27,356 research outputs found
Gaussian expansion analysis of a matrix model with the spontaneous breakdown of rotational symmetry
Recently the gaussian expansion method has been applied to investigate the
dynamical generation of 4d space-time in the IIB matrix model, which is a
conjectured nonperturbative definition of type IIB superstring theory in 10
dimensions. Evidence for such a phenomenon, which is associated with the
spontaneous breaking of the SO(10) symmetry down to SO(4), has been obtained up
to the 7-th order calculations. Here we apply the same method to a simplified
model, which is expected to exhibit an analogous spontaneous symmetry breaking
via the same mechanism as conjectured for the IIB matrix model. The results up
to the 9-th order demonstrate a clear convergence, which allows us to
unambiguously identify the actual symmetry breaking pattern by comparing the
free energy of possible vacua and to calculate the extent of ``space-time'' in
each direction.Comment: 23 pages, 20 figures, LaTe
Longitudinal static optical properties of hydrogen chains: finite field extrapolations of matrix product state calculations
We have implemented the sweep algorithm for the variational optimization of
SU(2) x U(1) (spin and particle number) invariant matrix product states (MPS)
for general spin and particle number invariant fermionic Hamiltonians. This
class includes non-relativistic quantum chemical systems within the
Born-Oppenheimer approximation. High-accuracy ab-initio finite field results of
the longitudinal static polarizabilities and second hyperpolarizabilities of
one-dimensional hydrogen chains are presented. This allows to assess the
performance of other quantum chemical methods. For small basis sets, MPS
calculations in the saturation regime of the optical response properties can be
performed. These results are extrapolated to the thermodynamic limit.Comment: Submitted to J. Chem. Phy
Theta dependence of SU(N) gauge theories in the presence of a topological term
We review results concerning the theta dependence of 4D SU(N) gauge theories
and QCD, where theta is the coefficient of the CP-violating topological term in
the Lagrangian. In particular, we discuss theta dependence in the large-N
limit.
Most results have been obtained within the lattice formulation of the theory
via numerical simulations, which allow to investigate the theta dependence of
the ground-state energy and the spectrum around theta=0 by determining the
moments of the topological charge distribution, and their correlations with
other observables. We discuss the various methods which have been employed to
determine the topological susceptibility, and higher-order terms of the theta
expansion. We review results at zero and finite temperature. We show that the
results support the scenario obtained by general large-N scaling arguments, and
in particular the Witten-Veneziano mechanism to explain the U(1)_A problem. We
also compare with results obtained by other approaches, especially in the
large-N limit, where the issue has been also addressed using, for example, the
AdS/CFT correspondence.
We discuss issues related to theta dependence in full QCD: the neutron
electric dipole moment, the dependence of the topological susceptibility on the
quark masses, the U(1)_A symmetry breaking at finite temperature.
We also consider the 2D CP(N) model, which is an interesting theoretical
laboratory to study issues related to topology. We review analytical results in
the large-N limit, and numerical results within its lattice formulation.
