Topological transitions in weakly monitored free fermions

• Published in: SciPost physics Vol. 14; no. 3; p. 031
• Main Authors: Kells, Graham, Meidan, Dganit, Romito, Alessandro
• Format: Journal Article
• Language: English
• Published: SciPost 01.03.2023
• ISSN: 2542-4653; 2542-4653
• DOI: 10.21468/SciPostPhys.14.3.031

We study a free fermion model where two sets of non-commuting non-projective measurements stabilize area-law entanglement scaling phases of distinct topological order. We show the presence of a topological phase transition that is of a different universality class than that observed in stroboscopic projective circuits. In the presence of unitary dynamics, the two topologically distinct phases are separated by a region with sub-volume scaling of the entanglement entropy. We find that this entanglement transition is well identified by a combination of the bipartite entanglement entropy and the topological entanglement entropy. We further show that the phase diagram is qualitatively captured by an analytically tractable non-Hermitian model obtained via post-selecting the measurement outcome. Finally we introduce a partial-post-selection continuous mapping, that uniquely associates topological indices of the non-Hermitian Hamiltonian to the distinct phases of the stochastic measurement-induced dynamics.