【时  间】25-October-2024（Friday）3:30pm (Beijing time)

【Zoom meeting】 Zoom id: 290 755 2745

【主  持】Gu Zhang   BAQIS

【题  目】Measurement-induced phase transitions in monitored fermionic systems

【摘  要】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. For d=2 we determine numerically the position of the transition and estimate the value of correlation length critical exponent ν.

【报告人简介】Igor Poboiko studied at the Moscow Institute of Physics and Technology (MIPT) and received his bachelor's degree in 2016. After that, Igor Poboiko worked at the Landau Institute for Theoretical Physics (Chernogolovka) and received his PhD in 2020. He has always been researching the physics of disordered systems, superconductivity, and spin glasses. He worked at the institute until 2022 and then moved to Karlsruhe, where he has been working at IQMT/TKM in Alexander Mirlin's team since then, focusing on the measurement of induced phase transitions.