Feynman path integrals for discrete-variable systems: Walks on Hamiltonian graphs
arXiv:2407.11231 · doi:10.1103/PhysRevResearch.7.013220
Abstract
We propose a natural, parameter-free, discrete-variable formulation of Feynman path integrals. We show that for discrete-variable quantum systems, Feynman path integrals take the form of walks on the graph whose weighted adjacency matrix is the Hamiltonian. By working out expressions for the partition function and transition amplitudes of discretized versions of continuous-variable quantum systems, and then taking the continuum limit, we explicitly recover Feynman's continuous-variable path integrals. We also discuss the implications of our result.
9 pages, 3 figures
References in corpus (13)
- Worm Algorithm and Diagrammatic Monte Carlo: A New Approach to Continuous-Space Path Integral Monte Carlo Simulations
- Gapless quantum spin liquid, stripe and antiferromagnetic phases in frustrated Hubbard models in two dimensions
- Off-Diagonal Expansion Quantum Monte Carlo
- Quantum fluctuations in the transverse Ising spin glass model: A field theory of random quantum spin systems
- Determining QMC simulability with geometric phases
- Resolution of the Sign Problem for a Frustrated Triplet of Spins
- Physics of integer spin antiferromagnetic chains : Haldane gaps and edge states
- Permutation Matrix Representation Quantum Monte Carlo
- Off-Diagonal Series Expansion for Quantum Partition Functions
- An integral-free representation of the Dyson series using divided differences
- Numerical Simulations of a Spin Dynamics Model Based on a Path Integral Approach
- A quantum Monte Carlo algorithm for Bose-Hubbard models on arbitrary graphs
- A quantum Monte Carlo algorithm for arbitrary spin-1/2 Hamiltonians