The Folded Spin-1/2 XXZ Model: I. Diagonalisation, Jamming, and Ground State Properties

Abstract

We study an effective Hamiltonian generating time evolution of states on intermediate time scales in the strong-coupling limit of the spin-1/2 XXZ model. To leading order, it describes an integrable model with local interactions. We solve it completely by means of a coordinate Bethe Ansatz that manifestly breaks the translational symmetry. We demonstrate the existence of exponentially many jammed states and estimate their stability under the leading correction to the effective Hamiltonian. Some ground state properties of the model are discussed.

The folded spin-1/2 XXZ model: II. Thermodynamics and hydrodynamics with a minimal set of charges

“…In the rest of the introduction we recapitulate the results of Ref. [1] necessary to understand the present work.…”

“…In Ref. [1] we have recast the strong coupling expansion κ → 0 of such models into a formulation termed "folded picture", in which operators and state time evolve according to O F (t) := e iκB z t (κ) e iκ −1 H I t Oe −iκ −1 H I t e −iκB z t (κ) , |Ψ(t)〉 F := e −iH F (κ)t e iκB 1 (κ) |Ψ(0)〉 , (3) where z t = e iκ −1 J t . Asymptotic expansions of H F (κ) and B z (κ) in the limit of small κ are reported in Ref.…”

“…Asymptotic expansions of H F (κ) and B z (κ) in the limit of small κ are reported in Ref. [1]. As long as J t κ −1 , the folded picture can be used at the leading order, where the state time evolves with H F (0) ≡ H F .…”

“…This is the second part of our investigation into the large-anisotropy limit of the Heisenberg spin-1/2 XXZ model. In the first part [1] we defined the "folded picture" as an asymptotic formulation of quantum mechanics of many-body systems that are described by Hamiltonians with a large coupling constant. In this picture the fast oscillatory part of the dynamics is attached to the operators, whereas the state evolves slowly in time through an effective "folded Hamiltonian".…”

“…In order to exploit the symmetries of that special point, we will however use the results of the non-nested Bethe Ansatz method of Ref. [1]. We first develop a thermodynamic Bethe Ansatz that describes the infinite chain in thermal states as well as in generalised Gibbs ensembles [4] constructed with the local conservation laws and a special pseudolocal charge.…”