Necklace Ansatz for strongly repulsive spin mixtures on a ring

TL;DR

This paper introduces a new approach called the Necklace Ansatz for solving strongly interacting spin mixtures on a ring, simplifying the computation of low-energy states compared to traditional Bethe Ansatz methods.

Contribution

The authors develop an alternative to Bethe Ansatz that reduces complexity by imposing periodic conditions on spin amplitudes, enabling exact solutions for large particle systems.

Findings

Provides a complete basis for low-energy solutions

Applicable to $SU(u00b6)$ and symmetry-breaking systems

Simplifies the analysis of strongly-interacting mixtures

Abstract

We propose an alternative to the Bethe Ansatz method for strongly-interacting fermionic (or bosonic) mixtures on a ring. Starting from the knowledge of the solution for single-component non-interacting fermions (or strongly-interacting bosons), we explicitly impose periodic condition on the amplitudes of the spin configurations. This reduces drastically the number of independent complex amplitudes that we determine by constrained diagonalization of an effective Hamiltonian. This procedure allows us to obtain a complete basis for the exact low-energy many-body solutions for mixtures with a large number of particles, both for $SU(\kappa)$ and symmetry-breaking systems.