Tensor Networks for Liquids in Heterogeneous Systems

TL;DR

This paper applies tensor network methods to efficiently compute equilibrium properties of liquids in complex heterogeneous environments, addressing high-dimensional challenges in many-body physics.

Contribution

It introduces tensor network decompositions for calculating density and correlation functions in confined heterogeneous liquids, highlighting their high compression potential.

Findings

High compression of density functions with quantized tensor trains.

Effective tensor network representation of spatial-coordinate dependence.

Limitations in compressing dependence on distinct particle coordinates.

Abstract

Many-body correlations in strongly coupled liquids and plasmas are critical for many applications in nanofluids, biology, and fusion-related plasma physics, but their description in fully heterogeneous environments remains challenging due to the high-dimensional equations involved. Recently, tensor network decompositions have emerged as powerful tools for tackling such equations by reducing memory usage and computational complexity. In this paper, we solve for equilibrium density and density-density correlation functions of liquids in confined heterogeneous environments using tensor network methods. We demonstrate that these functions admit high compression when their lengthscale dependence is encoded via quantized tensor trains or when their spatial-coordinate dependence is represented in standard tensor-train format, but not with respect to their dependence on distinct particle coordinates.