The walk-sum method for simulating quantum many-body systems

TL;DR

The paper introduces the walk-sum method, a new approach for simulating the real-time dynamics of quantum many-body systems with long-range interactions, offering polynomial computational cost and explicit operator expressions.

Contribution

The walk-sum method provides a novel, scalable way to compute parts of the evolution operator in quantum many-body systems, independent of system size and geometry.

Findings

Polynomial growth in computational cost with system size.

Applicable to systems with long-range interactions and arbitrary geometries.

Validated through examples with two physical systems.

Abstract

We present the method of walk-sum to study the real-time dynamics of interacting quantum many-body systems. The walk-sum method generates explicit expressions for any desired pieces of an evolution operator U independently of any others. The computational cost for evaluating any such piece at a fixed order grows polynomially with the number of particles. Walk-sum is valid for systems presenting long-range interactions and in any geometry. We illustrate the method by means of two physical systems.