497 research outputs found
Bosons Confined in Optical Lattices: the Numerical Renormalization Group revisited
A Bose-Hubbard model, describing bosons in a harmonic trap with a
superimposed optical lattice, is studied using a fast and accurate variational
technique (MF+NRG): the Gutzwiller mean-field (MF) ansatz is combined with a
Numerical Renormalization Group (NRG) procedure in order to improve on both.
Results are presented for one, two and three dimensions, with particular
attention to the experimentally accessible momentum distribution and possible
satellite peaks in this distribution. In one dimension, a comparison is made
with exact results obtained using Stochastich Series Expansion.Comment: 10 pages, 15 figure
Ghosts, Strong Coupling and Accidental Symmetries in Massive Gravity
We show that the strong self-interaction of the scalar polarization of a
massive graviton can be understood in terms of the propagation of an extra
ghost-like degree of freedom, thus relating strong coupling to the sixth degree
of freedom discussed by Boulware and Deser in their Hamiltonian analysis of
massive gravity. This enables one to understand the Vainshtein recovery of
solutions of massless gravity as being due to the effect of the exchange of
this ghost which gets frozen at distances larger than the Vainshtein radius.
Inside this region, we can trust the two-field Lagrangian perturbatively, while
at larger distances one can use the higher derivative formulation. We also
compare massive gravity with other models, namely deconstructed theories of
gravity, as well as DGP model. In the latter case we argue that the Vainshtein
recovery process is of different nature, not involving a ghost degree of
freedom.Comment: 21 page
Solving the Richardson equations for Fermions
Forty years ago Richardson showed that the eigenstates of the pairing
Hamiltonian with constant interaction strength can be calculated by solving a
set of non-linear coupled equations. However, in the case of Fermions these
equations lead to singularities which made them very hard to solve. This letter
explains how these singularities can be avoided through a change of variables
making the Fermionic pairing problem numerically solvable for arbitrary single
particle energies and degeneracies.Comment: 5 pages, 4 figures, submitted to Phys.Rev.
A quantum Monte-Carlo method for fermions, free of discretization errors
In this work we present a novel quantum Monte-Carlo method for fermions,
based on an exact decomposition of the Boltzmann operator . It
can be seen as a synthesis of several related methods. It has the advantage
that it is free of discretization errors, and applicable to general
interactions, both for ground-state and finite-temperature calculations. The
decomposition is based on low-rank matrices, which allows faster calculations.
As an illustration, the method is applied to an analytically solvable model
(pairing in a degenerate shell) and to the Hubbard model.Comment: 5 pages, 4 figures, submitted to Phys. Rev. Let
Optimal Monte Carlo Updating
Based on Peskun's theorem it is shown that optimal transition matrices in
Markov chain Monte Carlo should have zero diagonal elements except for the
diagonal element corresponding to the largest weight. We will compare the
statistical efficiency of this sampler to existing algorithms, such as
heat-bath updating and the Metropolis algorithm. We provide numerical results
for the Potts model as an application in classical physics. As an application
in quantum physics we consider the spin 3/2 XY model and the Bose-Hubbard model
which have been simulated by the directed loop algorithm in the stochastic
series expansion framework.Comment: 6 pages, 5 figures, replaced with published versio
Naturalness in Cosmological Initial Conditions
We propose a novel approach to the problem of constraining cosmological
initial conditions. Within the framework of effective field theory, we classify
initial conditions in terms of boundary terms added to the effective action
describing the cosmological evolution below Planckian energies. These boundary
terms can be thought of as spacelike branes which may support extra
instantaneous degrees of freedom and extra operators. Interactions and
renormalization of these boundary terms allow us to apply to the boundary terms
the field-theoretical requirement of naturalness, i.e. stability under
radiative corrections. We apply this requirement to slow-roll inflation with
non-adiabatic initial conditions, and to cyclic cosmology. This allows us to
define in a precise sense when some of these models are fine-tuned. We also
describe how to parametrize in a model-independent way non-Gaussian initial
conditions; we show that in some cases they are both potentially observable and
pass our naturalness requirement.Comment: 35 pages, 8 figure
Continuous Time Quantum Monte Carlo Method for Fermions: Beyond Auxiliary Field Framework
Numerically exact continuous-time Quantum Monte Carlo algorithm for finite
fermionic systems with non-local interactions is proposed. The scheme is
particularly applicable for general multi-band time-dependent correlations
since it does not invoke Hubbard-Stratonovich transformation. The present
determinantal grand-canonical method is based on a stochastic series expansion
for the partition function in the interaction representation. The results for
the Green function and for the time-dependent susceptibility of multi-orbital
super-symmetric impurity model with a spin-flip interaction are presented
Strong Coupling vs. 4-D Locality in Induced Gravity
We re-examine the problem of strong coupling in a regularized version of DGP
(or ``brane-induced'') gravity. We find that the regularization of ref.
hep-th/0304148 differs from DGP in that it does not exhibit strong coupling or
ghosts up to cubic order in the interactions. We suggest that the nonlocal
nature of the theory, when written in terms of the 4-D metric, is a plausible
reason for this phenomenon. Finally, we briefly discuss the possible behavior
of the model at higher-order in perturbation theory.Comment: 19 pages, accepted for publication in PR
Corney and Drummond Reply to "Gaussian quantum Monte Carlo methods for fermions and bosons"
A reply to S. M. A. Rombouts's (2006) comment on the article 'Gaussian quantum Monte Carlo methods for fermions and bosons', which appeared in Physical Review Letters 96 as article number 188901 (http://dx.doi.org/10.1103/PhysRevLett.96.188901). The original article by J. F. Corney and P. D. Drummond (2004) appeared in Physical Review Letters 93 as article number 260401 (http://dx.doi.org/10.1103/PhysRevLett.93.260401)
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