Title: Anomalous relaxation and the high-temperature structure factor of XXZ spin chains

Abstract

We compute the spin-structure factor of XXZ spin chains in the Heisenberg and gapped (Ising) regimes in the high-temperature limit for nonzero magnetization, within the framework of generalized hydrodynamics, including diffusive corrections. The structure factor shows a hierarchy of timescales in the gapped phase, owing to s-spin magnon bound states (“strings”) of various sizes. Although short strings move ballistically, long strings move primarily diffusively as a result of their collisions with short strings. The interplay between these effects gives rise to anomalous power-law decay of the spin-structure factor, with continuously varying exponents, at any fixed separation in the late-time limit. We elucidate the cross-over to diffusion (in the gapped phase) and to superdiffusion (at the isotropic point) in the half-filling limit. We verify our results via extensive matrix product operator calculations.

Authors:

Gopalakrishnan, Sarang ;

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Vasseur, Romain; Ware, Brayden

Publication Date:

2019-07-30

Sponsoring Org.:

USDOE

OSTI Identifier:

1557027

Grant/Contract Number:  

SC0019168

Resource Type:

Published Article

Journal Name:

Proceedings of the National Academy of Sciences of the United States of America

Additional Journal Information:

Journal Name: Proceedings of the National Academy of Sciences of the United States of America Journal Volume: 116 Journal Issue: 33; Journal ID: ISSN 0027-8424

Publisher:

Proceedings of the National Academy of Sciences

Country of Publication:

United States

Language:

English