Finally, we discuss the main features of the two-point correlation function
of the topological charge density.Comment: A typo in Eq. (3.9) has been corrected. An additional subsection
(5.2) has been inserted to demonstrate the nonrenormalizability of the
relevant theta parameter in the presence of massive fermions, which implies
that the continuum (a -> 0) limit must be taken keeping theta fixe
Lattice gauge theories simulations in the quantum information era
The many-body problem is ubiquitous in the theoretical description of
physical phenomena, ranging from the behavior of elementary particles to the
physics of electrons in solids. Most of our understanding of many-body systems
comes from analyzing the symmetry properties of Hamiltonian and states: the
most striking example are gauge theories such as quantum electrodynamics, where
a local symmetry strongly constrains the microscopic dynamics. The physics of
such gauge theories is relevant for the understanding of a diverse set of
systems, including frustrated quantum magnets and the collective dynamics of
elementary particles within the standard model. In the last few years, several
approaches have been put forward to tackle the complex dynamics of gauge
theories using quantum information concepts. In particular, quantum simulation
platforms have been put forward for the realization of synthetic gauge
theories, and novel classical simulation algorithms based on quantum
information concepts have been formulated. In this review we present an
introduction to these approaches, illustrating the basics concepts and
highlighting the connections between apparently very different fields, and
report the recent developments in this new thriving field of research.Comment: Pedagogical review article. Originally submitted to Contemporary
Physics, the final version will appear soon on the on-line version of the
journal. 34 page
Improving entanglement and thermodynamic R\'enyi entropy measurements in quantum Monte Carlo
We present a method for improving measurements of the entanglement R\'enyi
entropies in quantum Monte Carlo simulations by relating them with measurements
of participation R\'enyi entropies. Exploiting the capability of building
improved estimators for the latter allows to obtain very good estimates for
entanglement R\'enyi entropies. When considering a full system instead of a
bipartition, the method can be further ameliorated providing access to the
thermodynamic R\'enyi entropies with high accuracy. We also explore a
recently-proposed method for the reconstruction of the entanglement spectrum
from entanglement R\'enyi entropies and finally show how potential entanglement
Hamiltonians may be tested for their validity using a comparison with thermal
R\'enyi entropies.Comment: 15 pages, 11 figure
Pion mass dependence of the semileptonic scalar form factor within finite volume
We calculate the scalar semileptonic kaon decay in finite volume at the
momentum transfer , using chiral perturbation
theory. At first we obtain the hadronic matrix element to be calculated in
finite volume. We then evaluate the finite size effects for two volumes with and and find that the difference between the finite
volume corrections of the two volumes are larger than the difference as quoted
in \cite{Boyle2007a}. It appears then that the pion masses used for the scalar
form factor in ChPT are large which result in large finite volume corrections.
If appropriate values for pion mass are used, we believe that the finite size
effects estimated in this paper can be useful for Lattice data to extrapolate
at large lattice size.Comment: 19 pages, 5 figures, accepted for publication in EPJ
Series studies of the Potts model. I: The simple cubic Ising model
The finite lattice method of series expansion is generalised to the -state
Potts model on the simple cubic lattice.
It is found that the computational effort grows exponentially with the square
of the number of series terms obtained, unlike two-dimensional lattices where
the computational requirements grow exponentially with the number of terms. For
the Ising () case we have extended low-temperature series for the
partition functions, magnetisation and zero-field susceptibility to
from . The high-temperature series for the zero-field partition
function is extended from to . Subsequent analysis gives
critical exponents in agreement with those from field theory.Comment: submitted to J. Phys. A: Math. Gen. Uses preprint.sty: included. 24
page
On Nonperturbative Calculations in Quantum Electrodynamics
A new approach to nonperturbative calculations in quantum electrodynamics is
proposed. The approach is based on a regular iteration scheme for solution of
Schwinger-Dyson equations for generating functional of Green functions. The
approach allows one to take into account the gauge invariance conditions (Ward
identities) and to perform the renormalization program. The iteration scheme
can be realized in two versions. The first one ("perturbative vacuum")
corresponds to chain summation in the diagram language. In this version in
four-dimensional theory the non-physical singularity (Landau pole) arises which
leads to the triviality of the renormalized theory. The second version
("nonperturbative vacuum") corresponds to ladder summation and permits one to
make non-perturbative calculations of physical quantities in spite of the
triviality problem. For chiral-symmetrical leading approximation two terms of
the expansion of the first-step vertex function over photon momentum are
calculated. A formula for anomalous magnetic moment is obtained. A problem of
dynamical chiral symmetry breaking (DCSB) is considered, the calculations are
performed for renormalized theory in Minkowsky space. In the strong coupling
region DCSB-solutions arise. For the renormalized theory a DCSB-solution is
also possible in the weak coupling region but with a subsidiary condition on
the value of .Comment: 31 pages, Plain LaTex, no figures. Journal version: some discussion
and refs. are adde
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