1,283 research outputs found
Bose-Hubbard model on a star lattice
We analyze the Bose-Hubbard model of hardcore bosons with nearest neighbor
hopping and repulsive interactions on a star lattice using both quantum Monte
Carlo simulation and dual vortex theory. We obtain the phase diagram of this
model as a function of the chemical potential and the relative strength of
hopping and interaction. In the strong interaction regime, we find that the
Mott phases of the model at 1/2 and 1/3 fillings, in contrast to their
counterparts on square, triangular, and Kagome lattices, are either
translationally invariant resonant valence bond (RVB) phases with no
density-wave order or have coexisting density-wave and RVB orders. We also find
that upon increasing the relative strength of hopping and interaction, the
translationally invariant Mott states undergo direct second order
superfluid-insulator quantum phase transitions. We compute the critical
exponents for these transitions and argue using the dual vortex picture that
the transitions, when approached through the tip of the Mott lobe, belong to
the inverted XY universality class.Comment: 10 pages, 18 figures, minor changes, two references adde
Superfluid-Insulator transitions of bosons on Kagome lattice at non-integer fillings
We study the superfluid-insulator transitions of bosons on the Kagome lattice
at incommensurate filling factors f=1/2 and 2/3 using a duality analysis. We
find that at f=1/2 the bosons will always be in a superfluid phase and
demonstrate that the T_3 symmetry of the dual (dice) lattice, which results in
dynamic localization of vortices due to the Aharanov-Bohm caging effect, is at
the heart of this phenomenon. In contrast, for f=2/3, we find that the bosons
exhibit a quantum phase transition between superfluid and translational
symmetry broken Mott insulating phases. We discuss the possible broken
symmetries of the Mott phase and elaborate the theory of such a transition.
Finally we map the boson system to a XXZ spin model in a magnetic field and
discuss the properties of this spin model using the obtained results.Comment: 10 pages, 8 figures, a few typos correcte
Dipolar spin correlations in classical pyrochlore magnets
We study spin correlations for the highly frustrated classical pyrochlore
lattice antiferromagnets with O(N) symmetry in the limit T->0. We conjecture
that a local constraint obeyed by the extensively degenerate ground states
dictates a dipolar form for the asymptotic spin correlations, at all N 2
for which the system is paramagnetic down to T=0. We verify this conjecture in
the cases N=1 and N=3 by simulations and to all orders in the 1/N expansion
about the solvable N=infinity limit. Remarkably, the N=infinity formulae are an
excellent fit, at all distances, to the correlators at N=3 and even at N=1.
Thus we obtain a simple analytical expression also for the correlations of the
equivalent models of spin ice and cubic water ice, I_h.Comment: 4 pages revtex
Valence Bond Solids and Their Quantum Melting in Hard-Core Bosons on the Kagome Lattice
Using large scale quantum Monte Carlo simulations and dual vortex theory we
analyze the ground state phase diagram of hard-core bosons on the kagome
lattice with nearest neighbor repulsion. In contrast to the case of a
triangular lattice, no supersolid emerges for strong interactions. While a
uniform superfluid prevails at half-filling, two novel solid phases emerge at
densities and . These solids exhibit an only partial
ordering of the bosonic density, allowing for local resonances on a subset of
hexagons of the kagome lattice. We provide evidence for a weakly first-order
phase transition at the quantum melting point between these solid phases and
the superfluid.Comment: 4 pages, 7 figure
Universal behaviour of ideal and interacting quantum gases in two dimensions
I discuss ideal and interacting quantum gases obeying general fractional
exclusion statistics. For systems with constant density of single-particle
states, described in the mean field approximation, the entropy depends neither
on the microscopic exclusion statistics, nor on the interaction. Such systems
are called {\em thermodynamically equivalent} and I show that the microscopic
reason for this equivalence is a one-to-one correspondence between the excited
states of these systems. This provides a method, different from the
bosonisation technique, to transform between systems of different exclusion
statistics. In the last section the macroscopic aspects of this method are
discussed.
