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arXiv:2206.00013 · Physical Review A

Helical superfluid in a frustrated honeycomb Bose-Hubbard model

Tzu-Chi Hsieh, Han Ma, Leo Radzihovsky

Published Aug 29, 2022• 10 citations
arXivHTMLPDF

Abstract

We study a ``helical'' superfluid, a nonzero-momentum condensate in a frustrated bosonic model. At mean-field Bogoliubov level, such a novel state exhibits ``smectic'' fluctuation that are qualitatively stronger than that of a conventional superfluid. We develop a phase diagram and compute a variety of its physical properties, including the spectrum, structure factor, condensate depletion, momentum distribution, all of which are qualitatively distinct from that of a conventional superfluid. Interplay of fluctuations, interaction and lattice effects gives rise to the phenomenon of order by disorder, leading to a crossover from the smectic superfluid regime to the anisotropic $XY$ superfluid phase. We complement the microscopic lattice analysis with a field theoretic description for such a helical superfluid, which we derive from microscopics and justify on general symmetry grounds, reassuringly finding full consistency. Possible experimental realizations are discussed.

DOI
10.1103/physreva.106.023321

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We study a helical'' superfluid, a nonzero-momentum condensate in a frustrated bosonic model. At mean-field Bogoliubov level, such a novel state exhibits smectic'' fluctuation that are qualitatively stronger than that of a conventional superfluid. We develop a phase diagram and compute a variety of its physical properties, including the spectrum, structure factor, condensate depletion, momentum distribution, all of which are qualitatively distinct from that of a conventional superfluid. Interplay of fluctuations, interaction and lattice effects gives rise to the phenomenon of order by disorder, leading to a crossover from the smectic superfluid regime to the anisotropic XYXYXY superfluid phase. We complement the microscopic lattice analysis with a field theoretic description for such a helical superfluid, which we derive from microscopics and justify on general symmetry grounds, reassuringly finding full consistency. Possible experimental realizations are discussed.
We study the quantum phase transition between the insulating and the globally coherent superfluid phases in the Bose-Hubbard model with T3{\mathcal{T}}_{3}T3​ structure, the ``dice lattice.'' Even in the absence of any frustration the superfluid phase is characterized by modulation of the order parameter on the different sublattices of the T3{\mathcal{T}}_{3}T3​ structure. The zero-temperature critical point as a function of magnetic field shows the characteristic ``butterfly'' form. At full frustration the superfluid region is strongly suppressed. In addition, due to the existence of the Aharonov-Bohm cages at f=1∕2f=1∕2f=1∕2, we find some evidence for the existence of an intermediate insulating phase characterized by a zero superfluid stiffness but finite compressibility. In this intermediate phase bosons are localized due to the external frustration and the topology of the T3{\mathcal{T}}_{3}T3​ lattice. We name this new phase the Aharonov-Bohm insulator. In the presence of charge frustration the phase diagram acquires the typical lobe structure. The form and hierarchy of the Mott insulating states with fractional fillings are dictated by the particular topology of the T3{\mathcal{T}}_{3}T3​ lattice. The results presented were obtained by a variety of analytical methods: mean-field and variational techniques to approach the phase boundary from the superconducting side and a strongly coupled expansion appropriate for the Mott insulating region. In addition we performed quantum Monte Carlo simulations of the corresponding (2+1)(2+1)(2+1)-dimensional XYXYXY model to corroborate the analytical calculations with a more accurate quantitative analysis. We finally discuss experimental realization of the T3{\mathcal{T}}_{3}T3​ lattice both with optical lattices and with Josephson junction arrays.
Motivated by recent experiments on atomic Dirac fermions in a tunable honeycomb optical lattice, we study the attractive Hubbard model of superfluidity in the anisotropic honeycomb lattice. At weak coupling, we find that the maximum mean-field pairing transition temperature, as a function of density and interaction strength, occurs for the case with isotropic hopping amplitudes. In this isotropic case, we go beyond mean-field theory and study collective fluctuations, treating both pairing and density fluctuations for interaction strengths ranging from weak to strong coupling. We find evidence for a sharp sound mode, together with a well-defined Leggett mode over a wide region of the phase diagram. We also calculate the superfluid order parameter and collective modes in the presence of nonzero superfluid flow. The flow-induced softening of these collective modes leads to dynamical instabilities involving stripelike density modulations as well as a Leggett-mode instability associated with the natural sublattice symmetry-breaking charge-ordered state on the honeycomb lattice. The latter provides a nontrivial test for the experimental realization of the one-band Hubbard model. We delineate regimes of the phase diagram where the critical current is limited by depairing or by such collective instabilities, and discuss experimental implications of our results.
