• Letter

Transverse instability and universal decay of spin spiral order in the Heisenberg model

Joaquin F. Rodriguez-Nieva, Alexander Schuckert, Dries Sels, Michael Knap, and Eugene Demler
Phys. Rev. B 105, L060302 – Published 22 February 2022
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Abstract

We analyze the intrinsic stability of spin spiral states in the two-dimensional Heisenberg model isolated from its environment. Our analysis reveals that the SU(2) symmetric point hosts a dynamic instability that is enabled by the existence of energetically favorable transverse deformations—both in real and spin space—of the spiral order. The instability is universal in the sense that it applies to systems with any spin number, spiral wave vector, and spiral amplitude. Unlike the Landau or modulational instabilities which require impurities or periodic potential modulation of an optical lattice, quantum fluctuations alone are sufficient to trigger the transverse instability. We analytically find the most unstable mode and its growth rate, and compare our analysis with phase-space methods. By adding an easy-plane exchange coupling that reduces the Hamiltonian symmetry from SU(2) to U(1), the stability boundary is shown to continuously interpolate between the modulational instability and the transverse instability. This suggests that the transverse instability is an intrinsic mechanism that hinders long-range phase coherence even in the presence of exchange anisotropy.

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  • Received 3 January 2021
  • Revised 10 November 2021
  • Accepted 20 January 2022

DOI:https://doi.org/10.1103/PhysRevB.105.L060302

©2022 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied PhysicsNonlinear DynamicsAtomic, Molecular & Optical

Authors & Affiliations

Joaquin F. Rodriguez-Nieva1, Alexander Schuckert2,3, Dries Sels4,5, Michael Knap2,3, and Eugene Demler6

  • 1Department of Physics, Stanford University, Stanford, California 94305, USA
  • 2Department of Physics and Institute for Advanced Study, Technical University of Munich, 85748 Garching, Germany
  • 3Munich Center for Quantum Science and Technology (MCQST), Schellingstrasse 4, D-80799 München, Germany
  • 4Department of Physics, New York University, New York, 10003 New York, USA
  • 5Center for Computational Quantum Physics, Flatiron Institute, New York, 10010 New York, USA
  • 6Institute for Theoretical Physics, Wolfgang-Pauli-Str. 27, ETH Zurich, 8093 Zurich, Switzerland

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Issue

Vol. 105, Iss. 6 — 1 February 2022

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