Statistical mechanics in continuous space with tensor network methods

TL;DR

This paper extends tensor network methods to continuous-space particle systems by discretizing space and formulating an effective lattice model, enabling efficient computation of thermodynamic properties.

Contribution

It introduces a novel tensor network approach for continuous-space systems, bridging a gap in applying TN methods beyond lattice models.

Findings

Successfully applied to the 2D hard-disk problem

Demonstrated advantages over Monte Carlo simulations

Established a new framework for continuous-space statistical mechanics

Abstract

Tensor network (TN) methods are well established for computing partition functions in statistical mechanics, though this use has traditionally been limited to lattice models. We extend the scope of TN methodology to interacting particle systems in continuous space. Through a real-space discretization combined with a cell-based coarse-graining scheme, we formulate an effective lattice model that explicitly preserves spatial locality. The partition function of this model is represented as a TN, and the thermodynamic quantities are computed via boundary contraction. We apply this framework to the two-dimensional hard-disk problem and demonstrate the strengths of the TN formulation compared to existing Monte Carlo simulations.