The Kramers-Wannier duality is the prototypical example of a non-invertible symmetry, yet little is known about its fate away from criticality and out of equilibrium. We introduce the Kramers-Wannier entanglement asymmetry, a quantum-information measure that quantifies the breaking of this non-invertible symmetry in the transverse-field Ising chain. We first investigate its equilibrium properties, showing that it exhibits a striking crossover between the ordered and disordered phases together with a pronounced dip at the critical point that becomes increasingly sharp with subsystem size. We then study quantum quenches from both gapped phases to criticality and show that the Kramers-Wannier entanglement asymmetry decays to zero, signaling the dynamical restoration of the non-invertible symmetry. Remarkably, we uncover the emergence of a quantum Mpemba effect: under suitable conditions, states initially farther from equilibrium restore the Kramers-Wannier symmetry faster than states prepared closer to it. We provide both analytical and numerical evidence for this phenomenon and identify the mechanism responsible for its occurrence. Our work establishes entanglement asymmetry as a powerful probe of non-invertible symmetries beyond equilibrium and opens new perspectives on the dynamics of dualities in quantum many-body systems.
Milo Vescovo, Pasquale Calabrese, F. Ares· 1 citation
We study the critical properties of random quantum circuits with a $U(1)$ symmetry subject to local projective measurements that explicitly break this symmetry. We find that, at the measurement-induced phase transition, symmetry-breaking measurements act as a relevant perturbation at large scales, leading to the same universal critical properties as the corresponding monitored random circuit with non-symmetric unitary dynamics. In particular, we consider monitored $U(1)$-symmetric Haar-random circuits in the limit of large local Hilbert-space dimension, where the trajectory-averaged entanglement entropy can be exactly obtained in terms of a classical statistical mechanics model. In this model, the charge associated with the conservation law follows a symmetric simple exclusion process, in which symmetry-breaking measurements correspond to disordered defects that create and destroy charges. We prove that the charge correlation length remains finite for any measurement rate, ruling out a charge-sharpening transition, in contrast to the case of symmetry-preserving measurements. We further support our predictions at finite local Hilbert-space dimension through numerical finite-size scaling analyses of the entanglement transition in monitored $U(1)$-symmetric Haar and stabilizer random circuits.
Angelo Russotto, F. Ares, Pasquale Calabrese· 0 citations
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