Holographic quantum scars

We discuss a construction of quantum many-body scars in the context of holography. We consider two-dimensional conformal field theories and use their dynamical symmetries, naturally realized through the Virasoro algebra, to construct scarred states. By studying their Loschmidt amplitude, we evaluate the states’ periodic properties. A geometrical interpretation allows us to compute the expectation value of the stress tensor and entanglement entropy of these scarred states. We show that their holographic dual is related by a diffeomorphism to empty AdS, even for energies above the black hole threshold. We also demonstrate that expectation values in the scarred states are generally non-thermal and that their entanglement entropy grows with the energy as \log(E) <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mo>log</mml:mo> <mml:mrow> <mml:mo stretchy="true" form="prefix">(</mml:mo> <mml:mi>E</mml:mi> <mml:mo stretchy="true" form="postfix">)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> in contrast to \sqrt{E} <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msqrt> <mml:mi>E</mml:mi> </mml:msqrt> </mml:math> for the typical (bulk) states. Furthermore, we identify fixed points on the CFT plane associated with divergent or vanishing entanglement entropy in the limit where the scarred states have infinite energy.