions are studied by perturbation expansion in the field theory coupling constant. These are a model with one fermion and one boson species interacting via a scalar Yukawa coupling and the massive Thirring model. It is shown that on the random lattice ultraviolet finite diagrams and finite parts of ultraviolet divergent diagrams have the correct continuum limit. Ultraviolet divergent parts can be removed by the same renormalisation procedure as in the continuum, but do not exhibit the same dependence on the lagrangian mass. In the case of the massive Thirring model this causes a fermion mass correction of order the cut-off scale, which breaks the chiral symmetry of the remaining light fermion; there is consequently a fine-tuning problem. In the context of the same model we discuss the effect of the Goldstone boson associated with the spontaneous breakdown of the chiral symmetry of the doubles on two-dimensional models with vector couplings.     

The bond bending model on triangular lattice and square lattice

The bond bending model is studied using the series expansion method on a triangular lattice and on a square lattice. The elastic splay susceptibility χ_SR and the elastic compressional susceptibility χ_el are calculated up to 11th order for the triangular lattice and up to 14th order for the square lattice. The elastic splay crossover exponent, ζ_SP, is found to be ζ_SP ≈ 1.26 ± 0.05 for the triangular lattice and ζ_SP = 1.30 ± 0.04 for the square lattice which is close to the conductivity exponent, ζ_Re, of the resistor network. From the scaling relation ? _B = dv + ζ_SP, we found that the bulk modulus exponent ? _B = 3.93 ± 0.05 for the triangular lattice and ? _B = 3.97 ± 0.04 for the square lattice which is in good agreement with the result ? _B = 3.96 ± 0.04, obtained by Zabolitzky et al. using a transfer matrix technique on a honeycomb lattice.     

Mott transition and sign problem for a model of lattice fermions

We consider a model of spinless fermions on the square latticeZ ² with an interaction potential of strengthU>0 at distance one and strengthJ at distance two, in the largeU limit |t|, |J|U, wheret is the hopping amplitude. As the chemical potential is varied, ift=T=0 we find three different phases corresponding to full, half and zero filling fractions. We study the system at low temperatureT0 by a method involving a canonical transformation and a functional integral representation. IfT=0 we locate the phase boundaries of the Mott metal-insulator transition for all |J|U with upper and lower bounds, show that mean field theory is valid ifJ<0 but fails forJ=0 when also the Peierls condition is violated. This result is a quantum extension of the Pirogov-Sinai theory of phase transitions. IfT>0 we have only one sided bounds for the phase boundaries and we can't validate mean field theory in caseJ<0. We introduce a new resummation scheme for low temperature expansions which yields finite and convergent perturbation series and permits us to study issues like the sign problem. Our algorithm gives an optimal canonical transformation for the functional integral such that the expectation of the sign observableS is exp , whereV is the volume and =T ^–1.Partially supported by the Ambrose Monell Foundation during a visit to the Institute for Advanced study.     

Spontaneous magnetization of the Ising model on a layered square lattice

We have studied the Ising model on a layered square lattice with four different coupling constants and two different magnetic moments. The partition function at zero magnetic field is derived exactly. We propose a formula for the spontaneous magnetization which agrees with the exact low-temperature series expansion up to the 16th order and reduces to the exact result of Au-Yang and McCoy in a special case.     

London limit for the lattice model of a superconductor

The electromagnetic properties of superconductors are investigated as a function of the discreteness of the crystal lattice in the London limit. The dependence of the superconducting current on the magnitude of the order parameter is obtained in the framework of the lattice model. The dependence of the critical current on the degree of deviation from the continuous approximation is calculated.     

Simultaneous dimerization and SU(4) symmetry breaking of 4-color fermions on the square lattice

Using infinite projected entangled-pair states, exact diagonalization, and flavor-wave theory, we show that the SU(4) Heisenberg model undergoes a spontaneous dimerization on the square lattice, in contrast with its SU(2) and SU(3) counterparts, which develop Néel and three-sublattice stripelike long-range order. Since the ground state of a dimer is not a singlet for SU(4) but a 6-dimensional irreducible representation, this leaves the door open for further symmetry breaking. We provide evidence that, unlike in SU(4) ladders, where dimers pair up to form singlet plaquettes, here the SU(4) symmetry is additionally broken, leading to a gapless spectrum in spite of the broken translational symmetry.     

镶嵌正方晶格上Gauss模型的相图

利用等效变换和自旋重标相结合的方法, 研究了镶嵌正方晶格上的Gauss模型. 研究 发现, 该系统可以变换为正方晶格上具有最近邻和次近邻相互作用的Gauss系统, 由此严格求得了镶嵌正方晶格上Gauss模型的临界温度, 得到了该系统的精确相图.