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arXiv:0903.4713 · Laser Physics

Effect of random on-site energies on the critical temperature of a lattice Bose gas

Luca Dell’Anna, S. Fantoni, Pasquale Sodano, Andrea Trombettoni

Published Apr 1, 2009• 2 citations
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Abstract

We study the effect of random on-site energies on the critical temperature of a non-interacting Bose gas on a lattice. In our derivation the on-site energies are distributed according a Gaussian probability distribution function having vanishing average and variance ν 0 2 . By using the replicated action obtained by averaging on the disorder, we perform a perturbative expansion for the Green functions of the disordered system. We evaluate the shift of the chemical potential induced by the disorder and we compute, for ν 0 2 ≪ 1, the critical temperature for condensation. We find that, for large filling, disorder slightly enhances the critical temperature for condensation.

DOI
10.1134/s1054660x09040069

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We study the effect of random on-site energies on the critical temperature of a non-interacting Bose gas on a lattice. In our derivation the on-site energies are distributed according a Gaussian probability distribution function having vanishing average and variance ν 0 2 . By using the replicated action obtained by averaging on the disorder, we perform a perturbative expansion for the Green functions of the disordered system. We evaluate the shift of the chemical potential induced by the disorder and we compute, for ν 0 2 ≪ 1, the critical temperature for condensation. We find that, for large filling, disorder slightly enhances the critical temperature for condensation.
For a non-interacting Bose gas on a lattice we compute the shift of the critical temperature for condensation when random-bond and onsite disorder are present. We evidence that the shift depends on the space dimensionality D and the filling fraction f. For D -> infinity (infinite-range model), using results from the theory of random matrices, we show that the shift of the critical temperature is negative, depends on f, and vanishes only for large f. The connections with analogous results obtained for the spherical model are discussed. For D=3 we find that, for large f, the critical temperature Tc is enhanced by disorder and that the relative shift does not sensibly depend on f; at variance, for small f, Tc decreases in agreement with the results obtained for a Bose gas in the continuum. We also provide numerical estimates for the shift of the critical temperature due to disorder induced on a non-interacting Bose gas by a bichromatic incommensurate potential.
We investigate the thermodynamic properties of a dilute Bose gas in a correlated random potential using exact path integral Monte Carlo methods. The study is carried out in continuous space and disorder is produced in the simulations by a three-dimensional (3D) speckle pattern with tunable intensity and correlation length. We calculate the shift of the superfluid transition temperature due to disorder and we highlight the role of quantum localization by comparing the critical chemical potential with the classical percolation threshold. The equation of state of the gas is determined in the regime of strong disorder, where superfluidity is suppressed and the normal phase exists down to very low temperatures. We find a T 2 dependence of the energy in agreement with the expected behavior in the Bose glass phase. We also discuss the major role played by the disorder correlation length and we make contact with a Hartree–Fock mean-field approach that holds if the correlation length is very large. The density profiles are analyzed as a function of temperature and interaction strength. Effects of localization and the depletion of the order parameter are emphasized in the comparison between local condensate and total density. At very low temperature, we find that the energy and the particle distribution of the gas are very well described by the T =0 Gross–Pitaevskii theory, even in the regime of very strong disorder.
The momentum-shell renormalization group (RG) is used to study the condensation of interacting Bose gases without and with disorder. First of all, for the homogeneous disorder-free Bose gas the interaction-induced shifts in the critical temperature and chemical potential are determined up to second order in the scattering length. The approach does not make use of dimensional reduction and is thus independent of previous derivations. Secondly, the RG is used together with the replica method to study the interacting Bose gas with delta-correlated disorder. The flow equations are derived and found to reduce, in the high-temperature limit, to the RG equations of the classical Landau-Ginzburg model with random-exchange defects. The random fixed point is used to calculate the condensation temperature under the combined influence of particle interactions and disorder.
We consider a dilute Bose Gas moving in a harmonic trap with a superimposed frozen random potential which arises in experiments either naturally in wire traps or artificially and controllably with laser speckles. The critical temperature, which characterises the onset of Bose-Einstein condensation, depends on the disorder realization within the ensemble. Therefore, we introduce an effective grand-canonical potential from which we determine perturbatively the disorder averages of both the first and the second moment of the critical temperature in leading order. We discuss our results for a finite number of particles by assuming a Gaussian spatial correlation for the quenched disorder potential. Keywords: Disorder, Bose-Einstein condensation, critical temperature 1.
We perform quantum Monte Carlo simulations to study the 2D hard-core Bose–Hubbard model in a random potential. Our motivation is to investigate the effects of randomness on the Kosterlitz–Thouless (KT) transition and its quantum critical phenomenon. The chemical potential is assumed to be random, by site, with a Gaussian distribution. The KT transition is confirmed by a finite-size analysis of the superfluid density and the power-law decay of the correlation function. By changing the variance of the Gaussian distribution, we find that the transition temperature decreases as the variance increases. We obtain the phase diagram showing the superfluid and the disordered phases, and estimate the quantum critical point (QCP) and the critical exponent. Our results on the ground state show the existence of the Bose glass phase. Finally, we discuss what the variance of the QCP indicates from the viewpoint of quantum percolation .
We consider the physics of lattice bosons affected by disordered on-site interparticle interactions. Characteristic qualitative changes in the zero-temperature phase diagram are observed when compared to the case of randomness in the chemical potential. The Mott-insulating regions shrink and eventually vanish for any finite disorder strength beyond a sufficiently large filling factor. Furthermore, at low values of the chemical potential both the superfluid and Mott insulator are stable towards formation of a Bose glass leading to a possibly nontrivial tricritical point. We discuss feasible experimental realizations of our scenario in the context of ultracold atoms on optical lattices.