Beats, broken-symmetry superfluid on a one dimensional anyon Hubbard model (original) (raw)
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We study the (pseudo-) anyon Hubbard model on a one-dimensional lattice without the presence of a three-body hardcore constraint. In particular, for the pseudo-fermion limit of a large statistical angle θ ≈ π, we observe a wealth of exotic properties including a first order transition between different superfluid phases and a two-component partially paired phase for large fillings without need of an additional three-body hardcore constraint. In this limit, we analyze the effect of an induced hardcore constraint, which leads to the stabilization of superfluid ground states for vanishing or even small attractive on-site interactions. For finite statistical angles, we study the unconventional broken-symmetry superfluid peaked at a finite momentum, resulting in an interesting beat phenomenon of single particle correlation functions. We show how some features of various ground state phases, including an analog of the partially paired phase in the pseudo-fermion limit, may be reproduced in a naive mean field frame.
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Physica A: Statistical Mechanics and its Applications, 1996
Statistical mechanics of the bosonic Hubbard model is studied in the frame of an improved linearization scheme, applied in such a way so as to approximate in thermodynamically selfconsistent way the local interaction and keeping all long-range correlations exact in the linearized form. The hamiltonian spectrum can be obtained due to the resulting dynamical symmetry, and the self-consistent free energy allows us to obtain the temperature dependence of the diagonal and off-diagonal order parameters. The phase diagram exhibits a superfluid condensate phase possibly co-existing, for appropriate values of (U/t)v, with a fluctuation-mediated off-diagonal long-range-ordered phase. The corresponding transition can be thought of as a conductor-insulator transition.
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We calculate the superfluid weight and the polarization amplitude for the one-dimensional bosonic Hubbard model with focus on the strong-coupling regime via variational, exact diagonalization, and strong coupling calculations. Our variational approach is based on the Baeriswyl wave function, implemented via Monte Carlo sampling. We derive the superfluid weight appropriate in a variational setting. We emphasize the importance of implementing the Peierls phase in position space and to allow for many-body interference effects, rather than implementing the Peierls phase as single particle momentum shifts. At integer filling, the Baeriswyl wave function gives zero superfluid response at any coupling. At half-filling our variational superfluid weight is in reasonable agreement with exact diagonalziation results. We also calculate the polarization amplitude, the variance of the total position, and the associated size scaling exponent, which corroborate that this variational approach produces an insulating state at integer filling. Our Baeriswyl based variational method is applicable to significantly larger system sizes than exact diagonalization or quantum Monte Carlo.
Physical Review B, 2005
We use the finite-size density-matrix-renormalization-group (FSDMRG) method to obtain the phase diagram of the one-dimensional (d = 1) extended Bose-Hubbard model for density ρ = 1 in the U − V plane, where U and V are, respectively, onsite and nearest-neighbor interactions. The phase diagram comprises three phases: Superfluid (SF), Mott Insulator (MI) and Mass Density Wave (MDW). For small values of U and V , we get a reentrant SF-MI-SF phase transition. For intermediate values of interactions the SF phase is sandwiched between MI and MDW phases with continuous SF-MI and SF-MDW transitions. We show, by a detailed finite-size scaling analysis, that the MI-SF transition is of Kosterlitz-Thouless (KT) type whereas the MDW-SF transition has both KT and two-dimensional-Ising characters. For large values of U and V we get a direct, first-order, MI-MDW transition. The MI-SF, MDW-SF and MI-MDW phase boundaries join at a bicritical point at (U, V) = (8.5 ± 0.05, 4.75 ± 0.05).
Physical Review Letters, 2005
We study the nature of the superfluid-insulator quantum phase transition in a one-dimensional system of lattice bosons with off-diagonal disorder in the limit of large integer filling factor. Monte Carlo simulations of two strongly disordered models show that the universality class of the transition in question is the same as that of the superfluid-Mott-insulator transition in a pure system. This result can be explained by disorder self-averaging in the superfluid phase and applicability of the standard quantum hydrodynamic action. We also formulate the necessary conditions which should be satisfied by the stong-randomness universality class, if one exists.
