We extend the Worldline Monte Carlo approach to computationally simulating the Feynman path integral of non-relativistic multi-particle quantum-mechanical systems. We show how to generate an arbitrary number of worldlines distributed according to the (free) kinetic part of the multi-particle quantum dynamics and how to simulate interactions between worldlines in the ensemble. We test this formalism with two- and three-particle quantum mechanical systems, with both long range Coulomb-like interactions between the particles and external fields acting separately on the particles, in various spatial dimensionality. We extract accurate estimations of the ground state energy of these systems using the late-time behaviour of the propagator, validating our approach with numerically exact solutions obtained via straightforward diagonalisation of the Hamiltonian. Systematic benchmarking of the new approach, presented here for the first time, shows that the computational complexity of Wordline Monte Carlo scales more favourably with respect to standard numerical alternatives. The method, which is general, numerically exact, and computationally not intensive, can easily be generalised to relativistic systems.We extend the Worldline Monte Carlo approach to computationally simulating the Feynman path integral of non-relativistic multi-particle quantum-mechanical systems. We show how to generate an arbitrary number of worldlines distributed according to the (free) kinetic part of the multi-particle quantum dynamics and how to simulate interactions between worldlines in the ensemble. We test this formalism with two- and three-particle quantum mechanical systems, with both long range Coulomb-like interactions between the particles and external fields acting separately on the particles, in various spatial dimensionality. We extract accurate estimations of the ground state energy of these systems using the late-time behaviour of the propagator, validating our approach with numerically exact solutions obtained via straightforward diagonalisation of the Hamiltonian. Systematic benchmarking of the new approach, presented here for the first time, shows that the computational complexity of Wordline Monte Carlo scales more favourably with respect to standard numerical alternatives. The method, which is general, numerically exact, and computationally not intensive, can easily be generalised to relativistic systems.

quant-pharXiv:2512.24942Jan 1, 20260 citations

World-Line Quantum Monte Carlo

Richard T. Scalettar

Springer eBooksJan 1, 19991 citation

Lattice Monte Carlo simulations with two impurity worldlines

Fabian Hildenbrand, Serdar Elhatisari, Timo A. Lähde +2 more

Abstract We develop the impurity lattice Monte Carlo formalism for the case of two distinguishable impurities in a bath of polarized fermions. The majority particles are treated as explicit degrees of freedom, while the impurities are described by worldlines. The latter serve as localized auxiliary fields, which affect the majority particles. We apply the method to non-relativistic three-dimensional systems of two impurities and a number of majority particles where both the impurity–impurity interaction and the impurity–majority interaction have zero range. We consider the case of an attractive impurity–majority interaction, and we study the formation and disintegration of bound states as a function of the impurity–impurity interaction strength. We also discuss the potential applications of this formalism to other quantum many-body systems.Abstract We develop the impurity lattice Monte Carlo formalism for the case of two distinguishable impurities in a bath of polarized fermions. The majority particles are treated as explicit degrees of freedom, while the impurities are described by worldlines. The latter serve as localized auxiliary fields, which affect the majority particles. We apply the method to non-relativistic three-dimensional systems of two impurities and a number of majority particles where both the impurity–impurity interaction and the impurity–majority interaction have zero range. We consider the case of an attractive impurity–majority interaction, and we study the formation and disintegration of bound states as a function of the impurity–impurity interaction strength. We also discuss the potential applications of this formalism to other quantum many-body systems.

arXiv:2206.09459The European Physical Journal ASep 2, 202210 citations

Worldline Monte Carlo method for few-body nuclear physics

Shailesh Chandrasekharan A, Son T. Nguyen, Thomas R. Richardson

In this work we introduce a worldline-based fermion Monte Carlo algorithm for studying few body quantum mechanics of self-interacting fermions in the Hamiltonian lattice formulation. Our motivation to construct the method comes from our interest in studying renormalization of chiral nuclear effective-field theory with lattice regularization. In particular we wish to apply our method to compute the lattice spacing dependence of local lattice interactions as we take the continuum limit of the lattice theory. Our algorithm can compute matrix elements of the operator $exp(\ensuremath{-}\ensuremath{\beta}H)$, where $H$ is the lattice Hamiltonian and $\ensuremath{\beta}$ is a free real parameter. These elements help us compute deep bound states that are well separated from scattering states even at values of $\ensuremath{\beta}$ which are not very large. Computing these bound-state energies accurately can help us study renormalization of the lattice theory. In addition to developing the algorithm, in this work we also introduce a finite-volume renormalization scheme for the lattice Hamiltonian of the leading pionless effective-field theory and show how it would work in the one- and two-body sectors.In this work we introduce a worldline-based fermion Monte Carlo algorithm for studying few body quantum mechanics of self-interacting fermions in the Hamiltonian lattice formulation. Our motivation to construct the method comes from our interest in studying renormalization of chiral nuclear effective-field theory with lattice regularization. In particular we wish to apply our method to compute the lattice spacing dependence of local lattice interactions as we take the continuum limit of the lattice theory. Our algorithm can compute matrix elements of the operator $exp(\ensuremath{-}\ensuremath{\beta}H)$, where $H$ is the lattice Hamiltonian and $\ensuremath{\beta}$ is a free real parameter. These elements help us compute deep bound states that are well separated from scattering states even at values of $\ensuremath{\beta}$ which are not very large. Computing these bound-state energies accurately can help us study renormalization of the lattice theory. In addition to developing the algorithm, in this work we also introduce a finite-volume renormalization scheme for the lattice Hamiltonian of the leading pionless effective-field theory and show how it would work in the one- and two-body sectors.

arXiv:2402.15377Physical Review CAug 14, 20244 citations

H

is the lattice Hamiltonian and $\ensuremath{\beta}$ is a free real parameter. These elements help us compute deep bound states that are well separated from scattering states even at values of $\ensuremath{\beta}$ which are not very large. Computing these bound-state energies accurately can help us study renormalization of the lattice theory. In addition to developing the algorithm, in this work we also introduce a finite-volume renormalization scheme for the lattice Hamiltonian of the leading pionless effective-field theory and show how it would work in the one- and two-body sectors.