Physical review. B./Physical review. B

Full counting statistics across the entanglement phase transition of non-Hermitian Hamiltonians with charge conservation

Tian-Gang Zhou, Yi-Neng Zhou, Pengfei Zhang

Published Sep 22, 2023• 5 citations

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) $Z(\ensuremath{\phi},O)\ensuremath{\equiv}{\ensuremath{\sum}}_{o}{e}^{i\ensuremath{\phi}o}P(o)$, 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 one-dimensional systems described by non-Hermitian Sachdev-Ye-Kitaev-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 noninteracting systems, the conformal symmetry emerges, which gives $F(\ensuremath{\phi},{Q}_{A})\ensuremath{\equiv}lnZ(\ensuremath{\phi},{Q}_{A})\ensuremath{\sim}{\ensuremath{\phi}}^{2}ln|A|$. In short-range entangled phases, the FCS shows area-law behavior which can be approximated as $F(\ensuremath{\phi},{Q}_{A})\ensuremath{\sim}(1\ensuremath{-}cos\ensuremath{\phi})|\ensuremath{\partial}A|$ for $\ensuremath{\zeta}\ensuremath{\gg}J$, 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 consequences of discrete symmetry, long-range hopping, and generalizations to higher dimensions.

DOI: 10.1103/physrevb.108.094308

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Physical review. B./Physical review. B

Full counting statistics across the entanglement phase transition of non-Hermitian Hamiltonians with charge conservation

Tian-Gang Zhou, Yi-Neng Zhou, Pengfei Zhang

Published Sep 22, 2023• 5 citations

Publisher

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(\ensuremath{\phi},O)\ensuremath{\equiv}{\ensuremath{\sum}}_{o}{e}^{i\ensuremath{\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 one-dimensional systems described by non-Hermitian Sachdev-Ye-Kitaev-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 noninteracting systems, the conformal symmetry emerges, which gives

F(\ensuremath{\phi},{Q}_{A})\ensuremath{\equiv}lnZ(\ensuremath{\phi},{Q}_{A})\ensuremath{\sim}{\ensuremath{\phi}}^{2}ln|A|

. In short-range entangled phases, the FCS shows area-law behavior which can be approximated as

F(\ensuremath{\phi},{Q}_{A})\ensuremath{\sim}(1\ensuremath{-}cos\ensuremath{\phi})|\ensuremath{\partial}A|

for

\ensuremath{\zeta}\ensuremath{\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 consequences of discrete symmetry, long-range hopping, and generalizations to higher dimensions.

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) $Z(\ensuremath{\phi},O)\ensuremath{\equiv}{\ensuremath{\sum}}_{o}{e}^{i\ensuremath{\phi}o}P(o)$, 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 one-dimensional systems described by non-Hermitian Sachdev-Ye-Kitaev-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 noninteracting systems, the conformal symmetry emerges, which gives $F(\ensuremath{\phi},{Q}_{A})\ensuremath{\equiv}lnZ(\ensuremath{\phi},{Q}_{A})\ensuremath{\sim}{\ensuremath{\phi}}^{2}ln|A|$. In short-range entangled phases, the FCS shows area-law behavior which can be approximated as $F(\ensuremath{\phi},{Q}_{A})\ensuremath{\sim}(1\ensuremath{-}cos\ensuremath{\phi})|\ensuremath{\partial}A|$ for $\ensuremath{\zeta}\ensuremath{\gg}J$, 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 consequences of discrete symmetry, long-range hopping, and generalizations to higher dimensions.

DOI: 10.1103/physrevb.108.094308

Related papers

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

Tian-Gang Zhou, Yi-Neng Zhou, Pengfei Zhang

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) $Z(ϕ, O)\equiv \sum_o e^{iϕo}P(o)$ , 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 $F(ϕ, Q_A)\equiv \log Z(ϕ, Q_A)\sim ϕ^2\log |A|$ . In short-range entangled phases, the FCS shows area-law behavior which can be approximated as $F(ϕ, Q_A)\sim (1-\cosϕ) |\partial A|$ for $ζ\gg J$ , 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.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) $Z(ϕ, O)\equiv \sum_o e^{iϕo}P(o)$, 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 $F(ϕ, Q_A)\equiv \log Z(ϕ, Q_A)\sim ϕ^2\log |A|$. In short-range entangled phases, the FCS shows area-law behavior which can be approximated as $F(ϕ, Q_A)\sim (1-\cosϕ) |\partial A|$ for $ζ\gg J$, 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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Riccardo Senese

