Measurement induced entanglement phase transitions in monitored 1D spin chains

Entanglement phase transitions have attracted immense attention in recent years, especially in the context of monitored quantum circuits. In such systems, the dynamics due to unitary evolution competes with the localizing effects of measurements. The phase transition of a quantum system between a trivial volume-law phase of entanglement entropy – in case of weak monitoring, into a quantum Zeno-like phase for frequent and/or strong measurements where the entanglement entropy obeys area-law, is well known in many integrable models with unitary dynamics. However recently a critical phase with a logarithmic scaling of the entanglement entropy in a class of integrable models has been identified, in the presence of dissipation.

      We explore such a critical transition in a monitored one-dimensional quantum spin chain, the transverse field Ising model (TFIM), in presence of integrability-breaking field and dissipation. We show that it is qualitatively different from the trivial volume-law to area-law transition of the entanglement entropy, and present the phase diagram of such a system.