Fracton excitations in classical frustrated kagome spin models

Max Hering, Han Yan, and Johannes Reuther
Phys. Rev. B 104, 064406 – Published 4 August 2021

Abstract

Fractons are topological quasiparticles with limited mobility. While there exist a variety of models hosting these excitations, typical fracton systems require rather complicated many-particle interactions. Here, we discuss fracton behavior in the more common physical setting of classical kagome spin models with frustrated two-body interactions only. We investigate systems with different types of elementary spin degrees of freedom (three-state Potts, XY, and Heisenberg spins) which all exhibit characteristic subsystem symmetries and fractonlike excitations. The mobility constraints of isolated fractons and bound fracton pairs in the three-state Potts model are, however, strikingly different compared to the known type-I or type-II fracton models. One may still explain these properties in terms of type-I fracton behavior and construct an effective low-energy tensor gauge theory when considering the system as a two-dimensional cut of a three-dimensional cubic lattice model. Our extensive classical Monte Carlo simulations further indicate a crossover into a low-temperature glassy phase where the system gets trapped in metastable fracton states. Moving on to XY spins, we find that in addition to fractons the system hosts fractional vortex excitations. As a result of the restricted mobility of both types of defects, our classical Monte Carlo simulations do not indicate a Kosterlitz-Thouless transition but again show a crossover into a glassy low-temperature regime. Finally, the energy barriers associated with fractons vanish in the case of Heisenberg spins, such that defect states may continuously decay into a ground state. These decays, however, exhibit a power-law relaxation behavior which leads to slow equilibration dynamics at low temperatures.

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  • Received 11 January 2021
  • Revised 3 June 2021
  • Accepted 7 July 2021

DOI:https://doi.org/10.1103/PhysRevB.104.064406

©2021 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Max Hering1,2, Han Yan3, and Johannes Reuther1,2

  • 1Helmholtz-Zentrum Berlin für Materialien und Energie, Hahn-Meitner Platz 1, 14109 Berlin, Germany
  • 2Dahlem Center for Complex Quantum Systems and Fachbereich Physik, Freie Universität Berlin, 14195 Berlin, Germany
  • 3Theory of Quantum Matter Unit, Okinawa Institute of Science and Technology Graduate University, Onna-son, Okinawa 904-0412, Japan

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Issue

Vol. 104, Iss. 6 — 1 August 2021

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