Thermodynamical limit of general gl(N) spin chains: vacuum state and densities

TL;DR

This paper investigates the vacuum state of general gl(N) spin chains with arbitrary site representations, validating the string hypothesis for rectangular Young tableaux and deriving string densities, including cases with impurities.

Contribution

It proves the string hypothesis validity for certain representations and computes vacuum string densities, extending understanding of spin chain solutions.

Findings

String hypothesis is valid for representations with rectangular Young tableaux.

Derived the density of string centers for the vacuum state.

Analyzed specific examples, including impurity-laden spin chains.

Abstract

We study the vacuum state of spin chains where each site carry an arbitrary representation. We prove that the string hypothesis, usually used to solve the Bethe ansatz equations, is valid for representations characterized by rectangular Young tableaux. In these cases, we obtain the density of the center of the strings for the vacuum. We work out different examples and, in particular, the spin chains with periodic array of impurities.