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Title:
From coprime quantum spin ladder to partially integrable spin chain
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Abstract:
We present a quantum spin ladder made with N coupled chains of spin-1/2, with its degrees of freedom bearing a number theoretic interpretation of square-free numbers. The rung and leg Hamiltonian introduces competing phases of the ground state. One of them is given by the superposition of degrees of freedom encoding the first N prime numbers. This phase can be described by an emergent spin chain that is a minimal generalisation to the antiferromagnetic XXZ spin chain with enlarged local Hilbert space. Such a Hamiltonian is known be be partially integrable, due to the generic violation of Yang-Baxter’s equation. Nevertheless, we identify new Bethe Ansatz integrable excited states in the non-integrable Krylov subspace, which leads to slow thermalisation that interpolates between integrability and the eigenstate thermalisation hypothesis.
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