Berezinskii-Kosterlitz-Thouless transition and criticality of an elliptic deformation of the sine-Gordon model

We introduce and study the properties of a periodic model interpolating between the sine-- and the sinh--Gordon theories in $1+1$ dimensions. This model shows the peculiarities, due to the preservation of the functional form of their potential across RG flows, of the two limiting cases: the sine-Gordon, not having conventional order/magnetization at finite temperature, but exhibiting Berezinskii-Kosterlitz-Thouless (BKT) transition; and the sinh-Gordon, not having a phase transition, but being integrable. The considered interpolation, which we term as {\em sn-Gordon} model, is performed with potentials written in terms of Jacobi functions. The critical properties of the sn-Gordon theory are discussed by a renormalization-group approach. The critical points, except the sinh-Gordon one, are found to be of BKT type. Explicit expressions for the critical coupling as a function of the elliptic modulus are given.Comment: v2, 10 pages, 8 figures, accepted in J. Phys.

Expectation Values in the Lieb-Liniger Bose Gas

Taking advantage of an exact mapping between a relativistic integrable model and the Lieb-Liniger model we present a novel method to compute expectation values in the Lieb-Liniger Bose gas both at zero and finite temperature. These quantities, relevant in the physics of one-dimensional ultracold Bose gases, are expressed by a series that has a remarkable behavior of convergence. Among other results, we show the computation of the three-body expectation value at finite temperature, a quantity that rules the recombination rate of the Bose gas.Comment: Published version. Selected for the December 2009 issue of Virtual Journal of Atomic Quantum Fluid

Local Correlations in the Super Tonks-Girardeau Gas

We study the local correlations in the super Tonks-Girardeau gas, a highly excited, strongly correlated state obtained in quasi one-dimensional Bose gases by tuning the scattering length to large negative values using a confinement-induced resonance. Exploiting a connection with a relativistic field theory, we obtain results for the two-body and three-body local correlators at zero and finite temperature. At zero temperature our result for the three-body correlator agrees with the extension of the results of Cheianov et al. [Phys. Rev. A 73, 051604(R) (2006)], obtained for the ground-state of the repulsive Lieb-Liniger gas, to the super Tonks-Girardeau state. At finite temperature we obtain that the three-body correlator has a weak dependence on the temperature up to the degeneracy temperature. We also find that for temperatures larger than the degeneracy temperature the values of the three-body correlator for the super Tonks-Girardeau gas and the corresponding repulsive Lieb-Liniger gas are rather similar even for relatively small couplings

Scattering and Trapping of Nonlinear Schroedinger Solitons in External Potentials

Soliton motion in some external potentials is studied using the nonlinear Schr\"odinger equation. Solitons are scattered by a potential wall. Solitons propagate almost freely or are trapped in a periodic potential. The critical kinetic energy for reflection and trapping is evaluated approximately with a variational method.Comment: 9 pages, 7 figure

Computation of Microcanonical Entropy at Fixed Magnetization Without Direct Counting

We discuss a method to compute the microcanonical entropy at fixed magnetization without direct counting. Our approach is based on the evaluation of a saddle-point leading to an optimization problem. The method is applied to a benchmark Ising model with simultaneous presence of mean-field and nearest-neighbour interactions for which direct counting is indeed possible, thus allowing a comparison. Moreover, we apply the method to an Ising model with mean-field, nearest-neighbour and next-nearest-neighbour interactions, for which direct counting is not straightforward. For this model, we compare the solution obtained by our method with the one obtained from the formula for the entropy in terms of all correlation functions. This example shows that for general couplings our method is much more convenient than direct counting methods to compute the microcanonical entropy at fixed magnetization

Violation of cluster decomposition and absence of light cones in local integer and half-integer spin chains

We compute the ground-state correlation functions of an exactly solvable chain of integer spins, recently introduced in [R. Movassagh and P. W. Shor, arXiv:1408.1657], whose ground state can be expressed in terms of a uniform superposition of all colored Motzkin paths. Our analytical results show that for spin s≥2 there is a violation of the cluster decomposition property. This has to be contrasted with s=1, where the cluster property holds. Correspondingly, for s=1 one gets a light-cone profile in the propagation of excitations after a local quench, while the cone is absent for s=2, as shown by time dependent density-matrix renormalization group. Moreover, we introduce an original solvable model of half-integer spins, which we refer to as Fredkin spin chain, whose ground state can be expressed in terms of superposition of all Dyck paths. For this model we exactly calculate the magnetization and correlation functions, finding that for s=1/2, a conelike propagation occurs, while for higher spins, s≥3/2, the colors prevent any cone formation and clustering is violated, together with square root deviation from the area law for the entanglement entropy

Tunneling of polarized fermions in 3D double wells

We study the tunneling of a spin polarized Fermi gas in a three-dimensional double well potential, focusing on the time dynamics starting from an initial state in which there is an imbalance in the number of particles in the two wells. Although fermions in different doublets of the double well tunnel with different frequencies, we point out that (incoherent) oscillations of a large number of particles can arise, as a consequence of the presence of transverse degrees of freedom. Estimates of the doublet structure and of the occupation of transverse eigenstates for a realistic experimental setup are provided.Comment: 10 pages, Typos corrected and figures changed - published in Laser Physics, issue on the LPHYS'11 conference (Sarajevo, 2011

Anisotropic Ginzburg-Landau and Lawrence-Doniach Models for Layered Ultracold Fermi Gases

We study the anisotropic Ginzburg-Landau and Lawrence-Doniach models describing a layered superfluid ultracold Fermi gas in optical lattices. We derive the coefficients of the anisotropic Ginzburg-Landau and the mass tensor as a function of anisotropy, filling and interaction, showing that near the unitary limit the effective anisotropy of the masses is significantly reduced. The anisotropy parameter is shown to vary in realistic setups in a wide range of values. We also derive the Lawrence-Doniach model - often used to describe the 2D-3D dimensional crossover in layered superconductors - for a layered ultracold Fermi gas, obtaining a relation between the interlayer Josephson couplings and the Ginzburg-Landau masses. Comparing to the Ginzburg-Landau description, we find that the region of validity of the Lawrence-Doniach model is near the unitary limit.Comment: 15 pages, 4 figure

One-Dimensional Bose Gases with N-Body Attractive Interactions

We study the ground state properties of a one-dimensional Bose gas with N-body attractive contact interactions. By using the explicit form of the bright soliton solution of a generalized nonlinear Schroedinger equation, we compute the chemical potential and the ground state energy. For N=3, a localized soliton wave-function exists only for a critical value of the interaction strength: in this case the ground state has an infinite degeneracy that can be parameterized by the chemical potential. The stabilization of the bright soliton solution by an external harmonic trap is also discussed, and a comparison with the effect of N-body attractive contact interactions in higher dimensions is presented.Comment: 12 pages, 8 Postscript figure

Finite-Temperature Renormalization Group Analysis of Interaction Effects in 2D Lattices of Bose-Einstein Condensates

By using a renormalization group analysis, we study the effect of interparticle interactions on the critical temperature at which the Berezinskii-Kosterlitz-Thouless (BKT) transition occurs for Bose-Einstein condensates loaded at finite temperature in a 2D optical lattice. We find that the critical temperature decreases as the interaction energy decreases; when U/J=36/\pi one has a vanishing critical temperature, signaling the possibility of a quantum phase transition of BKT type