Free-Fermion Measurement-Induced Volume- to Area-Law Entanglement Transition in the Presence of Fermion Interactions

Abstract

At a generic volume- to area-law entanglement transition in a many-body system, quantum chaos is arrested. We argue that this tends to imply the vanishing of a certain "mass" term in the field theory of the measurement-induced phase transition (MIPT) for monitored, interacting fermions. To explore this idea, we consider the MIPT with no conserved quantities that describes 1D monitored, interacting Majorana fermions in class DIII. We conjecture that the MIPT is the noninteracting DIII one in this case; the volume-law phase arises through the dangerously irrelevant mass. We propose numerical tests of our conjecture and analytically identify a candidate noninteracting critical point.

Figures (2)

• Figure 1: The mass operator for the NLsM encodes interparticle scattering, and acts like an entanglement-sector jump term. Green boxes represent the effects of 2-particle interaction operators applied simultaneously to the "ket" and "bra" sides of the density matrix; red dots indicate measurements.
• Figure 2: RG flows in the negative stiffness deviation $y_K$, vortex fugacity $y_V$ plane, from Eq. (\ref{['NABRGe']}). Here we set $\varepsilon = 1$ and $x = 3$ (see text). Subpanel (a) shows the flow in the noninteracting plane $y_M = 0$; the noninteracting MIPT [Eq. (\ref{['yNI']})] is indicated by the red dot. The mass parameter $y_M$ is an irrelevant perturbation to this fixed point. Subpanel (b) shows the flow in the plane $y_M = |y_K^*| > 0$; the red dot still labels the MIPT at $y_M = 0$. This flow shows that the mass is a dangerously irrelevant perturbation, because flow through the dot now runs towards $y_K \rightarrow -\infty$ (large stiffness) and $y_V \rightarrow 0$ (vanishing fugacity). In turn, this drives a flow towards large $y_M$, signaling the onset of the volume-law entangled phase.