Entanglement asymmetry in periodically driven quantum systems

We study the dynamics of entanglement asymmetry in periodically driven quantum systems. Using a periodically driven XY chain as a model for a driven integrable quantum system, we provide semi-analytic results for the behavior of the dynamics of the entanglement asymmetry, \Delta S <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>Δ</mml:mi> <mml:mi>S</mml:mi> </mml:mrow> </mml:math> , as a function of the drive frequency. Our analysis identifies special drive frequencies at which the driven XY chain exhibits dynamic symmetry restoration and displays quantum Mpemba effect over a long timescale; we identify an emergent approximate symmetry in its Floquet Hamiltonian which plays a crucial role for realization of both these phenomena. We follow these results by numerical computation of \Delta S <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>Δ</mml:mi> <mml:mi>S</mml:mi> </mml:mrow> </mml:math> for the non-integrable driven Rydberg atom chain and obtain similar emergent-symmetry-induced symmetry restoration and quantum Mpemba effect in the prethermal regime for such a system. Finally, we provide an exact analytic computation of the entanglement asymmetry for a periodically driven conformal field theory (CFT) on a strip. Such a driven CFT, depending on the drive amplitude and frequency, exhibits two distinct phases, heating and non-heating, that are separated by a critical line. Our results show that for m <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>m</mml:mi> </mml:math> cycles of a periodic drive with time period T <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>T</mml:mi> </mml:math> , \Delta S \sim \ln mT <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>Δ</mml:mi> <mml:mi>S</mml:mi> <mml:mo>∼</mml:mo> <mml:mo>ln</mml:mo> <mml:mi>m</mml:mi> <mml:mi>T</mml:mi> </mml:mrow> </mml:math> [ \ln (\ln mT) <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mo>ln</mml:mo> <mml:mo stretchy="false" form="prefix">(</mml:mo> <mml:mo>ln</mml:mo> <mml:mi>m</mml:mi> <mml:mi>T</mml:mi> <mml:mo stretchy="false" form="postfix">)</mml:mo> </mml:mrow> </mml:math> ] in the heating phase [on the critical line] for a generic CFT; in contrast, in the non-heating phase, \Delta S <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>Δ</mml:mi> <mml:mi>S</mml:mi> </mml:mrow> </mml:math> displays small amplitude oscillations around it’s initial value as a function of mT <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>m</mml:mi> <mml:mi>T</mml:mi> </mml:mrow> </mml:math> . We provide a phase diagram for the behavior of \Delta S <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>Δ</mml:mi> <mml:mi>S</mml:mi> </mml:mrow> </mml:math> for such driven CFTs as a function of the drive frequency and amplitude.