We give a brief review of recent developments by the variational Monte Carlo method, in addition to some new results. We discuss $t$ - $J$ -type models: the ordinary $t$ - $J$ model in one and two dimensions, and the one-dimensional supersymmetric $t$ - $J$ model with the long-range coupling of inverse square.We give a brief review of recent developments by the variational Monte Carlo method, in addition to some new results. We discuss $t$-$J$-type models: the ordinary $t$-$J$ model in one and two dimensions, and the one-dimensional supersymmetric $t$-$J$ model with the long-range coupling of inverse square.

arXiv:cond-mat/9506078Jun 19, 19950 citations

Aspects of supersymmetric quantum mechanics

Barry A. Freedman

Annals of PhysicsMar 1, 198311 citations

On Supersymmetric Quantum Mechanics

M. Kibler, Mohammed Daoud A

Springer eBooksJan 1, 20043 citations

Variational Monte Carlo simulation with tensor networks of a pure Z3 gauge theory in (2+1)D

Patrick Emonts, Mari Carmen Bañuls, J. I. Cirac +1 more

Variational minimization of tensor network states enables the exploration of low energy states of lattice gauge theories. However, the exact numerical evaluation of high-dimensional tensor network states remains challenging in general. In [E. Zohar and J. I. Cirac, Phys. Rev. D 97, 034510 (2018)] it was shown how, by combining gauged Gaussian projected entangled pair states with a variational Monte Carlo procedure, it is possible to efficiently compute physical observables. In this paper we demonstrate how this approach can be used to investigate numerically the ground state of a lattice gauge theory. More concretely, we explicitly carry out the variational Monte Carlo procedure based on such contraction methods for a pure gauge Kogut-Susskind Hamiltonian with a ${\mathbb{Z}}_{3}$ gauge field in two spatial dimensions. This is a first proof of principle to the method, which provides an inherent way to increase the number of variational parameters and can be readily extended to systems with physical fermions.Variational minimization of tensor network states enables the exploration of low energy states of lattice gauge theories. However, the exact numerical evaluation of high-dimensional tensor network states remains challenging in general. In [E. Zohar and J. I. Cirac, Phys. Rev. D 97, 034510 (2018)] it was shown how, by combining gauged Gaussian projected entangled pair states with a variational Monte Carlo procedure, it is possible to efficiently compute physical observables. In this paper we demonstrate how this approach can be used to investigate numerically the ground state of a lattice gauge theory. More concretely, we explicitly carry out the variational Monte Carlo procedure based on such contraction methods for a pure gauge Kogut-Susskind Hamiltonian with a ${\mathbb{Z}}_{3}$ gauge field in two spatial dimensions. This is a first proof of principle to the method, which provides an inherent way to increase the number of variational parameters and can be readily extended to systems with physical fermions.

arXiv:2008.00882Physical review. D/Physical review. D.Oct 1, 202036 citations

A Supersymmetric Approach to Excited States via Quantum Monte Carlo

Eric R. Bittner, Jeremy B. Maddox, Donald Jack Kouri

We present here a supersymmetric (SUSY) approach for determining excitation energies within the context of a quantum Monte Carlo scheme. By using the fact that SUSY quantum mechanics gives rises to a series of isospectral Hamiltonians, we show that Monte Carlo ground-state calculations in the SUSY partners can be used to reconstruct accurately both the spectrum and states of an arbitrary Schrödinger equation. Since the ground-state of each partner potential is node-less, we avoid any ``node''-problem typically associated with the Monte Carlo technique. While we provide an example of using this approach to determine the tunneling states in a double-well potential, the method is applicable to any 1D potential problem. We conclude by discussing the extension to higher dimensions.We present here a supersymmetric (SUSY) approach for determining excitation energies within the context of a quantum Monte Carlo scheme. By using the fact that SUSY quantum mechanics gives rises to a series of isospectral Hamiltonians, we show that Monte Carlo ground-state calculations in the SUSY partners can be used to reconstruct accurately both the spectrum and states of an arbitrary Schrödinger equation. Since the ground-state of each partner potential is node-less, we avoid any ``node''-problem typically associated with the Monte Carlo technique. While we provide an example of using this approach to determine the tunneling states in a double-well potential, the method is applicable to any 1D potential problem. We conclude by discussing the extension to higher dimensions.

arXiv:0903.4827Mar 27, 20090 citations

An Efficient Adaptive Monte Carlo Approach for Multidimensional Quantum Mechanics

Venelin Todorov, Ivan Dimov

Studies in computational intelligenceJan 1, 20220 citations

We give a brief review of recent developments by the variational Monte Carlo method, in addition to some new results. We discuss

t

J

-type models: the ordinary

t

J

model in one and two dimensions, and the one-dimensional supersymmetric

t

J

model with the long-range coupling of inverse square.

{\mathbb{Z}}_{3}

gauge field in two spatial dimensions. This is a first proof of principle to the method, which provides an inherent way to increase the number of variational parameters and can be readily extended to systems with physical fermions.