Quantum mereology and subsystems from the spectrum

TL;DR

This paper investigates how the spectrum of a quantum system can determine its subsystems and their number, proposing a spectrum-based approach called quantum mereology that links spectral properties to subsystem decomposition.

Contribution

It introduces a top-down method where subsystems emerge from the spectrum, establishing an equivalence between subsystem decomposition and spectral decomposition, and infers subsystem count from spectral data.

Findings

Subsystem decomposition is equivalent to spectral decomposition.

Subsystem count can be inferred from spectral properties.

Finite size corrections encode subsystem information.

Abstract

The minimal ingredients to describe a quantum system are a Hamiltonian, an initial state, and a preferred tensor product structure that encodes a decomposition into subsystems. We explore a top-down approach in which the subsystems emerge from the spectrum of the whole system. This approach has been referred to as quantum mereology. First we show that decomposing a system into subsystems is equivalent to decomposing a spectrum into other spectra. Then we argue that the number of subsystems (the volume of the system) can be inferred from the spectrum itself. In local models, this information is encoded in finite size corrections to the Gaussian density of states.