Bulletin of the American Physical Society
APS March Meeting 2014
Volume 59, Number 1
Monday–Friday, March 3–7, 2014; Denver, Colorado
Session Z35: The Bose-Hubbard Model |
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Sponsoring Units: DAMOP Chair: Ana Maria Rey, JILA Room: 702 |
Friday, March 7, 2014 11:15AM - 11:27AM |
Z35.00001: Replica Symmetry Breaking in the Bose Glass Steven Thomson, Frank Kruger We investigate the nature of the Bose glass phase of the disordered Bose-Hubbard model and demonstrate the existence of a glass-like replica symmetry breaking (RSB) order parameter in terms of particle number fluctuations. Starting from a strong-coupling expansion around the atomic limit, we study the instability of the Mott insulator towards the formation of a Bose glass. We add some infinitesimal RSB, following the Parisi hierarchical approach in the most general form, and observe its flow under the momentum-shell renormalization group scheme. We find a new fixed point with one-step RSB, corresponding to the transition between the Mott insulator and a Bose glass phase with hitherto unseen RSB. This finding is consistent with the expectation of glassy behavior and previous results showing the breakdown of self-averaging. We discuss the possibility of measuring the glass-like order parameter in optical lattice experiments. [Preview Abstract] |
Friday, March 7, 2014 11:27AM - 11:39AM |
Z35.00002: Hard-core lattice bosons: new insights from algebraic graph theory Randall W. Squires, David L. Feder Determining the characteristics of hard-core lattice bosons is a problem of long-standing interest in condensed matter physics. While in one-dimensional systems the ground state can be formally obtained via a mapping to free fermions, various properties (such as correlation functions) are often difficult to calculate. In this work we discuss the application of techniques from algebraic graph theory to hard-core lattice bosons in one dimension. Graphs are natural representations of many-body Hamiltonians, with vertices representing Fock basis states and edges representing matrix elements. ~We prove that the graphs for hard-core bosons and non-interacting bosons have identical connectivity; the only difference is the existence of edge weights. ~A formal mapping between the two is therefore possible by manipulating the graph incidence matrices. We explore the implications of these insights, in particular the intriguing possibility that ground-state properties of hard-core bosons can be calculated directly from those of non-interacting bosons. [Preview Abstract] |
Friday, March 7, 2014 11:39AM - 11:51AM |
Z35.00003: Excitations and quantum phase transitions of Supersolid and Haldane Insulator phases in the extended one-dimensional bosonic Hubbard model George Batrouni, Valery Rousseau, Richard Scalettar, Beno\^It Gr\'emaud The Haldane Insulator is a gapped phase characterized by an exotic non-local order parameter. It appears in reduced dimensionality models such as spin chains and the one-dimensional bosonic Hubbard model (BHM) with contact and near neighbor repulsive interactions. The parameter regimes at which it might exist, and how it competes with alternate types of order, such as supersolidity, are studied using the Stochastic Green Function quantum Monte Carlo and the Density Matrix Renormalization Group. We show that, depending on the ratio of the near neighbor to contact interactions, this model exhibits charge density waves (CDW), superfluid (SF), supersolid (SS) and the recently identified Haldane insulating (HI) phases. We show that the HI exists only at the tip of the unit filling CDW lobe and that there is a stable SS phase over a very wide range of parameters. We also present results for the excitation spectra in the various quantum phases. [Preview Abstract] |
Friday, March 7, 2014 11:51AM - 12:03PM |
Z35.00004: Ferromagnetic Phase Separated Region in the Polarized Two-species Bose Hubbard Model Kalani Hettiarachchilage, Valery G. Rousseau, Ka-Ming Tam, Juana Moreno, Mark Jarrell We study a doped two-dimensional bosonic Hubbard model with two hard-core species using quantum Monte Carlo simulations [Phys. Rev. B 88, 161101(R) (2013)] . Upon doping away from half-filling, we find several distinct phases including a phase separated ferromagnet with Mott behavior for the heavy species and both Mott and superfluid behaviors for the light species. Introducing an imbalance in the population between two species, we find a perfect phase separated ferromagnet. This phase exists for a broad range of temperatures and polarizations. By using finite size scaling of the susceptibilities, we find the critical exponent of the correlation length, $\nu = \displaystyle \frac{7}{4}$ which is the critical exponent for a two-dimensional Ising ferromagnet. Importantly, since the global entropy of this phase is relatively high, experimental observations in cold atoms may be achievable. [Preview Abstract] |
Friday, March 7, 2014 12:03PM - 12:15PM |
Z35.00005: ABSTRACT WITHDRAWN |
Friday, March 7, 2014 12:15PM - 12:27PM |
