Measuring fermionic entanglement: Entropy, negativity, and spin structure

Cornfeld, Eyal; Sela, Eran; Goldstein, Moshe

doi:10.1103/physreva.99.062309

Cited by 60 publications

(49 citation statements)

References 105 publications

(197 reference statements)

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“…We have also showed that the transition classification and the existence of V min depend on whether the system is led to ordinary or full localization, and to the best of our knowledge such distinction has not been considered before. Additionally, as the experimental detection and characterization of entanglement via several protocols have been a current achievement 34,63–67 , our results could contribute to the detection of quantum phase transitions in experiments.…”

Section: Resultsmentioning

confidence: 86%

Superfluid-Insulator Transition unambiguously detected by entanglement in one-dimensional disordered superfluids

Canella

França

2019

Sci Rep

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We use entanglement to track the superfluid-insulator transition (SIT) in disordered fermionic superfluids described by the one-dimensional Hubbard model. Entanglement is found to have remarkable signatures of the SIT driven by i) the disorder strength V, ii) the concentration of impurities C and iii) the particle density n. Our results reveal the absence of a critical potential intensity on the SIT driven by V, i.e. any small V suffices to decrease considerably the degree of entanglement: it drops ∼50% for V = −0.25t. We also find that entanglement is non-monotonic with the concentration C, approaching to zero for a certain critical value CC. This critical concentration is found to be related to a special type of localization, here named as fully-localized state, which can be also reached for a particular density nC. Our results show that the SIT driven by n or C has distinct nature whether it leads to the full localization or to the ordinary one: it is a first-order quantum phase transition only when leading to full localization. In contrast, the SIT driven by V is never a first-order quantum phase transition independently on the type of localization reached.

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Section: Resultsmentioning

confidence: 86%

Superfluid-Insulator Transition unambiguously detected by entanglement in one-dimensional disordered superfluids

Canella

França

2019

Sci Rep

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“…Note that some works normalize each block by each trace [21,22,23] before calculating the entropies, which thus quantify the entanglement after a projective charge measurement. We prefer not to do so and instead use (6), following [19,20], because the resulting entropies are not only more accessible to calculations, but are also directly experimentally measurable, using either the replica trick [20,24,25], or random time evolution which conserves the charge [26,27]. Let us also note that S 1 (Q A ) is simply the distribution P (Q A ) of charge in subsystem A. WhenQ can assume any integer value (e.g., when particle number or total S z are conserved), we define the flux-resolved REE as S n (α) = Tr ρ n A e iαQ A .…”

Section: Introductionmentioning

confidence: 99%

Symmetry resolved entanglement: exact results in 1D and beyond

Fraenkel¹,

Goldstein²

2020

J. Stat. Mech.

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106

160

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In a quantum many-body system that possesses an additive conserved quantity, the entanglement entropy of a subsystem can be resolved into a sum of contributions from different sectors of the subsystem's reduced density matrix, each sector corresponding to a possible value of the conserved quantity. Recent studies have discussed the basic properties of these symmetry-resolved contributions, and calculated them using conformal field theory and numerical methods. In this work we employ the generalized Fisher-Hartwig conjecture to obtain exact results for the characteristic function of the symmetry-resolved entanglement ("flux-resolved entanglement") for certain 1D spin chains, or, equivalently, the 1D fermionic tight binding and the Kitaev chain models. These results are true up to corrections of order o L −1 where L is the subsystem size. We confirm that this calculation is in good agreement with numerical results. For the gapless tight binding chain we report an intriguing periodic structure of the characteristic functions, which nicely extends the structure predicted by conformal field theory. For the Kitaev chain in the topological phase we demonstrate the degeneracy between the even and odd fermion parity sectors of the entanglement spectrum due to virtual Majoranas at the entanglement cut. We also employ the Widom conjecture to obtain the leading behavior of the symmetry-resolved entanglement entropy in higher dimensions for an ungapped free Fermi gas in its ground state.

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“…1(b), which are readily available in NISQ devices and have been already successfully applied to measure entanglement entropies, many-body state fidelities, and out-of-time ordered correlators [10,[33][34][35]. In contrast to previous proposals for measuring PT moments, our protocol does not rely on many-body interference between identical state copies [6,29,36], or on using global entangling random unitaries [37] built from interacting Hamiltonians [16,[38][39][40]. Instead, it only requires singlequbit control, and allows for the estimation of many distinct PT moments from the same data.…”

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confidence: 99%