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.
Highlights
Thermalisation in isolated quantum systems has received enormous attention in the last few decades, partly due to the advancement of the experimental techniques that allow one to manipulate a large number of quantum particles [4, 5]
We have proposed a framework for studying time evolution in quantum many-body systems on intermediate time scales at large coupling constant
We have investigated the effective Hamiltonian that arises in the limit of large anisotropy ∆ in the Heisenberg spin1 2 XXZ model
Summary
Thermalisation in isolated quantum systems has received enormous attention in the last few decades (see review articles [1,2,3] and references therein), partly due to the advancement of the experimental techniques that allow one to manipulate a large number of quantum particles [4, 5]. Based on the results of MacDonald et al, we consider an asymptotic formulation of quantum mechanics that attaches the fast oscillatory part of the dynamics to the operators, letting the state evolve gently in time under an effective Hamiltonian. We term this formulation “asymptotic folded picture”, to emphasise that the spectrum of the effective “folded Hamiltonian” is the same as that of the original Hamiltonian, modulo a typical energy proportional to the largest coupling constant. We consider the large anisotropy limit of the spin-1 2 XXZ chain and present a Bethe Ansatz solution of the model described by the corresponding local folded Hamiltonian. A subset of the latter states is stable under the perturbation by the leading correction to the strong coupling limit
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