561 research outputs found
Wilson Loops, Bianchi Constraints and Duality in Abelian Lattice Models
We introduce new modified Abelian lattice models, with inhomogeneous local
interactions, in which a sum over topological sectors are included in the
defining partition function. The dual models, on lattices with arbitrary
topology, are constructed and they are found to contain sums over topological
sectors, with modified groups, as in the original model. The role of the sum
over sectors is illuminated by deriving the field-strength formulation of the
models in an explicitly gauge-invariant manner. The field-strengths are found
to satisfy, in addition to the usual local Bianchi constraints, global
constraints. We demonstrate that the sum over sectors removes these global
constraints and consequently softens the quantization condition on the global
charges in the system. Duality is also used to construct mappings between the
order and disorder variables in the theory and its dual. A consequence of the
duality transformation is that correlators which wrap around non-trivial cycles
of the lattice vanish identically. For particular dimensions this mapping
allows an explicit expression for arbitrary correlators to be obtained.Comment: LaTeX 30 pages, 6 figures and 2 tables. References updated and
connection with earlier work clarified, final version to appear in Nucl.
Phys.
Dual Quantum Monte Carlo Algorithm for Hardcore Bosons
We derive the exact dual representation of the bosonic Hubbard model which
takes the form of conserved current loops. The hardcore limit, which
corresponds to the quantum spin- Heisenberg antiferromagnet, is
also obtained. In this limit, the dual partition function takes a particularly
simple form which is very amenable to numerical simulations. In addition to the
usual quantities that we can measure (energy, density-density correlation
function and superfluid density) we can with this new algorithm measure
efficiently the order parameter correlation function, . We demonstrate this with numerical tests in one dimension.Comment: 15 pages, 4 figures . Talk given at CCP1998, Granada, Spai
Haldane phase in the sawtooth lattice: Edge states, entanglement spectrum and the flat band
Using density matrix renormalization group numerical calculations, we study
the phase diagram of the half filled Bose-Hubbard system in the sawtooth
lattice with strong frustration in the kinetic energy term. We focus in
particular on values of the hopping terms which produce a flat band and show
that, in the presence of contact and near neighbor repulsion, three phases
exist: Mott insulator (MI), charge density wave (CDW), and the topological
Haldane insulating (HI) phase which displays edge states and particle imbalance
between the two ends of the system. We find that, even though the entanglement
spectrum in the Haldane phase is not doubly degenerate, it is in excellent
agreement with the entanglement spectrum of the Affleck-Kennedy-Lieb-Tasaki
(AKLT) state built in the Wannier basis associated with the flat band. This
emphasizes that the absence of degeneracy in the entanglement spectrum is not
necessarily a signature of a non-topological phase, but rather that the
(hidden) protecting symmetry involves non-local states. Finally, we also show
that the HI phase is stable against small departure from flatness of the band
but is destroyed for larger ones.Comment: 10 pages, 16 figure
Langevin Simulations of a Long Range Electron Phonon Model
We present a Quantum Monte Carlo (QMC) study, based on the Langevin equation,
of a Hamiltonian describing electrons coupled to phonon degrees of freedom. The
bosonic part of the action helps control the variation of the field in
imaginary time. As a consequence, the iterative conjugate gradient solution of
the fermionic action, which depends on the boson coordinates, converges more
rapidly than in the case of electron-electron interactions, such as the Hubbard
Hamiltonian. Fourier Acceleration is shown to be a crucial ingredient in
reducing the equilibration and autocorrelation times. After describing and
benchmarking the method, we present results for the phase diagram focusing on
the range of the electron-phonon interaction. We delineate the regions of
charge density wave formation from those in which the fermion density is
inhomogeneous, caused by phase separation. We show that the Langevin approach
is more efficient than the Determinant QMC method for lattice sizes and that it therefore opens a potential path to problems including,
for example, charge order in the 3D Holstein model
Bragg spectroscopy of trapped one dimensional strongly interacting bosons in optical lattices: Probing the cake-structure
We study Bragg spectroscopy of strongly interacting one dimensional bosons
loaded in an optical lattice plus an additional parabolic potential. We
calculate the dynamic structure factor by using Monte Carlo simulations for the
Bose-Hubbard Hamiltonian, exact diagonalizations and the results of a recently
introduced effective fermionization (EF) model. We find that, due to the
system's inhomogeneity, the excitation spectrum exhibits a multi-branched
structure, whose origin is related to the presence of superfluid regions with
different densities in the atomic distribution. We thus suggest that Bragg
spectroscopy in the linear regime can be used as an experimental tool to unveil
the shell structure of alternating Mott insulator and superfluid phases
characteristic of trapped bosons.Comment: 7 pages, 4 figure
Reply to Comment on "Roughness of Interfacial Crack Fronts: Stress-Weighted Percolation in the Damage Zone"
This is the reply to a Comment by Alava and Zapperi (cond-mat/0401568) on
Schmittbuhl, Hansen and Batrouni, PRL, 90, 045505 (2003)
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