arXiv subjects
Publications and source records attributed to Matteo Beccaria.
We study a Hamiltonian lattice version of the two-dimensional Wess-Zumino model. Preliminary results obtained by Quantum Monte Carlo with a many-parameter guiding wave function are presented. We analyze the pattern of supersymmetry breaking by measuring the ground state energy and a set of supersymmetric Ward identities. The algorithm is quite effective and allows very precise measurements.
The accuracy of Green Function Monte Carlo (GFMC) simulations can be greatly improved by a clever choice of the approximate ground state wave function that controls configuration sampling. This trial wave function typically depends on many free parameters whose fixing is a non trivial task. Here, we discuss a general purpose adaptive algorithm for their non-linear optimization. As a non trivial application we test the method on the two dimensional Wess-Zumino model, a relativistically invariant supersymmetric field theory with interacting bosonic and fermionic degrees of freedom.
We present an improved upper bound for the ground state energy of lattice fermion models with sign problem. The bound can be computed by numerical simulation of a recently proposed family of deformed Hamiltonians with no sign problem. For one dimensional models, we expect the bound to be particularly effective and practical extrapolation procedures are discussed. In particular, in a model of spinless interacting fermions and in the Hubbard model at various filling and Coulomb repulsion we show how such techniques can estimate ground state energies and correlation function with great accuracy.
We present a simulation algorithm for Hamiltonian fermion lattice models. A guiding trial wave function is adaptively optimized during Monte Carlo evolution. We apply the method to the two dimensional Gross-Neveu model and analyze systematc errors in the study of ground state properties. We show that accurate measurements can be achieved by a proper extrapolation in the algorithm free parameters.
We study four dimensional SU(2) lattice gauge theory in the Hamiltonian formalism by Green's Function Monte Carlo methods. A trial ground state wave function is introduced to improve the configuration sampling and we discuss the interplay between its complexity and the simulation systematic errors. As a case study, we compare the leading strong coupling approximation and an improved 4 parameters wave function with 1X1 and 1X2 plaquette terms. Our numerical results favors the second option.
We apply a recently proposed Green Function Monte Carlo to the study of Hamiltonian lattice gauge theories. This class of algorithms computes quantum vacuum expectation values by averaging over a set of suitable weighted random walkers. By means of a procedure called Stochastic Reconfiguration the long standing problem of keeping fixed the walker population without a priori knowledge on the ground state is completely solved. In the $U(1)_2$ model, which we choose as our theoretical laboratory, we evaluate the mean plaquette and the vacuum energy per plaquette. We find good agreement with previous works using model dependent guiding functions for the random walkers.
We propose a new Monte Carlo algorithm for the numerical study of general lattice models in Hamiltonian form. The algorithm is based on an initial Ansatz for the ground state wave function depending on a set of free parameters which are dynamically optimized. The method is discussed in details and results are reported from explicit simulations of U(1) lattice gauge theory in 1+1 dimensions.
We present a simple derivation of a Feynman-Kac type formula to study fermionic systems. In this approach the real time or the imaginary time dynamics is expressed in terms of the evolution of a collection of Poisson processes. A computer implementation of this formula leads to a family of algorithms parametrized by the values of the jump rates of the Poisson processes. From these an optimal algorithm can be chosen which coincides with the Green Function Monte Carlo (GFMC) method in the limit when the latter becomes exact.
We discuss New Physics effects in fermion pair production at LC in the framework of the ``Z-peak subtracted approach'', a theoretical scheme that exploits the experimental measurements at LEP1 and SLC as input parameters. In particular, we discuss the role of the longitudinal polarization asymmetry $A_{LR,μ}$ which turns out to be a very sensitive probe to New Physics of universal type. The extension of the method to non universal effects is discussed and an application is given in two examples: general contact interactions and low energy gravity models with graviton exchange.
We derive an exact probabilistic representation for the evolution of a Hubbard model with site- and spin-dependent hopping coefficients and site-dependent interactions in terms of an associated stochastic dynamics of a collection of Poisson processes.
For a class of generalized Hubbard models, we determine the maximal stability region for the superconducting eta-pairing ground state. We exploit the Optimized Ground State (OGS) approach and the Lanczos diagonalization procedure to derive a sequence of improved bounds. We show that some pieces of the stability boundary are asymptotic, namely independent on the OGS cluster size. In this way, necessary and sufficient conditions are obtained to realize superconductivity in terms of an eta-pairing ground state. The phenomenon is explained by studying the properties of certain exact eigenstates of the OGS hamiltonians.
We present a simple derivation of a Feynman-Kac type formula to study fermionic systems. In this approach the real time or the imaginary time dynamics is expressed in terms of the evolution of a collection of Poisson processes. A computer implementation of this formula leads to a family of algorithms parametrized by the values of the jump rates of the Poisson processes. From these an optimal algorithm can be chosen which coincides with the Green Function Monte Carlo method in the limit when the latter becomes exact.
We study the numerical simulation of supersymmetric models having a local Nicolai map. The mapping can be regarded as a stochastic equation and its numerical integration provides an algorithm for the simulation of the original model. In this paper, the method is discussed in details and applied to examples in 0+1 and 1+1 dimensions.
Nonlinear systems of the reaction-diffusion type, including Gierer-Meinhardt models of autocatalysis, are studied by using Lie algebras coming from the prolongation structure. The consequences of this analytical approach, as the determination of special exact solutions, are compared with the corresponding results obtained via numerical simulations.
The aim of this work is to show how it is possible to build an on line whitening filter in an adaptive way. We have modeled the VIRGO noise spectrum as an autoregressive stochastic process, after a pre-filtering of the theoretical curve which flattens the low frequency part of the spectrum. We have tested some very popular adaptive algorithms, based on the gradient methods and on the least squares methods with a lattice structure filter.
The $(g_2^{(1)}, d_4^{(3)})$\ pair of non simply laced affine Toda theories is studied from the point of view of non perturbative duality. The classical spectrum of each member is composed of two massive scalar particles. The exact S-matrix prediction for the dual behaviour of the coupling dependent mass ratio is found to be in strong agreement with Monte Carlo data.
We consider the $U_q[SU(2)]$ symmetric Heisenberg chain when $q=e^{iπ/(m+1)}$ and $m$ is integer. We consider the cases $m=3$ and $m=5$ which correspond to the Ising and 3-state Potts models. We study the finite size scaling (FSS) of the ground states in different quantum spin sectors and restricting to highest weights of type-II representations. We compute the levels by a diagrammatic technique which needs only the commutation relations of the underlying Temperley-Lieb algebra. The results match the FSS predictions which hold for the Bethe levels. (2 PostScript figures (or the corresponding tables) available from the author)
We consider the lattice formulation of bosonized quantum field theories. As a non trivial example, we study the two dimensional Gross-Neveu model. Analytical investigations and direct numerical simulation strongly suggest that the lattice model reproduces the continuum physics. Anticommuting fields are not required and there are not related doubling problems. (3 PostScript figures available from the author)