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 $(p+ip)$ 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 $13\times 13$-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 $\nu$ describing the vanishing of the physical mass at the critical point is equal to $\nu_\theta/ d_w$. $d_w$ is the Hausdorff dimension of the walk. $\nu_\theta$ 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 $\nu_\theta=\varphi$, where $\varphi$ is the crossover exponent known in the context of field theory. This implies that the Hausdorff dimension of the walk is $\varphi/\nu$ 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