Symmetric inseparability and number entanglement in charge-conserving mixed states

Ma, Zhanyu; Han, Cheolhee; Meir, Yigal; Sela, Eran

doi:10.1103/physreva.105.042416

Cited by 30 publications

(20 citation statements)

References 49 publications

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“…It is very easy to evaluate (5.17) with these contributions and to recover the known formula for the total von Neumann entropy of a state of two distinct excitations −2r log r − 2(1 − r) log(1 − r) as found in [55,56]. We note also that the number entropy takes its maximum (absolute) value 3/2 log 2 at r = 1/2, and that it can itself be considered a measure of entanglement, as discussed for other examples in [87,88].…”

Section: Jhep12(2022)127supporting

confidence: 59%

Symmetry resolved entanglement of excited states in quantum field theory. Part I. Free theories, twist fields and qubits

Capizzi

Castro-Alvaredo

Fazio

et al. 2022

J. High Energ. Phys.

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The excess entanglement resulting from exciting a finite number of quasiparticles above the ground state of a free integrable quantum field theory has been investigated quite extensively in the literature. It has been found that it takes a very simple form, depending only on the number of excitations and their statistics. There is now mounting evidence that such formulae also apply to interacting and even higher-dimensional quantum theories. In this paper we study the entanglement content of such zero-density excited states focusing on the symmetry resolved entanglement, that is on 1+1D quantum field theories that possess an internal symmetry. The ratio of charged moments between the excited and grounds states, from which the symmetry resolved entanglement entropy can be obtained, takes a very simple and universal form, which in addition to the number and statistics of the excitations, now depends also on the symmetry charge. Using form factor techniques, we obtain both the ratio of moments and the symmetry resolved entanglement entropies in complex free theories which possess U(1) symmetry. The same formulae are found for simple qubit states.

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Section: Jhep12(2022)127supporting

confidence: 59%

Symmetry resolved entanglement of excited states in quantum field theory. Part I. Free theories, twist fields and qubits

Capizzi

Castro-Alvaredo

Fazio

et al. 2022

J. High Energ. Phys.

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show abstract

“…Also at more practical level, it can help to speed-up the numerical algorithms to simulate quantum many-body systems [40]. All that has been the breeding ground for a plethora of works that analyse the resolution of entanglement from different perspectives: spin chains [38,[43][44][45][46][47][48][49][50][51][52][53][54][55][56][57][58][59], integrable quantum field theories [60][61][62][63][64], CFTs [39,40,56,[65][66][67][68][69][70][71][72][73][74][75][76], holography [77][78][79][80], out-ofequilibrium [81][82][83][84][85][86] and disordered...…”

Section: Jhep09(2022)051mentioning

confidence: 99%

Multi-charged moments of two intervals in conformal field theory

Ares

Calabrese

Giulio

et al. 2022

J. High Energ. Phys.

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We study the multi-charged moments for two disjoint intervals in the ground state of two 1 + 1 dimensional CFTs with central charge c = 1 and global U(1) symmetry: the massless Dirac field theory and the compact boson (Luttinger liquid). For this purpose, we compute the partition function on the higher genus Riemann surface arising from the replica method in the presence of background magnetic fluxes between the sheets of the surface. We consider the general situation in which the fluxes generate different twisted boundary conditions at each branch point. The obtained multi-charged moments allow us to derive the symmetry resolution of the Rényi entanglement entropies and the mutual information for non complementary bipartitions. We check our findings against exact numerical results for the tight-binding model, which is a lattice realisation of the massless Dirac theory.

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“…As a consequence of the above, considerable efforts have been spent towards making such entanglement features measurable in the laboratory [20][21][22][23][24]. Among the many, the so-called number entanglement entropy is gaining a prominent role: Its operational definition refers to the probability density function (PDF) of a U(1) globally conserved charge in an extensive sub-portion of the system, also for mixed states [25]. Evidences of its distinctive dynamical behaviour as a hallmark for many-body localization have been recently obtained numerically and experimentally [26][27][28].…”

Section: Introductionmentioning

confidence: 99%

Phase Diagram Detection via Gaussian Fitting of Number Probability Distribution

Contessi¹,

Recati²,

Rizzi³

2022

Preprint

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We investigate the number probability density function that characterizes sub-portions of a quantum many-body system with globally conserved number of particles. We put forward a linear fitting protocol capable of mapping out the ground-state phase diagram of the rich one-dimensional extended Bose-Hubbard model: The results are quantitatively comparable with more sophisticated traditional and machine learning techniques. We argue that the studied quantity should be considered among the most informative bipartite properties, being moreover readily accessible in atomic gases experiments.

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Symmetric inseparability and number entanglement in charge-conserving mixed states

Cited by 30 publications

References 49 publications

Symmetry resolved entanglement of excited states in quantum field theory. Part I. Free theories, twist fields and qubits

Symmetry resolved entanglement of excited states in quantum field theory. Part I. Free theories, twist fields and qubits

Multi-charged moments of two intervals in conformal field theory

Phase Diagram Detection via Gaussian Fitting of Number Probability Distribution

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