Symmetry-resolved entanglement in critical non-Hermitian systems

Fossati, Michele; Ares, Filiberto; Calabrese, Pasquale

doi:10.1103/physrevb.107.205153

Phys. Rev. B

2023

DOI: 10.1103/physrevb.107.205153

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Symmetry-resolved entanglement in critical non-Hermitian systems

Michele Fossati

Filiberto Ares

Pasquale Calabrese

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Cited by 13 publications

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“…For some values of t/ℓ we report the numerical value of the symmetry-resolved entropy obtained through exact simulations of the dynamics (symbols). We clearly observe a delay time in agreement with equation(66), which does not depend on the dissipative term γ + .…”

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confidence: 82%

Symmetry-resolved entanglement in fermionic systems with dissipation

Murciano,

Calabrese,

Alba

2023

J. Stat. Mech.

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We investigate symmetry-resolved entanglement in out-of-equilibrium fermionic systems subject to gain and loss dissipation, which preserves the block-diagonal structure of the reduced density matrix. We derive a hydrodynamic description of the dynamics of several entanglement-related quantities, such as the symmetry-resolved von Neumann entropy and the charge-imbalance-resolved fermionic negativity. We show that all these quantities admit a hydrodynamic description in terms of entangled quasiparticles. While the entropy is dominated by dissipative processes, the resolved negativity is sensitive to the presence of entangled quasiparticles, and it shows the typical ‘rise and fall’ dynamics. Our results hold in the weak-dissipative hydrodynamic limit of large intervals, long times and weak dissipation rates.

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confidence: 82%

Symmetry-resolved entanglement in fermionic systems with dissipation

Murciano,

Calabrese,

Alba

2023

J. Stat. Mech.

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Symmetry resolution of the computable cross-norm negativity of two disjoint intervals in the massless Dirac field theory

Bruno,

Ares,

Murciano

et al. 2024

J. High Energ. Phys.

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We investigate how entanglement in the mixed state of a quantum field theory can be described using the cross-computable norm or realignment (CCNR) criterion, employing a recently introduced negativity. We study its symmetry resolution for two disjoint intervals in the ground state of the massless Dirac fermion field theory, extending previous results for the case of adjacent intervals. By applying the replica trick, this problem boils down to computing the charged moments of the realignment matrix. We show that, for two disjoint intervals, they correspond to the partition function of the theory on a torus with a non-contractible charged loop. This confers a great advantage compared to the negativity based on the partial transposition, for which the Riemann surfaces generated by the replica trick have higher genus. This result empowers us to carry out the replica limit, yielding analytic expressions for the symmetry-resolved CCNR negativity. Furthermore, these expressions provide also the symmetry decomposition of other related quantities such as the operator entanglement of the reduced density matrix or the reflected entropy.

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Entanglement entropy along a massless renormalisation flow: the tricritical to critical Ising crossover

Rottoli,

Ares,

Calabrese

et al. 2024

J. High Energ. Phys.

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We study the Rényi entanglement entropies along the massless renormalisation group flow that connects the tricritical and critical Ising field theories. Similarly to the massive integrable field theories, we derive a set of bootstrap equations, from which we can analytically calculate the twist field form factors in a recursive way. Additionally, we also obtain them as a non-trivial ‘roaming limit’ of the sinh-Gordon theory. Then the Rényi entanglement entropies are obtained as expansions in terms of the form factors of these branch point twist fields. We find that the form factor expansion of the entanglement entropy along the flow organises in two different kind of terms. Those that couple particles with the same chirality, and reproduce the entropy of the infrared Ising theory, and those that couple particles with different chirality, which provide the ultraviolet contributions. The massless flow under study possesses a global ℤ2 spin-flip symmetry. We further consider the composite twist fields associated to this group, which enter in the study of the symmetry resolution of the entanglement. We derive analytical expressions for their form factors both from the bootstrap equations and from the roaming limit of the sinh-Gordon theory.

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Symmetry-resolved entanglement in critical non-Hermitian systems

Cited by 13 publications

References 118 publications

Symmetry-resolved entanglement in fermionic systems with dissipation

Symmetry-resolved entanglement in fermionic systems with dissipation

Symmetry resolution of the computable cross-norm negativity of two disjoint intervals in the massless Dirac field theory

Entanglement entropy along a massless renormalisation flow: the tricritical to critical Ising crossover

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