Conformal Floquet dynamics with a continuous drive protocol

Abstract

A bstract We study the properties of a conformal field theory (CFT) driven periodically with a continuous protocol characterized by a frequency ω D . Such a drive, in contrast to its discrete counterparts (such as square pulses or periodic kicks), does not admit exact analytical solution for the evolution operator U . In this work, we develop a Floquet perturbation theory which provides an analytic, albeit perturbative, result for U that matches exact numerics in the large drive amplitude limit. We find that the drive yields the well-known heating (hyperbolic) and non-heating (elliptic) phases separated by transition lines (parabolic phase boundary). Using this and starting from a primary state of the CFT, we compute the return probability ( P n ), equal ( C n ) and unequal ( G n ) time two-point primary correlators, energy density( E n ), and the m th Renyi entropy ( $$ {S}_n^m $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>S</mml:mi> <mml:mi>n</mml:mi> <mml:mi>m</mml:mi> </mml:msubsup> </mml:math> ) after n drive cycles. Our results show that below a crossover stroboscopic time scale n c , P n , E n and G n exhibits universal power law behavior as the transition is approached either from the heating or the non-heating phase; this crossover scale diverges at the transition. We also study the emergent spatial structure of C n , G n and E n for the continuous protocol and find emergence of spatial divergences of C n and G n in both the heating and non-heating phases. We express our results for $$ {S}_n^m $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>S</mml:mi> <mml:mi>n</mml:mi> <mml:mi>m</mml:mi> </mml:msubsup> </mml:math> and C n in terms of conformal blocks and provide analytic expressions for these quantities in several limiting cases. Finally we relate our results to those obtained from exact numerics of a driven lattice model.

Topics & Concepts