Measurement-induced entanglement transitions in the quantum Ising chain: From infinite to zero clicks

Year: 2021

Authors: Turkeshi X.; Biella A.; Fazio R.; Dalmonte M.; Schiro M.

Autors Affiliation: SISSA, Via Bonomea 265, I-34136 Trieste, Italy; Abdus Salam Int Ctr Theoret Phys ICTP, Str Costiera 11, I-34151 Trieste, Italy; PSL Res Univ, Coll France, JEIP, USR 3573 CNRS, 11 Pl Marcelin Berthelot, F-75321 Paris 05, France; Univ Paris Saclay, LPTMS, CNRS, F-91405 Orsay, France; Univ Trento, INO CNR BEC Ctr, I-38123 Povo, Italy; Univ Trento, Dipartimento Fis, I-38123 Povo, Italy; Univ Napoli Federico II, Dipartimento Fis, I-80126 Naples, Italy.

Abstract: We investigate measurement-induced phase transitions in the quantum Ising chain coupled to a monitoring environment. We compare two different limits of the measurement problem: the stochastic quantum-state diffusion protocol corresponding to infinite small jumps per unit of time and the no-click limit, corresponding to postselection and described by a non-Hermitian Hamiltonian. In both cases we find a remarkably similar phenomenology as the measurement strength ? is increased, namely, a sharp transition from a critical phase with logarithmic scaling of the entanglement to an area-law phase, which occurs at the same value of the measurement rate in the two protocols. An effective central charge, extracted from the logarithmic scaling of the entanglement, vanishes continuously at the common transition point, although with different critical behavior possibly suggesting different universality classes for the two protocols. We interpret the central charge mismatch near the transition in terms of noise-induced disentanglement, as suggested by the entanglement statistics which displays emergent bimodality upon approaching the critical point. The non-Hermitian Hamiltonian and its associated subradiance spectral transition provide a natural framework to understand both the extended critical phase, emerging here for a model which lacks any continuous symmetry, and the entanglement transition into the area law.

Journal/Review: PHYSICAL REVIEW B

Volume: 103 (22)      Pages from: 224210-1  to: 224210-13

KeyWords: THERMALIZATION; DYNAMICS; MODEL
DOI: 10.1103/PhysRevB.103.224210

Citations: 114
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