Z35.00006: Renormalization of Bose-Hubbard Parameters from Few Body Correlations of Cold Atoms Nikhil Monga, John Shumway, Kaden Hazzard, Erich Mueller, Steven Desch Cold atoms in an optical lattices can be a nearly ideal physical realization of a Bose-Hubbard model. However, the effective lattice-model parameters $t$ and $J$ are significantly renormalized by quantum correlations of the atoms, and this renormalization can depend on the site occupations. This occurs because interactions populate low energy states not explicitly present in the Bose-Hubbard model. We use path integral quantum Monte Carlo (PI-QMC) to calculate the effective matrix element, $t_{mn}$, for a bosonic atom to hop from a site with $m$ atoms to a neighbor site with $n$ atoms. We consider systems of up to five bosonic atoms on two sites. For the simple case of two atoms on two sites, the imaginary-time exchange frequency and double-occupation probability uniquely determine $t$ and $U$. For more particles, we extend our analysis to dynamics correlations of the site-occupation numbers, $\langle P_{mn}(\tau) P_{m'n'}(0)\rangle$, which are calculated by PI-QMC and compared with Bose-Hubbard correlations to infer the renormalized parameters. Unlike the present state-of-art determinations of these renormalizations, which use exact diagonalization for two-particles, our Monte Carlo approach is efficient for renormalizations arising from much larger numbers of atoms. [Preview Abstract] |
Friday, March 7, 2014 12:27PM - 12:39PM |
Z35.00007: Two leg bosonic ladder in an external magnetic field at unit filling Antoine Sterdyniak, Marcello Dalmonte, Salvatore Manmana, Peter Zoller, Andreas L\"auchli Motivated by the recent experimental realizations of artificial gauge field on optical lattices, we study the two-leg bosonic ladder in an external magnetic field, both analytically using bozonization techniques and numerically using finite size density matrix renormalization group algorithm. At unit filling, interacting bosons can exhibit a rich variety of phases on ladders. At large interaction, they form a Mott insulator phase while, at smaller interaction, they exhibit a Meissner phase and, more intriguing floating and staggered vortex phases. A weak chiral Mott insulator phase is also found for intermediate interaction strength. We determine the phase diagram and Luttinger parameters from correlations functions and entanglement spectrum. While usually thought to be second order, some of the phase transitions appear to be first order. [Preview Abstract] |
Friday, March 7, 2014 12:39PM - 12:51PM |
Z35.00008: Spectral functions in the 1D and 2D Bose Hubbard model Robert Ivancic, Eric Duchon, Nandini Trivedi We use state of the art numerical techniques including quantum Monte Carlo and maximum entropy methods to obtain the low energy excitation spectra in the superfluid and Mott-insulator phases of the Bose Hubbard model. These results are checked in 1D against Bethe Ansatz and tDMRG results and extended to 2D where such approaches are impossible. In the superfluid, we find linearly dispersing Bogoliubov sound modes as well as additional gapped modes broadened by interaction effects. In the Mott insulator, we find evidence for a finite gap and well defined quasiparticle excitations. We examine properties such as the excitation lifetime, density of states, and speed of sound as the system is tuned across the quantum phase transition that separates the superfluid and Mott states. These results provide an important theoretical framework for upcoming ultracold atom experiments in one and two dimensions. [Preview Abstract] |
Friday, March 7, 2014 12:51PM - 1:03PM |
Z35.00009: Chiral Bosonic Mott Insulator on the Frustrated Triangular Lattice Siddharth Parameswaran, Michael Zaletel, Andreas R\"uegg, Ehud Altman We study the superfluid and insulating phases of interacting bosons on the triangular lattice with an inverted dispersion, corresponding to frustrated hopping between sites. The resulting single-particle dispersion has multiple minima at nonzero wavevectors in momentum space, in contrast to the unique zero-wavevector minimum of the unfrustrated problem. As a consequence, the superfluid phase is unstable against developing additional chiral order that breaks time reversal (T) and parity (P) symmetries by forming a condensate at nonzero wavevector. We demonstrate that the loss of superfluidity can lead to an even more exotic phase, the chiral Mott insulator, with nontrivial current order that breaks T, P. These results are obtained via variational estimates, as well as a combination of bosonization and DMRG of triangular ladders, which taken together permit a fairly complete characterization of the phase diagram. We discuss the relevance of these phases to optical lattice experiments, as well as signatures of chiral symmetry breaking in time-of-flight images. [Preview Abstract] |
Friday, March 7, 2014 1:03PM - 1:15PM |
Z35.00010: Universal thermodynamics of the superfluid to Mott insulator transition Nicolas Dupuis, Adam Rancon The superfluid--Mott-insulator transition of a Bose gas in an optical lattice, when it occurs at constant density, belongs to the universality class of the quantum XY model. We discuss the thermodynamics of the two-dimensional quantum O(N) model for $N\geq 2$ in the vicinity of its zero-temperature quantum critical point, and in particular the universal scaling function ${\cal F}_N$ which determines the pressure $P(T)$. We show that the large-$N$ approach is unable to predict the (non-monotonuous) shape of ${\cal F}_N$ for $N < 10$, but ${\cal F}_N$ can be computed from a renormalization-group approach. Finally, we discuss the experimental determination of the scaling function ${\cal F}_2$ from the pressure of a Bose gas in an optical lattice near the superfluid--Mott-insulator transition. [Preview Abstract] |
