Optimization of Trial Wave Functions for Hamiltonian Lattice Models

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 ...

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 relativ...

This review covers applications of quantum Monte Carlo methods to quantum mechanical problems in the study of electronic and atomic structure, as well as applications to statistical mechanical problems both of static and dynamic nature. The common thread in all these applications is optimization of many-parameter trial states, which is done by minimization of the variance of the local or, more generally for arbitrary eigenvalue problems, minimization of the variance of the co...

We address an old problem in lattice gauge theory - the computation of the spectrum and wave functions of excited states. Our method is based on the Hamiltonian formulation of lattice gauge theory. As strategy, we propose to construct a stochastic basis of Bargmann link states, drawn from a physical probability density distribution. Then we compute transition amplitudes between stochastic basis states. From a matrix of transition elements we extract energy spectra and wave fu...

We present an algorithm for Monte Carlo simulations which is able to overcome the suppression of transitions between the phases in compact U(1) lattice gauge theory in 4 dimensions.

Monte Carlo techniques have been widely employed in statistical physics as well as in quantum theory in the Lagrangian formulation. However, in some areas of application to quantum theories computational progress has been slow. Here we present a recently developed approach: the Monte Carlo Hamiltonian method, designed to overcome the difficulties of the conventional approach.

Monte Carlo techniques with importance sampling have been extensively applied to lattice gauge theory in the Lagrangian formulation. Unfortunately, it is extremely difficult to compute the excited states using the conventional Monte Carlo algorithm. Our recently developed approach: the Monte Carlo Hamiltonian method, has been designed to overcome the difficulties of the conventional approach. In this paper, we extend the method to many body systems and quantum field theory. T...

We discuss how the concept of the Monte Carlo Hamiltonian can be applied to lattice gauge theories.

Gauge Theory plays a crucial role in many areas in science, including high energy physics, condensed matter physics and quantum information science. In quantum simulations of lattice gauge theory, an important step is to construct a wave function that obeys gauge symmetry. In this paper, we have developed gauge equivariant neural network wave function techniques for simulating continuous-variable quantum lattice gauge theories in the Hamiltonian formulation. We have applied t...