Measurement-induced phase transitions in monitored fermionic systems

by Igor Poboiko (KIT Karlsruhe)

Tuesday 10 Dec 2024, 11:00 → 12:00 Europe/Zurich

WHGA/121

We develop a theory of measurement-induced phase transitions (MIPT) for d-dimensional lattice free fermions subject to random projective measurements of local site occupation numbers. Our analytical approach is based on the Keldysh path-integral formalism and replica trick. In the limit of rare measurements, γ ≪ J (where γ is measurement rate per site and J is hopping constant), we derive a non-linear sigma model (NLSM) as an effective field theory of the problem. Its replica-symmetric sector is a U(2)/U(1)×U(1) NLSM describing diffusive behavior of average density fluctuations. The replica-asymmetric sector, which describes propagation of quantum information in a system, is a (d+1)-dimensional isotropic NLSM defined on SU(R) manifold with the replica limit R → 1, establishing close relation between MIPT and Anderson transitions. On the Gaussian level, valid in the limit γ/J → 0, this model predicts "critical" (i.e. logarithmic enhancement of area law) behavior for the entanglement entropy. However, one-loop renormalization group analysis shows [1] that for d=1, the logarithmic growth saturates at a finite value ∼(J/γ)^2 even for rare measurements, implying existence of a single area-law phase. The crossover between logarithmic growth and saturation, however, happens at an exponentially large scale, ln(l_corr)∼J/γ, thus making it easy to confuse with a transition in a finite-size system. Furthermore, utilizing ε-expansion, we demonstrate [2] that the "critical" phase is stabilized for d>1 with a transition to the area-law phase at a finite value of γ/J. The analytical calculations are supported by and are in excellent agreement with the extensive numerical simulations [1,2] for d=1,2. Finally, we will discuss the emergence and origin of the volume-law phase for the entanglement entropy for weakly interacting systems, and the phenomenon of information-charge separation [3]

[1] I.P., P. Pöpperl, I. Gornyi, A.D. Mirlin, Phys. Rev. X 13, 041046 (2023)
[2] I.P., I. Gornyi,  A.D. Mirlin, Phys. Rev. Lett. 132, 110403 (2024)
[3] I.P,  P. Pöpperl, I.V. Gornyi, A.D. Mirlin, arXiv:2410.07334