Exact finite reduced density matrix and von Neumann entropy for the Calogero model

TL;DR

This paper analytically derives the exact finite reduced density matrices and von Neumann entropy for the ground state of the Calogero model at specific interaction parameters, providing precise entanglement measures.

Contribution

It presents the first exact analytical expressions for the reduced density matrices and entanglement spectrum of the Calogero model at certain interaction values.

Findings

Exact finite reduced density matrices obtained

Exact entanglement spectrum calculated

Von Neumann entropy explicitly derived

Abstract

The information content of continuous quantum variables systems is usually studied using a number of well known approximation methods. The approximations are made to obtain the spectrum, eigenfunctions or the reduced density matrices that are essential to calculate the entropy-like quantities that quantify the information. Even in the sparse cases where the spectrum and eigenfunctions are exactly known the entanglement spectrum, {\em i.e.} the spectrum of the reduced density matrices that characterize the problem, must be obtained in an approximate fashion. In this work, we obtain analytically a finite representation of the reduced density matrices of the fundamental state of the N-particle Calogero model for a discrete set of values of the interaction parameter. As a consequence, the exact entanglement spectrum and von Neumann entropy is worked out.