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Complex and tunable heating in conformal field theories with structured drives via classical ergodicity breaking

Liang-Hong Mo1,2,3, Roderich Moessner1, and Hongzheng Zhao2,1,*

  • *Contact author: hzhao@pku.edu.cn
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Phys. Rev. B 112, 184304 – Published 6 November, 2025

DOI: https://doi.org/10.1103/dvlw-hl7t

Abstract

Emission and absorption of energy are fundamental aspects of nonequilibrium dynamics. The heating induced by driving a many-body system is perhaps the most straightforward diagnostic of the process of equilibration, or the lack thereof. Gapless systems are particularly susceptible to drive-induced heating, and the capacity to control such heating is of experimental importance. Our study addresses this challenge in the framework of conformal field theory (CFT), for which we study families of structured drives up to the aperiodic Thue-Morse sequence. Concretely, we consider a class of spatially inhomogeneous Hamiltonians, where the operator evolution is governed by a nonlinear classical dynamical system K. The existence of invariant regions and fixed points of K leads to different levels of ergodicity breaking. Upon bridging the gap between this dynamical system and the driven CFT, we classify various dynamical phases of matter, including the heating and nonheating phases, as well as a prethermal phase with a controllably slow heating rate. We further generalize the discussion to η-random multipolar driving, characterized by ηth-order multipolar correlation in time. A “triply tunable” parametric dependence of the prethermal lifetime arises as K−2(η−ξ), where K quantifies the deviation from the preimages of the fixed points of K, the multipolar order η, and the order of the preimages ξ. Upon sacrificing Hermiticity by considering SU(2) deformed CFTs, we find another nonheating phase with a nonzero measure, inaccessible via purely unitary CFTs. This is underpinned by an emergent compact subspace in the generic SL(2,C) group structure, which we also identify in the transfer matrix in non-Hermitian systems with binary disorder.

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Phys. Rev. B 112, 184304– Published 6 November, 2025
  • Received 29 May 2025
  • Revised 2 October 2025
  • Accepted 3 October 2025
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