In Appendix A I calculate the fluctuation of the ground state population of a
condensed Bose gas in grandcanonical ensemble and mean field approximation,
while in Appendix B I show a situation where although the system exhibits
fractional exclusion properties on microscopic energy intervals, a rigorous
calculation of the population of single particle states reveals a condensation
phenomenon. This also implies a malfunction of the usual and simplified
calculation technique of the most probable statistical distributions.Comment: About 14 journal pages, with 1 figure. Changes: Body of paper: same
content, with slight rephrasing. Apendices are new. In the original
submission I just mentioned the condensation, which is now detailed in
Appendix B. They were intended for a separate paper. Reason for changes:
rejection from Phys. Rev. Lett., resubmission to J. Phys. A: Math. Ge
On the isospin dependence of the mean spin-orbit field in nuclei
By the use of the latest experimental data on the spectra of Sb and
Sn and on the analysis of properties of other odd nuclei adjacent to
doubly magic closed shells the isospin dependence of a mean spin-orbit
potential is defined. Such a dependence received the explanation in the
framework of different theoretical approaches.Comment: 52 pages, Revtex, no figure
On the difference between proton and neutron spin-orbit splittings in nuclei
The latest experimental data on nuclei at Sn permit us for the first
time to determine the spin-orbit splittings of neutrons and protons in
identical orbits in this neutron-rich doubly-magic region and compare the case
to that of Pb. Using the new results, which are now consistent for the
two neutron-rich doubly magic regions, a theoretical analysis defines the
isotopic dependence of the mean field spin-orbit potential and leads to a
simple explicit expression for the difference between the spin-orbit splittings
of neutrons and protons. The isotopic dependence is explained in the framework
of different theoretical approaches.Comment: 8 pages, revte
An embedding potential definition of channel functions
We show that the imaginary part of the embedding potential, a generalised
logarithmic derivative, defined over the interface between an electrical lead
and some conductor, has orthogonal eigenfunctions which define conduction
channels into and out of the lead. In the case of an infinitely extended
interface we establish the relationship between these eigenfunctions and the
Bloch states evaluated over the interface. Using the new channel functions, a
well-known result for the total transmission through the conductor system is
simply derived.Comment: 14 pages, 2 figure
Effective quantum volume, fidelity and computational cost of noisy quantum processing experiments
Today's experimental noisy quantum processors can compete with and surpass
all known algorithms on state-of-the-art supercomputers for the computational
benchmark task of Random Circuit Sampling [1-5]. Additionally, a circuit-based
quantum simulation of quantum information scrambling [6], which measures a
local observable, has already outperformed standard full wave function
simulation algorithms, e.g., exact Schrodinger evolution and Matrix Product
States (MPS). However, this experiment has not yet surpassed tensor network
contraction for computing the value of the observable. Based on those studies,
we provide a unified framework that utilizes the underlying effective circuit
volume to explain the tradeoff between the experimentally achievable
signal-to-noise ratio for a specific observable, and the corresponding
computational cost. We apply this framework to recent quantum processor
experiments of Random Circuit Sampling [5], quantum information scrambling [6],
and a Floquet circuit unitary [7]. This allows us to reproduce the results of
Ref. [7] in less than one second per data point using one GPU.Comment: 14 pages, 13 figure
Bosonic and fermionic single-particle states in the Haldane approach to statistics for identical particles
We give two formulations of exclusion statistics (ES) using a variable number
of bosonic or fermionic single-particle states which depend on the number of
particles in the system. Associated bosonic and fermionic ES parameters are
introduced and are discussed for FQHE quasiparticles, anyons in the lowest
Landau level and for the Calogero-Sutherland model. In the latter case, only
one family of solutions is emphasized to be sufficient to recover ES;
appropriate families are specified for a number of formulations of the
Calogero-Sutherland model. We extend the picture of variable number of
single-particle states to generalized ideal gases with statistical interaction
between particles of different momenta. Integral equations are derived which
determine the momentum distribution for single-particle states and distribution
of particles over the single-particle states in the thermal equilibrium.Comment: 6 pages, REVTE
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