Measurement-induced dynamics of many-body systems at quantum criticality

Abstract

We consider a dynamic protocol for quantum many-body systems, which enables to study the interplay between unitary Hamiltonian driving and random local projective measurements. While the unitary dynamics tends to increase entanglement, local measurements tend to disentangle, thus favoring decoherence. Close to a quantum transition where the system develops critical correlations with diverging length scales, the competition of the two drivings is analyzed within a dynamic scaling framework, allowing us to identify a regime (dynamic scaling limit) where the two mechanisms develop a nontrivial interplay. We perform a numerical analysis of this protocol in a measurementdriven Ising chain, which supports the scaling laws we put forward. The local measurement process generally tends to suppress quantum correlations, even in the dynamic scaling limit. The power law of the decay of the quantum correlations turns out to be enhanced at the quantum transition.

Measurement-induced entanglement transitions in many-body localized systems

“…In this section we focus on unitary MBL dynamics interspersed with random projective measurements in the Z basis, and demonstrate the fact that there is a qualitative difference once measurements are introduced with any arbitrarily small probability p. That this transition occurs at p Z c = 0 is similar to previously studied integrable systems [12,17,20], which is consistent with the picture of MBL as a form of quasiintegrability robust to local perturbations. Figure 2 shows a comparison of the dynamics of the tripartite information I 3 between p = 0 and p > 0.…”

“…With measurements in the X basis, the transition from volume to area-law entanglement occurs at a nonzero measurement probability p X c > 0, similar to previously studied chaotic systems [9][10][11][12][13][14][15][16]18,19,[21][22][23][24][25]32,33]. On the other hand, with measurements in the Z basis, the volume law is destroyed for any nonzero p, similar to previously studied integrable systems [12,17,20].…”

Dissipative Floquet Dynamics: from Steady State to Measurement Induced Criticality in Trapped-ion Chains

“…This illustrates the crucial impact of the range of interactions α on the symmetry breaking transition. At α = 2 our model behaves similarly to the short-range model investigated in [123] in which there is no stable long-range order.…”

“…The unitary time evolution enhances the ferromagnetic correlations in the steady state for J > 0 and sufficiently small h > 0. In contrast, the resetting process favors a paramagnetic state [123]. Indeed, in the limit p → 1, all spins are always reset, so that the steady state is trivially |↓ ↓ ... ↓ .…”

“…The entanglement transitions were firstly described in quantum circuits with projective measurements [37,38,43] and arise due to the competition between unitary dynamics, that tends to increase the entanglement, and local measurements, which suppress the long-range entanglement in the system. Entanglement transitions were found also in many-body systems undergoing Hamiltonian evolution with random measurements [123,[126][127][128]. From the perspective of protection of quantum information against the non-unitary evolution of the system, the volume-law phase can be identified as a quantum error-correcting phase in which initially mixed state gets purified at time scale exponential in system size, whereas in the area-law phase the purification time is system size independent [46].…”