Measurement-induced entanglement transitions in many-body localized systems

Abstract

The resilience of quantum entanglement to a classicality-inducing environment is tied to fundamental aspects of quantum many-body systems. The dynamics of entanglement has recently been studied in the context of measurement-induced entanglement transitions, where the steady-state entanglement collapses from a volume law to an area law at a critical measurement probability p c. Interestingly, there is a distinction in the value of p c depending on how well the underlying unitary dynamics scramble quantum information. For strongly chaotic systems, p c > 0, whereas for weakly chaotic systems, such as integrable models, p c = 0. In this work, we investigate these measurement-induced entanglement transitions in a system where the underlying unitary dynamics are many-body localized (MBL). We demonstrate that the emergent integrability in an MBL system implies a qualitative difference in the nature of the measurement-induced transition depending on the measurement basis, with p c > 0 when the measurement basis is scrambled and p c = 0 when it is not. This feature is not found in Haar-random circuit models, where all local operators are scrambled in time. When the transition occurs at p c > 0, we use finite-size scaling to obtain the critical exponent ν = 1.3(2), close to the value for (2+0)-dimensional percolation. We also find a dynamical critical exponent of z = 0.98(4) and logarithmic scaling of the Rényi entropies at criticality, suggesting an underlying conformal symmetry at the critical point. This work further demonstrates how the nature of the measurement-induced entanglement transition depends on the scrambling nature of the underlying unitary dynamics. This leads to further questions on the control and simulation of entangled quantum states by measurements in open quantum systems.

Measurement-induced criticality and entanglement clusters: A study of one-dimensional and two-dimensional Clifford circuits

“…These measurement-induced transitions occur in a wide variety of models, including random circuits , Hamiltonian systems [36][37][38][39][40][41][42][43][44], and measurement-only models [28,45,46,57], and they exhibit universal behavior. However, the determination of the relevant universality classes has proved to be a subtle issue.…”

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

“…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].…”

Continuous gaussian measurements of the free boson CFT: A model for exactly solvable and detectable measurement-induced dynamics

“…( 30) with finite N = 30 and η 0 = 1; the dashed lines correspond to the analytical result from Eq. (45). The predominant feature is an emerging gap in the imaginary part of the eigenvalues corresponding to the measurementinduced mass.…”

“…It has a modified dispersion h(q) → ε(q), displayed in Eq. (45). To probe how physical this spectral information is we attempt the ansatz…”