Full Counting Statistics across the Entanglement Phase Transition of Non-Hermitian Hamiltonians with Charge Conservations

• URL: http://arxiv.org/abs/2302.09470v3
• Date: Sun, 10 Sep 2023 04:17:18 GMT
• Title: Full Counting Statistics across the Entanglement Phase Transition of Non-Hermitian Hamiltonians with Charge Conservations
• Authors: Tian-Gang Zhou, Yi-Neng Zhou and Pengfei Zhang
• Abstract summary: We study the full counting statistics (FCS) $Z(phi, O)equiv sum_o eiphi oP(o)$ for 1D systems described by non-Hermitian SYK-like models. In both the volume-law entangled phase for interacting systems and the critical phase for non-interacting systems, the conformal symmetry emerges, which gives $F(phi, Q_A)equiv log Z(phi, Q_A)sim phi2log |A|$
• Score: 4.923287660970805
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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) $Z(\phi, O)\equiv \sum_o e^{i\phi o}P(o)$, a Fourier transform of this distribution, contains the complete information of the measurement outcome. In this work, we study the FCS of $Q_A$, 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 $F(\phi, Q_A)\equiv \log Z(\phi, Q_A)\sim \phi^2\log |A|$. In short-range entangled phases, the FCS shows area-law behavior which can be approximated as $F(\phi, Q_A)\sim (1-\cos\phi) |\partial A|$ for $\zeta \gg J$, 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.

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