1,336 research outputs found
Efficient simulation of relativistic fermions via vertex models
We have developed an efficient simulation algorithm for strongly interacting
relativistic fermions in two-dimensional field theories based on a formulation
as a loop gas. The loop models describing the dynamics of the fermions can be
mapped to statistical vertex models and our proposal is in fact an efficient
simulation algorithm for generic vertex models in arbitrary dimensions. The
algorithm essentially eliminates critical slowing down by sampling two-point
correlation functions and it allows simulations directly in the massless limit.
Moreover, it generates loop configurations with fluctuating topological
boundary conditions enabling to simulate fermions with arbitrary periodic or
anti-periodic boundary conditions. As illustrative examples, the algorithm is
applied to the Gross-Neveu model and to the Schwinger model in the strong
coupling limit.Comment: 5 pages, 4 figure
Bose-Einstein Condensation in the presence of an artificial spin-orbit interaction
Bose-Einstein condensation in the presence of a synthetic spin-momentum
interaction is considered, focusing on the case where a Dirac or Rashba
potential is generated via a tripod scheme. We found that the ground states can
be either plane wave states or superpositions of them, each characterized by
their unique density distributions.Comment: 5 pages, no figure
Combinatorics of 1-particle irreducible n-point functions via coalgebra in quantum field theory
We give a coalgebra structure on 1-vertex irreducible graphs which is that of
a cocommutative coassociative graded connected coalgebra. We generalize the
coproduct to the algebraic representation of graphs so as to express a bare
1-particle irreducible n-point function in terms of its loop order
contributions. The algebraic representation is so that graphs can be evaluated
as Feynman graphs
Arbitrary Dimensional Majorana Dualities and Network Architectures for Topological Matter
Motivated by the prospect of attaining Majorana modes at the ends of
nanowires, we analyze interacting Majorana systems on general networks and
lattices in an arbitrary number of dimensions, and derive various universal
spin duals. Such general complex Majorana architectures (other than those of
simple square or other crystalline arrangements) might be of empirical
relevance. As these systems display low-dimensional symmetries, they are
candidates for realizing topological quantum order. We prove that (a) these
Majorana systems, (b) quantum Ising gauge theories, and (c) transverse-field
Ising models with annealed bimodal disorder are all dual to one another on
general graphs. As any Dirac fermion (including electronic) operator can be
expressed as a linear combination of two Majorana fermion operators, our
results further lead to dualities between interacting Dirac fermionic systems.
The spin duals allow us to predict the feasibility of various standard
transitions as well as spin-glass type behavior in {\it interacting} Majorana
fermion or electronic systems. Several new systems that can be simulated by
arrays of Majorana wires are further introduced and investigated: (1) the {\it
XXZ honeycomb compass} model (intermediate between the classical Ising model on
the honeycomb lattice and Kitaev's honeycomb model), (2) a checkerboard lattice
realization of the model of Xu and Moore for superconducting arrays,
and a (3) compass type two-flavor Hubbard model with both pairing and hopping
terms. By the use of dualities, we show that all of these systems lie in the 3D
Ising universality class. We discuss how the existence of topological orders
and bounds on autocorrelation times can be inferred by the use of symmetries
and also propose to engineer {\it quantum simulators} out of these Majorana
networks.Comment: v3,19 pages, 18 figures, submitted to Physical Review B. 11 new
figures, new section on simulating the Hubbard model with nanowire systems,
and two new appendice
Solutions of Podolsky's Electrodynamics Equation in the First-Order Formalism
The Podolsky generalized electrodynamics with higher derivatives is
formulated in the first-order formalism. The first-order relativistic wave
equation in the 20-dimensional matrix form is derived. We prove that the
matrices of the equation obey the Petiau-Duffin-Kemmer algebra. The
Hermitianizing matrix and Lagrangian in the first-order formalism are given.
The projection operators extracting solutions of field equations for states
with definite energy-momentum and spin projections are obtained, and we find
the density matrix for the massive state. The -matrix Schrodinger
form of the equation is derived, and the Hamiltonian is obtained. Projection
operators extracting the physical eigenvalues of the Hamiltonian are found.Comment: 17 pages, minor corrections, published versio
The Hausdorff dimension of random walks and the correlation length critical exponent in Euclidean field theory
We study the random walk representation of the two-point function in
statistical mechanics models near the critical point. Using standard scaling
arguments we show that the critical exponent describing the vanishing of
the physical mass at the critical point is equal to . is
the Hausdorff dimension of the walk. is the exponent describing
the vanishing of the energy per unit length of the walk at the critical point.
For the case of O(N) models, we show that , where
is the crossover exponent known in the context of field theory. This implies
that the Hausdorff dimension of the walk is for O(N) models.Comment: 11 pages (plain TeX
A model independent analysis of gluonic pole matrix elements and universality of TMD fragmentation functions
Gluonic pole matrix elements explain the appearance of single spin
asymmetries (SSA) in high-energy scattering processes. They involve a
combination of operators which are odd under time reversal (T-odd). Such matrix
elements appear in principle both for parton distribution functions and parton
fragmentation functions. We show that for parton fragmentation functions these
gluonic pole matrix elements vanish as a consequence of the analytic structure
of scattering amplitudes in Quantum Chromodynamics. This result is important in
the study of the universality of transverse momentum dependent (TMD)
fragmentation functions.Comment: 5 pages, 5 figures, version to appear in Phys. Rev.
Landauer-type transport theory for interacting quantum wires: Application to carbon nanotube Y junctions
We propose a Landauer-like theory for nonlinear transport in networks of
one-dimensional interacting quantum wires (Luttinger liquids). A concrete
example of current experimental focus is given by carbon nanotube Y junctions.
Our theory has three basic ingredients that allow to explicitly solve this
transport problem: (i) radiative boundary conditions to describe the coupling
to external leads, (ii) the Kirchhoff node rule describing charge conservation,
and (iii) density matching conditions at every node.Comment: final version, to be published in PR
Statistics of trajectories in two-state master equations
We derive a simple expression for the probability of trajectories of a master
equation. The expression is particularly useful when the number of states is
small and permits the calculation of observables that can be defined as
functionals of whole trajectories. We illustrate the method with a two-state
master equation, for which we calculate the distribution of the time spent in
one state and the distribution of the number of transitions, each in a given
time interval. These two expressions are obtained analytically in terms of
modified Bessel functions.Comment: 4 pages, 3 figure
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