1,504 research outputs found
High density QCD on a Lefschetz thimble?
It is sometimes speculated that the sign problem that afflicts many quantum
field theories might be reduced or even eliminated by choosing an alternative
domain of integration within a complexified extension of the path integral (in
the spirit of the stationary phase integration method). In this paper we start
to explore this possibility somewhat systematically. A first inspection reveals
the presence of many difficulties but - quite surprisingly - most of them have
an interesting solution. In particular, it is possible to regularize the
lattice theory on a Lefschetz thimble, where the imaginary part of the action
is constant and disappears from all observables. This regularization can be
justified in terms of symmetries and perturbation theory. Moreover, it is
possible to design a Monte Carlo algorithm that samples the configurations in
the thimble. This is done by simulating, effectively, a five dimensional
system. We describe the algorithm in detail and analyze its expected cost and
stability. Unfortunately, the measure term also produces a phase which is not
constant and it is currently very expensive to compute. This residual sign
problem is expected to be much milder, as the dominant part of the integral is
not affected, but we have still no convincing evidence of this. However, the
main goal of this paper is to introduce a new approach to the sign problem,
that seems to offer much room for improvements. An appealing feature of this
approach is its generality. It is illustrated first in the simple case of a
scalar field theory with chemical potential, and then extended to the more
challenging case of QCD at finite baryonic density.Comment: Misleading footnote 1 corrected: locality deserves better
investigations. Formula (31) corrected (we thank Giovanni Eruzzi for this
observation). Note different title in journal versio
Matrix product states and variational methods applied to critical quantum field theory
We study the second-order quantum phase-transition of massive real scalar
field theory with a quartic interaction ( theory) in (1+1) dimensions
on an infinite spatial lattice using matrix product states (MPS). We introduce
and apply a naive variational conjugate gradient method, based on the
time-dependent variational principle (TDVP) for imaginary time, to obtain
approximate ground states, using a related ansatz for excitations to calculate
the particle and soliton masses and to obtain the spectral density. We also
estimate the central charge using finite-entanglement scaling. Our value for
the critical parameter agrees well with recent Monte Carlo results, improving
on an earlier study which used the related DMRG method, verifying that these
techniques are well-suited to studying critical field systems. We also obtain
critical exponents that agree, as expected, with those of the transverse Ising
model. Additionally, we treat the special case of uniform product states (mean
field theory) separately, showing that they may be used to investigate
non-critical quantum field theories under certain conditions.Comment: 24 pages, 21 figures, with a minor improvement to the QFT sectio
First-principles perturbative computation of dielectric and Born charge tensors in finite electric fields
We present a perturbative treatment of the response properties of insulating
crystals under a dc bias field, and use this to study the effects of such bias
fields on the Born effective charge tensor and dielectric tensor of insulators.
We start out by expanding a variational field-dependent total-energy functional
with respect to the electric field within the framework of density-functional
perturbation theory. The second-order term in the expansion of the total energy
is then minimized with respect to the first-order wave functions, from which
the Born effective charge tensor and dielectric tensor are easily computed. We
demonstrate an implementation of the method and perform illustrative
calculations for the III-V semiconductors AlAs and GaAs under finite bias
field
Perturbative corrections to the Gutzwiller mean-field solution of the Mott-Hubbard model
We study the Mott-insulator transition of bosonic atoms in optical lattices.
Using perturbation theory, we analyze the deviations from the mean-field
Gutzwiller ansatz, which become appreciable for intermediate values of the
ratio between hopping amplitude and interaction energy. We discuss corrections
to number fluctuations, order parameter, and compressibility. In particular, we
improve the description of the short-range correlations in the one-particle
density matrix. These corrections are important for experimentally observed
expansion patterns, both for bulk lattices and in a confining trap potential.Comment: 10 pages, 10 figue
Recent Developments in the Theory of Tunneling
Path-integral approach in imaginary and complex time has been proven
successful in treating the tunneling phenomena in quantum mechanics and quantum
field theories. Latest developments in this field, the proper valley method in
imaginary time, its application to various quantum systems, complex time
formalism, asympton theory for the large order analysis of the perturbation
theory, are reviewed in a self-contained manner.Comment: 100 pages, LaTeX, PTPTeX.sty, 36 eps figures, To be published in
Progress of Theoretical Physics Supplimen
On the Inversion of High Energy Proton
Inversion of the K-fold stochastic autoconvolution integral equation is an
elementary nonlinear problem, yet there are no de facto methods to solve it
with finite statistics. To fix this problem, we introduce a novel inverse
algorithm based on a combination of minimization of relative entropy, the Fast
Fourier Transform and a recursive version of Efron's bootstrap. This gives us
power to obtain new perspectives on non-perturbative high energy QCD, such as
probing the ab initio principles underlying the approximately negative binomial
distributions of observed charged particle final state multiplicities, related
to multiparton interactions, the fluctuating structure and profile of proton
and diffraction. As a proof-of-concept, we apply the algorithm to ALICE
proton-proton charged particle multiplicity measurements done at different
center-of-mass energies and fiducial pseudorapidity intervals at the LHC,
available on HEPData. A strong double peak structure emerges from the
inversion, barely visible without it.Comment: 29 pages, 10 figures, v2: extended analysis (re-projection ratios,
2D
- …