2023/02/19 by Zhou, Tian-Gang, Zhou, Yi-Neng, Zhang, Pengfei
#Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Physical sciences #Quantum Gases (cond-mat.quant-gas) #Quantum Physics (quant-ph) #Statistical Mechanics (cond-mat.stat-mech) #Strongly Correlated Electrons (cond-mat.str-el)
paper · doi:10.48550/arxiv.2302.09470
Performing quantum measurements produces not only the expectation value of a physical observable O but also the probability distribution P(o) of all possible outcomes o. The full counting statistics (FCS) Z(ϕ, O)≡ ∑o eiϕoP(o), a Fourier transform of this distribution, contains the complete information of the measurement outcome. In this work, we study the FCS of QA, the charge operator in subsystem A, for 1D systems described by non-Hermitian SYK-like models, which are solvable in the large-N limit. In both the volume-law entangled phase for interacting systems and the critical phase for non-interacting systems, the conformal symmetry emerges, which gives F(ϕ, QA)≡ log Z(ϕ, QA)∼ ϕ2log |A|. In short-range entangled phases, the FCS shows area-law behavior which can be approximated as F(ϕ, QA)∼ (1-cosϕ) |∂ A| for ζ≫ J, regardless of the presence of interactions. Our results suggest the FCS is a universal probe of entanglement phase transitions in non-Hermitian systems with conserved charges, which does not require the introduction of multiple replicas. We also discuss the consequence of discrete symmetry, long-range hopping, and generalizations to higher dimensions.