We consider theoretically the problem of an artificial gauge potential applied to a cold atomic system of interacting neutral bosons in a tight-binding optical lattice. Using the Bose-Hubbard model, we show that an effective magnetic field leads to superfluid phases with simultaneous spatial order, which we analyze using Bogliubov theory. This gives a consistent expansion in terms of quantum and thermal fluctuations, in which the lowest order gives a Gross-Pitaevskii equation determining the condensate configuration. We apply an analysis based on the magnetic symmetry group to show how the spatial structure of this configuration depends on commensuration between the magnetic field and the lattice. Higher orders describe the quasiparticle excitations, whose spectrum combines the intricacy of the Hofstadter butterfly with the characteristic features of the superfluid phase. We use the depletion of the condensate to determine the range of validity of our approximations and also to find an estimate for the onset of the Mott insulator phase. Our theory provides concrete experimental predictions for both time-of-flight imagery and Bragg spectroscopy.
The realization of optical lattices of cold atoms has opened up the possibility of engineering interacting lattice systems of bosons and fermions, stimulating a frenzy of research over the last decade. More recently, experimental techniques have been developed to apply synthetic gauge fields to these optical lattices. As a result, it has become possible to study quantum Hall physics and the effects of frustration in lattices of cold atoms. In this article we describe the combined effect of frustration and interactions on the superfluidity of bosons. By focussing on a frustrated ladder of interacting bosons, we show that the effect of frustration is for ``chiral'' order to develop, which manifests itself as an alternating pattern of circulating supercurrents. Remarkably, this order persists even when superfluidity is lost and the system enters a Mott phase giving rise to a novel chiral Mott insulator. We describe the combined physics of frustration and interactions by studying a fully frustrated one dimensional model of interacting bosons. The model is studied using mean-field theory, a direct quantum simulation and a higher dimensional classical theory in order to offer a full description of the different quantum phases contained in it and transitions between the different phases. In addition, we provide physical descriptions of the chiral Mott insulator as a vortex-anitvortex super solid and indirect excitonic condensate in addition to obtaining a variational wavefunction for it. We also briefly describe the chiral Mott states arising in other microscopic models.
We investigate the ground-state and finite-temperature phase diagrams of the Bose-Hubbard model on a honeycomb superlattice. The interplay between the superlattice potential depth $\mathrm{\ensuremath{\Delta}}/t$ and the on-site interaction U/tU/tU/t gives rise to three distinct quantum phases at zero temperature: a superfluid phase, a Mott insulator I phase with unit filling on each site, and a Mott insulator II phase characterized by density imbalance---double occupancy on one sublattice and vacancy on the other at unit filling. The SF-MI transitions are found to be continuous, consistent with second-order quantum phase transitions. We further extend our analysis to finite temperatures within the superfluid regime. Our work highlights how a honeycomb superlattice geometry enables access to interaction- and lattice-modulation-driven quantum phases, including a density-imbalanced Mott insulator and a robust superfluid regime, offering concrete theoretical predictions for cold-atom experiments.
Abstract We determine the hydrodynamic modes of the superfluid analog of a smectic-A liquid crystal phase, i.e., a state in which both gauge invariance and translational invariance along a single direction are spontaneously broken. Such a superfluid smectic provides an idealized description of the incommensurate supersolid state realized in Bose–Einstein condensates with strong dipolar interactions as well as of the stripe phase in Bose gases with spin–orbit coupling. We show that the presence of a finite normal fluid density in the ground state of these systems gives rise to a well-defined second-sound type mode even at zero temperature. It replaces the diffusive permeation mode of a normal smectic phase and is directly connected with the classic description of supersolids by Andreev and Lifshitz in terms of a propagating defect mode. An analytic expression is derived for the two sound velocities that appear in the longitudinal excitation spectrum. It only depends on the low-energy parameters associated with the two independent broken symmetries, which are the effective layer compression modulus and the superfluid fraction.