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Jan 1, 20250 citations

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Chang-Yan Wang, Xue-Feng Zhang

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cond-mat.str-elCross-listedarXiv:2606.04086Jun 4, 20260 citations

Full counting statistics of charge in quenched quantum gases

Dávid X. Horváth, Colin Rylands

Unless constrained by symmetry, measurement of an observable on an ensemble of identical quantum systems returns a distribution of values which are encoded in the full counting statistics. While the mean value of this distribution is important for determining certain properties of a system, the full distribution can also exhibit universal behavior. In this paper we study the full counting statistics of particle number in one-dimensional interacting Bose and Fermi gases which have been quenched far from equilibrium. In particular, we consider the time evolution of the Lieb-Liniger and Gaudin-Yang models quenched from a Bose-Einstein condensate initial state and calculate the full counting statistics of the particle number within a subsystem. We show that the scaled cumulants of the charge in the initial state and at long times are simply related and, in particular, the latter are independent of the model parameters. Using the quasiparticle picture we obtain the full time evolution of the cumulants and find that although their end points are fixed, the finite-time dynamics depends strongly on the model parameters. We go on to construct the scaled cumulant generating functions and from this determine the limiting charge probability distributions at long time which are shown to exhibit distinct, nontrivial, and non-Gaussian fluctuations and large deviations. Published by the American Physical Society 2024Unless constrained by symmetry, measurement of an observable on an ensemble of identical quantum systems returns a distribution of values which are encoded in the full counting statistics. While the mean value of this distribution is important for determining certain properties of a system, the full distribution can also exhibit universal behavior. In this paper we study the full counting statistics of particle number in one-dimensional interacting Bose and Fermi gases which have been quenched far from equilibrium. In particular, we consider the time evolution of the Lieb-Liniger and Gaudin-Yang models quenched from a Bose-Einstein condensate initial state and calculate the full counting statistics of the particle number within a subsystem. We show that the scaled cumulants of the charge in the initial state and at long times are simply related and, in particular, the latter are independent of the model parameters. Using the quasiparticle picture we obtain the full time evolution of the cumulants and find that although their end points are fixed, the finite-time dynamics depends strongly on the model parameters. We go on to construct the scaled cumulant generating functions and from this determine the limiting charge probability distributions at long time which are shown to exhibit distinct, nontrivial, and non-Gaussian fluctuations and large deviations. Published by the American Physical Society 2024

arXiv:2312.02929Physical Review AApr 1, 202416 citations

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(\ensuremath{\phi},O)\ensuremath{\equiv}{\ensuremath{\sum}}_{o}{e}^{i\ensuremath{\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 one-dimensional systems described by non-Hermitian Sachdev-Ye-Kitaev-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 noninteracting systems, the conformal symmetry emerges, which gives

F(\ensuremath{\phi},{Q}_{A})\ensuremath{\equiv}lnZ(\ensuremath{\phi},{Q}_{A})\ensuremath{\sim}{\ensuremath{\phi}}^{2}ln|A|

. In short-range entangled phases, the FCS shows area-law behavior which can be approximated as

F(\ensuremath{\phi},{Q}_{A})\ensuremath{\sim}(1\ensuremath{-}cos\ensuremath{\phi})|\ensuremath{\partial}A|

for

\ensuremath{\zeta}\ensuremath{\gg}J

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)\equiv \sum_o e^{iϕo}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(ϕ, Q_A)\equiv \log Z(ϕ, Q_A)\sim ϕ^2\log |A|

. In short-range entangled phases, the FCS shows area-law behavior which can be approximated as

F(ϕ, Q_A)\sim (1-\cosϕ) |\partial A|

for

ζ\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.

\lnΔE(r)\sim -π^2 r^2/(12 S_\ell)

up to subleading terms, where

S_\ell

is the entanglement entropy between the two halves of a quantum string. We confirm the theory using high-precision numerical calculations and finite-size FCS estimates. Our results reveal FCS as a direct route to effective interactions between quantum topological line-defects, which may also be extended to higher-form charge.