Many-Body Quantum Zeno Effect and Measurement-Induced Subradiance Transition

Abstract

It is well known that by repeatedly measuring a quantum system it is possible to completely freeze its dynamics into a well defined state, a signature of the quantum Zeno effect. Here we show that for a many-body system evolving under competing unitary evolution and variable-strength measurements the onset of the Zeno effect takes the form of a sharp phase transition. Using the Quantum Ising chain with continuous monitoring of the transverse magnetization as paradigmatic example we show that for weak measurements the entanglement produced by the unitary dynamics remains protected, and actually enhanced by the monitoring, while only above a certain threshold the system is sharply brought into an uncorrelated Zeno state. We show that this transition is invisible to the average dynamics, but encoded in the rare fluctuations of the stochastic measurement process, which we show to be perfectly captured by a non-Hermitian Hamiltonian which takes the form of a Quantum Ising model in an imaginary valued transverse field. We provide analytical results based on the fermionization of the non-Hermitian Hamiltonian in supports of our exact numerical calculations.

Entanglement Phase Transition Induced by the Non-Hermitian Skin Effect

“…Under the skin effect, the system soon reaches a nonequilibrium steady state in which an extensive number of particles are localized at an edge. It is noteworthy that the frozen correlation propagation due to the skin effect is different from the supersonic correlation propagation in non-Hermitian quantum systems with reciprocal dissipation [65,66,68]. This difference also shows a unique role of the skin effect in open quantum systems.…”

“…Non-Hermitian systems have been realized in several open quantum systems, including atoms [52][53][54], photons [55][56][57][58], exciton-polaritons [59], electronic spins [60,61], and superconducting qubits [62]. On the theoretical side, researchers have studied open quantum dynamics of non-Hermitian systems [63][64][65][66][67][68][69][70][71]. Notably, non-Hermitian systems at critical points support anomalous singularities called exceptional points [72][73][74], at which the non-Hermitian Hamiltonians are no longer diagonalizable.…”

“…Despite the significance of the skin effect for non-Hermitian topological phases, its impact on the genuine quantum nature has remained unclear. While several recent works studied the entanglement dynamics in non-Hermitian quantum systems [65][66][67][68][69][70][71], they focused only on non-Hermitian systems that are subject to reciprocal dissipation and free from the skin effect. On the basis of the important role of the skin effect in non-Hermitian physics, it may crucially change the entanglement dynamics in open quantum systems.…”

A Testable Theory for the Emergence of the Classical World

“…Generally, if two states > are perfectly distinguishable, i.e., orthogonal, then we have perfectly indistinguishable; hence, we can measure [ 20 ], first of all, the average time taken for one state (say in our case this is one state initially formed of QZE or collective actualization) to transform into another in general non-orthogonal state before decoherence takes over. This can be shown as the time average of .…”

“… Hence, we preserve the overall competition between unitary many body dynamics and the stochastic measurements of single members of an entangled subset of the CAS. Authors have observed [ 20 , 21 ] that such processes involve degrees of freedom that do not commute with each other, for example different components of spin (directions). Starting with a simple one dimensional Ising model, such many body QZE can produce a frozen/localized many body state when the coupling is above critical threshold strength.…”