64 research outputs found
DMRG studies on linear-exchange quantum spin models in one dimension
We study a class of spin-1/2 quantum antiferromagnetic chains using DMRG
technique. The exchange interaction in these models decreases linearly as a
function of the separation between the spins, for . For the separations beyond , the interaction is zero. The range
parameter takes positive integer values. The models corresponding to all
the odd values of are known to have the same exact doubly degenerate dimer
ground state as for the Majumdar-Ghosh (MG) model. In fact, R=3 is the MG
model. For even , the exact ground state is not known in general, except for
R=2 (the Bethe ansatz solvable Heisenberg chain) and in the asymptotic limit of
where the two MG dimer states again emerge as the exact ground state. In
the present work, we numerically investigate the even- models whose ground
state is not known analytically. In particular, for R=4, 6 and 8, we have
computed a number of ground state properties. We find that, unlike R=2, the
higher even- models are spin-gapped, and show strong dimer-dimer
correlations of the MG type. Moreover, the spin-spin correlations decay very
rapidly, albeit showing weak periodic revivals.Comment: 8 pages, 12 figure
Mean field analysis of quantum phase transitions in a periodic optical superlattice
In this paper we analyze the various phases exhibited by a system of
ultracold bosons in a periodic optical superlattice using the mean field
decoupling approximation. We investigate for a wide range of commensurate and
incommensurate densities. We find the gapless superfluid phase, the gapped Mott
insulator phase, and gapped insulator phases with distinct density wave orders.Comment: 6 pages, 7 figures, 4 table
Phases and phase transitions of frustrated hard-core bosons on a triangular ladder
We study hardcore bosons on a triangular ladder at half filling in the
presence of a frustrating hopping term and a competing nearest neighbor
repulsion which promotes crystallization. Using the finite-size
density-matrix renormalization group method, we obtain the phase diagram which
contains three phases: a uniform superfluid (SF), an insulating charge density
wave (CDW) crystal and a bond ordered insulator (BO). We find that the
transitions from SF to CDW and SF to BO are continuous in nature, with critical
exponents varying continously along the phase boundaries, while the transition
from CDW to BO is found to be first order. The phase diagram is also shown to
contain an exactly solvable Majumdar Ghosh point, and re-entrant SF to CDW
phase transitions.Comment: 10 pages, 16 figure
Bose-Hubbard Models in Confining Potentials: An Inhomogeneous Mean-Field Theory
We present an extensive study of Mott insulator (MI) and superfluid (SF)
shells in Bose-Hubbard (BH) models for bosons in optical lattices with harmonic
traps. For this we develop an inhomogeneous mean-field theory. Our results for
the BH model with one type of spinless bosons agrees quantitatively with
quantum Monte Carlo (QMC) simulations. Our approach is numerically less
intensive than such simulations, so we are able to perform calculation on
experimentally realistic, large 3D systems, explore a wide range of parameter
values, and make direct contact with a variety of experimental measurements. We
also generalize our inhomogeneous mean-field theory to study BH models with
harmonic traps and (a) two species of bosons or (b) spin-1 bosons. With two
species of bosons we obtain rich phase diagrams with a variety of SF and MI
phases and associated shells, when we include a quadratic confining potential.
For the spin-1 BH model we show, in a representative case, that the system can
display alternating shells of polar SF and MI phases; and we make interesting
predictions for experiments in such systems.Comment: 17 pages, 18 figure
Hardcore bosons in a zig-zag optical superlattice
We study a system of hard-core bosons at half-filling in a one-dimensional
optical superlattice. The bosons are allowed to hop to nearest and next-nearest
neighbor sites producing a zig-zag geometry and we obtain the ground state
phase diagram as a function of microscopic parameters using the finite-size
density matrix renormalization group (FS-DMRG) method. Depending on the sign of
the next-nearest neighbor hopping and the strength of the superlattice
potential the system exhibits three different phases, namely the bond-order
(BO) solid, the superlattice induced Mott insulator (SLMI) and the superfluid
(SF) phase. When the signs of both hopping amplitudes are the same (the
"unfrustrated" case), the system undergoes a transition from the SF to the SLMI
at a non-zero value of the superlattice potential. On the other hand, when the
two amplitudes differ in sign (the "frustrated" case), the SF is unstable to
switching on a superlattice potential and also exists only up to a finite value
of the next nearest neighbor hopping. This part of the phase diagram is
dominated by the BO phase which breaks translation symmetry spontaneously even
in the absence of the superlattice potential and can thus be characterized by a
bond order parameter. The transition from BO to SLMI appears to be first order.Comment: 6 pages, 11 figure
Phases and transitions in the spin-1 Bose-Hubbard model: systematics of a mean-field theory
We generalize the mean-field theory for the spinless Bose-Hubbard model to account for the different types of superfluid phases that can arise in the spin-1 case. In particular, our mean-field theory can distinguish polar and ferromagnetic superfluids, Mott insulator, that arise at integer fillings at zero temperature, and normal Bose liquids into which the Mott insulators evolve at finite temperatures. We find, in contrast to the spinless case, that several of the superfluid-Mott insulator transitions are of first order at finite temperatures. Our systematic study yields rich phase diagrams that include first-order and second-order transitions and a variety of tricritical points. We discuss the possibility of realizing such phase diagrams in experimental systems
Supersolid and solitonic phases in one-dimensional Extended Bose-Hubbard model
We report our findings on quantum phase transitions in cold bosonic atoms in
a one dimensional optical lattice using the finite size density matrix
renormalization group method in the framework of the extended Bose-Hubbard
model. We consider wide ranges of values for the filling factors and the
nearest neighbor interactions. At commensurate fillings, we obtain two
different types of charge density wave phases and a Mott insulator phase.
However, departure from commensurate fillings yield the exotic supersolid phase
where both the crystalline and the superfluid orders coexist. In addition, we
obtain signatures for solitary waves and also superfluidity.Comment: 7 pages, 11 figure
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