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

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 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mi mathvariant="script">K</a:mi> </a:math> . The existence of invariant regions and fixed points of <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mi mathvariant="script">K</c:mi> </c:math> 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 <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"> <e:mi>η</e:mi> </e:math> -random multipolar driving, characterized by <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"> <f:mrow> <f:mi>η</f:mi> <f:mi>th</f:mi> </f:mrow> </f:math> -order multipolar correlation in time. A “triply tunable” parametric dependence of the prethermal lifetime arises as <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"> <g:msup> <g:mi>K</g:mi> <g:mrow> <g:mo>−</g:mo> <g:mn>2</g:mn> <g:mo>(</g:mo> <g:mi>η</g:mi> <g:mo>−</g:mo> <g:mi>ξ</g:mi> <g:mo>)</g:mo> </g:mrow> </g:msup> </g:math> , where <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"> <h:mi>K</h:mi> </h:math> quantifies the deviation from the preimages of the fixed points of <i:math xmlns:i="http://www.w3.org/1998/Math/MathML"> <i:mi mathvariant="script">K</i:mi> </i:math> , the multipolar order <k:math xmlns:k="http://www.w3.org/1998/Math/MathML"> <k:mi>η</k:mi> </k:math> , and the order of the preimages <l:math xmlns:l="http://www.w3.org/1998/Math/MathML"> <l:mi>ξ</l:mi> </l:math> . 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 <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mi>SL</m:mi> <m:mo>(</m:mo> <m:mn>2</m:mn> <m:mo>,</m:mo> <m:mi mathvariant="double-struck">C</m:mi> <m:mo>)</m:mo> </m:mrow> </m:math> group structure, which we also identify in the transfer matrix in non-Hermitian systems with binary disorder.