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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