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Physical Review Letters, 2008
We show that the dynamics of cold bosonic atoms in a two-dimensional square optical lattice produced by a bichromatic light-shift potential is described by a Bose-Hubbard model with an additional effective staggered magnetic field. In addition to the known uniform superfluid and Mott insulating phases, the zero-temperature phase diagram exhibits a novel kind of finite-momentum superfluid phase, characterized by a quantized staggered rotational flux. An extension for fermionic atoms leads to an anisotropic Dirac spectrum, which is relevant to graphene and high-Tc superconductors.
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Physical review letters, 2009
Vortices, which are introduced into a boson superfluid by rotation or a magnetic field, tend to localize in a lattice configuration which coexists with superfluidity . In two dimensions a vortex lattice can melt by quantum fluctuations resulting in a non-superfluid Quantum Vortex Liquid (QVL). Present microscopic understanding of vortex dynamics of lattice bosons is insufficient to predict the actual melting density. A missing energy scale, which is difficult to obtain perturbatively or semiclassically, is the "bare" vortex hopping rate t v on the dual lattice. Another puzzle is the temperature dependent Hall conductivity σ H (T ), which reflects the effective vortex Magnus dynamics in the QVL phase. In this paper we compute t v and σ H (T ) by exact diagonalization of finite clusters near half filling. Mapping our effective Hamiltonian to the Boson Coloumb Liquid simulated by Ref.
Physical Review B, 2011
Among the various numerical techniques to study the physics of strongly correlated quantum many-body systems, the self-energy functional approach (SFA) has become increasingly important. In its previous form, however, SFA is not applicable to Bose-Einstein condensation or superfluidity. In this paper we show how to overcome this shortcoming. To this end we identify an appropriate quantity, which we term D, that represents the correlation correction of the condensate order parameter, as it does the self-energy for the Green's function. An appropriate functional is derived, which is stationary at the exact physical realizations of D and of the self-energy. Its derivation is based on a functional-integral representation of the grand potential followed by an appropriate sequence of Legendre transformations. The approach is not perturbative and therefore applicable to a wide range of models with local interactions. We show that the variational cluster approach based on the extended self-energy functional is equivalent to the "pseudoparticle" approach introduced in Phys. Rev. B, 83, 134507 (2011). We present results for the superfluid density in the two-dimensional Bose-Hubbard model, which show a remarkable agreement with those of Quantum-Monte-Carlo calculations.
Superfluidity of bosons on a deformable lattice
Physical Review B, 2001
We study the superfluid properties of a system of interacting bosons on a lattice which, moreover, are coupled to the vibrational modes of this lattice, treated here in terms of Einstein phonon model. The ground state corresponds to two correlated condensates: that of the bosons and that of the phonons. Two competing effects determine the common collective soundwave-like mode with sound velocity v, arising from gauge symmetry breaking: i) The sound velocity v0 (corresponding to a weakly interacting Bose system on a rigid lattice) in the lowest order approximation is reduced due to reduction of the repulsive boson-boson interaction, arising from the attractive part of phonon mediated interaction in the static limit. ii) the second order correction to the sound velocity is enhanced as compared to the one of bosons on a rigid lattice when the the boson-phonon interaction is switched on due to the retarded nature of phonon mediated interaction. The overall effect is that the sound velocity is practically unaffected by the coupling with phonons, indicating the robustness of the superfluid state. The induction of a coherent state in the phonon system, driven by the condensation of the bosons could be of experimental significance, permitting spectroscopic detections of superfluid properties of the bosons. Our results are based on an extension of the Beliaev-Popov formalism for a weakly interacting Bose gas on a rigid lattice to that on a deformable lattice with which it interacts.
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Using an imaginary-time path integral approach, we develop the perturbation theory suited to the boson Hubbard model, and apply it to calculate the effects of a dilute gas of spin-polarized fermions weakly interacting with the bosons. The full theory captures both the static and the dynamic effects of the fermions on the generic superfluid-insulator phase diagram. We find that, in a homogenous system described by a single-band boson Hubbard Hamiltonian, the intrinsic perturbative effect of the fermions is to generically suppress the insulating lobes and to enhance the superfluid phase.