Structures of Identical Particle Systems : Efficient Computation of Many-Body Density of States

TL;DR

This paper introduces a computationally efficient method for approximating the many-body density of states of quantum identical particles, utilizing combinatorial techniques and enabling scalable, parallelizable calculations.

Contribution

The authors develop a novel formalism based on many-body combinatorics that reduces computational costs and allows incremental, parallel computations of the density of states.

Findings

The method achieves significant reduction in computational cost compared to full calculations.

It enables approximation of bosonic density of states with tunable accuracy.

The approach can recover Bose-Einstein-like distributions without explicit particle statistics.

Abstract

We present a method for approximating the many-body density of states of a system of quantum identical particles, with a reduction of the computational cost by a combinatorial factor compared to the full calculation. This is carried out by considering an isolated quantum system of identical particles, and studying its non-interacting many-body spectrum through the use of a new approach based on a separation of universal combinatorial properties from the system-specific quantities. In this paper we focus on a practical computation method that leverages our formalism of many-body combinatorics, in order to perform an efficient numerical computation of the many-body density of states. In addition, this method provides further computational improvements by allowing most of the results to be cached in persistent storage and computed incrementally, making way for efficient use of parallelization and dynamic programming techniques. We give an extensive description of the method and provide several detailed examples of approximations of bosonic many-body density of states with tunable accuracy requirements. Lastly, we demonstrate how one such approximation can be used to recover Bose-Einstein-like distributions without any particle statistics assumptions.