The deformed Inozemtsev spin chain

TL;DR

This paper introduces a new integrable generalization of the Inozemtsev spin chain with U(1) symmetry, bridging short-range Heisenberg and long-range Haldane-Shastry models, and extends the elliptic Ruijsenaars system to include spins.

Contribution

It presents a novel U(1)-symmetric, integrable spin chain interpolating between well-known models, and develops an extended elliptic Ruijsenaars system with potential applications across physics.

Findings

New integrable spin chain model with U(1) symmetry

Extension of elliptic Ruijsenaars system to include spins

Potential applications in condensed matter and high-energy physics

Abstract

The Inozemtsev chain is an exactly solvable interpolation between the short-range Heisenberg and long-range Haldane-Shastry (HS) chains. In order to unlock its potential to study spin interactions with tunable interaction range using the powerful tools of integrability, the model's mathematical properties require better understanding. As a major step in this direction, we present a new generalisation of the Inozemtsev chain with spin symmetry reduced to U(1), interpolating between a Heisenberg xxz chain and the xxz-type HS chain, and integrable throughout. Underlying it is a new quantum many-body system that extends the elliptic Ruijsenaars system by including spins, contains the trigonometric spin-Ruijsenaars-Macdonald system as a special case, and yields our spin chain by 'freezing'. Our models have potential applications from condensed-matter to high-energy theory, and provide a crucial step towards a general theory for long-range integrability.