Integrable hard rod deformation of the Heisenberg spin chains

Abstract

We present new integrable models of interacting spin-1/2 chains, which can be interpreted as hard rod deformations of the XXZ Heisenberg chains. The models support multiple particle types: dynamical hard rods of length $\ell$ and particles with lengths ${\ell }^{\prime }<\ell$ that are immobile except for the interaction with the hard rods. We encounter a remarkable phenomenon in these interacting models: exact spectral degeneracies across different deformations and volumes. The algebraic integrability of these systems is also treated using a recently developed formalism for medium range integrable spin chains. We present the detailed Bethe Ansatz solution for the case $\ell =2$.

arXiv comment13 pages, v2: reference added and a few new formulas for the XXX case

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• New classical integrable systems from generalized $T\bar{T}$-deformations
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• Growing Schrödinger's cat states by local unitary time evolution of product states
• Weak ergodicity breaking with isolated integrable sectors
• Systematic construction of asymptotic quantum many-body scar states and their relation to supersymmetric quantum mechanics
• Simulating generalised fluids via interacting wave packets evolution
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• Dynamic structure factor of quantum hard rods from exact form-factors
• Almost local integrable models from supersymmetry algebras
• Emergent dipole field theory in atomic ladders