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Violation of the Arrhenius law for memory time below magnetic and topological transition temperature

Beni Yoshida, California Institute of Technology

(Session 7 : Friday from 11:45am - 12:15pm)

When interacting spin systems possess non-zero magnetization or topological entanglement entropy below the transition temperature, they often serve as classical or quantum self-correcting memory whose memory time grows exponentially in the system size due to polynomially growing energy barrier. Here, we argue that this is not always the case; we demonstrate that memory time of classical clock model (a generalization of ferromagnet to q-state spins) or Zq Toric code may be only polynomially long even when the system possesses finite magnetization or topological entanglement entropy. This violation of the Arrhenius law occurs above the percolation temperature (but below the transition temperature) where excitation droplets percolate the entire lattice while the system as a whole still remains ordered. We present numerical evidences for polynomial scaling as well as analytical argument showing that energy barrier is effectively suppressed and is only logarithmically divergent. The models we study are physically natural as they converge to 2d XY model and U(1) gauge theory as q goes to infinity where excitations are vortex-like with logarithmically divergent excitation energy. We also derive an asymptotic formula of mutual information and topological entanglement entropy at finite temperature for 2d clock model and 3d toric code as a function of q, which is consistent with large q behaviors.