Loschmidt echo, emerging dual unitarity and scaling of generalized temporal entropies after quenches to the critical point

TL;DR

This paper demonstrates how conformal field theories can predict the Loschmidt echo and temporal entropies after quenches to critical points, revealing universal CFT data and emergent dual unitarity with efficient numerical methods.

Contribution

It introduces a CFT-based framework to predict Loschmidt echoes and temporal entropies, and uncovers emergent dual unitarity in quantum quenches at criticality.

Findings

Excellent agreement between CFT predictions and tensor network simulations.

Loschmidt echo reveals universal CFT information like central charge.

Emerging dual unitarity of the evolution operator at late times.

Abstract

We show how the Loschmidt echo of a product state after a quench to a conformal invariant critical point and its leading finite time corrections can be predicted by using conformal field theories (CFT). We check such predictions with tensor networks, finding excellent agreement. As a result, we can use the Loschmidt echo to extract the universal information of the underlying CFT including the central charge, the operator content, and its generalized temporal entropies. We are also able to predict and confirm an emerging dual-unitarity of the evolution at late times, since the spatial transfer matrix operator that evolves the system in space becomes unitary in such limit. Our results on the growth of temporal entropies also imply that, using state-of-the art tensor networks algorithms, such calculations only require resources that increase polynomially with the duration of the quench, thus providing an example of numerically efficiently solvable out-of-equilibrium scenario.