Full counting statistics and symmetry resolved entanglement for free conformal theories with interface defects

Capizzi, Luca; Murciano, Sara; Calabrese, Pasquale

doi:10.1088/1742-5468/ace3b8

Cited by 10 publications

(3 citation statements)

References 97 publications

(92 reference statements)

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“…Since the long-range limit is the focus of this paper, equation (37) was the expression used for the correlation matrix entries when numerical results were computed using equations (30) and (31). As we explain in detail in the following sections, equation (37) was also used as the starting point for some parts of the analytical derivation, whereas in other parts the long-range limit was taken only in a later stage of the calculation.…”

Section: J Stat Mech (2024) 033107mentioning

confidence: 99%

“…We may point out that equation (37) entails that, in the long-range limit, the twopoint correlation function between a site in A L and another in A R vanishes either when the impurity is trivial or when k F ,L = k F ,R . Then, it is straightforward to see through equations ( 30) and ( 31) that in either of these two cases the Rényi MI vanishes identically and the Rényi negativity satisfies…”

Section: J Stat Mech (2024) 033107mentioning

confidence: 99%

“…Moreover, while the initial focus of this vast body of work has been naturally put on homogeneous systems, a recent surge of interest has been directed toward the nontrivial signatures that inhomogeneities (e.g. boundaries and defects) may imprint on correlation and entanglement structures, either in equilibrium [33][34][35][36][37] or out of equilibrium [38][39][40][41][42][43][44]. This avenue of research raises particular technical challenges when one attempts to adapt well-established analytical methods that originally relied on the translation invariance of the system in question.…”

Section: Introductionmentioning

confidence: 99%

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Exact asymptotics of long-range quantum correlations in a non-equilibrium steady state

Fraenkel,

Goldstein

2024

J. Stat. Mech.

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Out-of-equilibrium states of many-body systems tend to evade a description by standard statistical mechanics, and their uniqueness is epitomized by the possibility of certain long-range correlations that cannot occur in equilibrium. In quantum many-body systems, coherent correlations of this sort may lead to the emergence of remarkable entanglement structures. In this work, we analytically study the asymptotic scaling of quantum correlation measures—the mutual information (MI) and the fermionic negativity—within the zero-temperature steady state of voltage-biased free fermions on a one-dimensional lattice containing a non-interacting impurity. Previously, we have shown that two subsystems on opposite sides of the impurity exhibit volume-law entanglement, which is independent of the absolute distances of the subsystems from the impurity. Here, we go beyond that result and derive the exact form of the subleading logarithmic corrections to the extensive terms of correlation measures, in excellent agreement with numerical calculations. In particular, the logarithmic term of the MI asymptotics can be encapsulated in a concise formula, depending only on simple four-point ratios of subsystem length scales and on the impurity scattering probabilities at the Fermi energies. This echoes the case of equilibrium states, where such logarithmic terms may convey universal information about the physical system. To compute these exact results, we devise a hybrid method that relies on Toeplitz determinant asymptotics for correlation matrices in both real space and momentum space, successfully circumventing the inhomogeneity of the system. This method could potentially find wider use for analytical calculations of entanglement measures in similar scenarios.

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Section: J Stat Mech (2024) 033107mentioning

confidence: 99%

Section: J Stat Mech (2024) 033107mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Exact asymptotics of long-range quantum correlations in a non-equilibrium steady state

Fraenkel,

Goldstein

2024

J. Stat. Mech.

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Multi-charged moments and symmetry-resolved Rényi entropy of free compact boson for multiple disjoint intervals

Gaur,

Yajnik

2024

J. High Energ. Phys.

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We study multi-charged moments and symmetry-resolved Rényi entropy of free compact boson for multiple disjoint intervals. The Rényi entropy evaluation involves computing the partition function of the theory on Riemann surfaces with genus g > 1. This makes Rényi entropy sensitive to the local conformal algebra of the theory. The free compact boson possesses a global U(1) symmetry with respect to which we resolve Rényi entropy. The multi-charged moments are obtained by studying the correlation function of flux-generating vertex operators on the associated Riemann surface. Symmetry-resolved Rényi entropy is then obtained from the Fourier transforms of the charged moments. Rényi entropy is shown to have the familiar equipartition into local charge sectors upto the leading order. The multi-charged moments are also essential in studying the symmetry resolution of mutual information. The multi-charged moments of the self-dual compact boson and massless Dirac fermion are also shown to match for the cases when the associated reduced density moments are known to be the same. Finally, we numerically check our results against the tight-binding model.

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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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Full counting statistics and symmetry resolved entanglement for free conformal theories with interface defects

Cited by 10 publications

References 97 publications

Exact asymptotics of long-range quantum correlations in a non-equilibrium steady state

Exact asymptotics of long-range quantum correlations in a non-equilibrium steady state

Multi-charged moments and symmetry-resolved Rényi entropy of free compact boson for multiple disjoint intervals

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

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