Friday, March 7, 2014 1:15PM - 1:27PM |
Z35.00011: Novel Quantum States of Bosons in Moat Bands Tigran Sedrakyan, Leonid Glazman, Alex Kamenev We study hard-core bosons on a class of frustrated lattices with the lowest Bloch band having a degenerate minimum along a closed contour in the reciprocal space -- the Moat. We suggest that the ground state of the system is given by non-condensed state, which may be viewed as a state of fermions subject to Chern-Simons gauge field. At fixed density of bosons, such a state exhibits domains of incompressible liquids. Their fixed densities are given by fractions of the reciprocal area enclosed by the minimal energy contour. [Preview Abstract] |
Friday, March 7, 2014 1:27PM - 1:39PM |
Z35.00012: Self-localization in bosonic optical lattices: beyond mean-field theory Tadeusz Pudlik, Holger Hennig, Dirk Witthaut, David Campbell The combination of nonlinearity and discreteness allows cold bosonic atoms in optical lattices to support stable excitations, known as discrete breathers or intrinsic localized modes. Prior mean-field theory studies suggest such structures form spontaneously in the presence of dissipation, as long as the nonlinearity is strong enough. But how many atoms must be present in the lattice before these effects are observed? In our work, we address this question using numerically exact treatments of the dissipative Bose-Hubbard model. Our results suggest interesting phenomena may be seen in near-term experiments with just a few atoms per lattice site. [Preview Abstract] |
Friday, March 7, 2014 1:39PM - 1:51PM |
Z35.00013: Quantum tricriticality at the superfluid-insulator transition of binary Bose mixtures: A quantum Monte-Carlo study Yasuyuki Kato, Daisuke Yamamoto, Ippei Danshita Criticality emerging near a tricritical point (TCP) is referred to as tricriticality. We study quantum tricriticality in the two-component Bose-Hubbard model on square lattices that describes Bose-Bose mixtures confined in optical lattices. We confirm the existence of quantum TCPs on a boundary of superfluid-insulator transition by means of the unbiased quantum Monte-Carlo method. Moreover, we analyze an effective field theory to derive the quantum tricritical behaviors analytically. We show that the quantum tricritical behaviors are pronounced in the chemical potential dependence of the superfluid transition temperature and the density fluctuation. We suggest that the quantum tricriticality may be observed in existing experimental setups of Bose-Bose mixtures in optical lattice.~ [Preview Abstract] |
Friday, March 7, 2014 1:51PM - 2:03PM |
Z35.00014: Bose-Hubbard model with ferromagnetic-like occupation-parity couplings and its realization in imbalanced fermionic superfluids in tubular optical lattices Kuei Sun, Carlos J. Bolech We study a Bose-Hubbard model with a nearest-neighbor occupation-parity coupling that can be considered as energy cost for a domain-wall link between two adjacent sites if their occupation parity is different (one even and the other odd). Our analysis shows that the parity coupling has non-trivial interplay with the tunneling and onsite repulsion, resulting in several exotic quantum phases. For example, a uniform system with zero tunneling can exhibit a pair-liquid phase or phase separation of two Mott insulators, while a trapped system with finite tunneling shows a wedding-cake structure of only even-filling Mott insulators or a structure of central regular superfluid and outer pair superfluid. In addition, we find similar physics in a recent experimental system of imbalanced Fermi gases in optical lattices producing a 2D array of 1D tubes, with the presence of an oscillatory superfluid order parameter (the Fulde-Ferrell-Larkin-Ovchinnikov or FFLO state). We show that the unpaired majority fermions on each tube have a bosonic behavior with cross-tube tunneling, on-tube repulsion, and interplay with the spatial parity of the FFLO order that contributes to the occupation-parity coupling. Therefore, such system provides a realization of our model in two dimensions. [Preview Abstract] |
Friday, March 7, 2014 2:03PM - 2:15PM |
Z35.00015: Fermionic sound in Bose-Fermi mixtures Andrey Gromov, Barry Bradlyn Sound waves emerge as a result of spontaneously broken symmetry- translational in the case of solids and normal fluids and U(1) phase symmetry in the case of superfluids. Collective modes like these, which result from the breaking of conventional symmetries, usually have bosonic statistics. We explore the consequences of a subtle fermionic symmetry that appears in Bose-Fermi mixtures when both species have equal mass. In particular, we predict the existence of a novel fermionic collective excitation and comment on its properties. We show that this mode persists in the presence of a trapping potential and contact interaction. We describe the fate of these excitations when there is a small mass difference between the two particle species. Lastly, we discuss the possibility of observing this mode in experiments, for example in trapped $^{174}Yb-^{173}Yb$ Bose-Fermi mixtures. [Preview Abstract] |
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