Partial time-reversal transformation and entanglement negativity in fermionic systems

Shapourian, Hassan; Shiozaki, Ken; Ryu, Shinsei

doi:10.1103/physrevb.95.165101

Cited by 157 publications

(241 citation statements)

References 85 publications

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“…(D1), |Ψ ) is the ground state of the interacting Kitaev chain under the PBC (APBC). We note that the same result has also been presented 74,75 , but for the reader's convenience we give an explicit proof of this fact. Since |Ψ The change of the parity between the PBC and the APBC for the interacting Kitaev model again indicates the ground-state degeneracy at some point on a path (φ 1 (s), φ 2 (s)) that connects H int | a=b=1;(0,0) and H int | a=b=1;(π,π) .…”

Section: Odd Lsupporting

confidence: 65%

Exact zero modes in twisted Kitaev chains

Kawabata

Kobayashi

et al. 2017

Phys. Rev. B

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We study the Kitaev chain under generalized twisted boundary conditions, for which both the amplitudes and the phases of the boundary couplings can be tuned at will. We explicitly show the presence of exact zero modes for large chains belonging to the topological phase in the most general case, in spite of the absence of "edges" in the system. For specific values of the phase parameters, we rigorously obtain the condition for the presence of the exact zero modes in finite chains, and show that the zero modes obtained are indeed localized. The full spectrum of the twisted chains with zero chemical potential is analytically presented. Finally, we demonstrate the persistence of zero modes (level crossing) even in the presence of disorder or interactions.

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Section: Odd Lsupporting

confidence: 65%

Exact zero modes in twisted Kitaev chains

Kawabata

Kobayashi

et al. 2017

Phys. Rev. B

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“…In a (1+1)-dimensional quantum field theory, this quantity is the partition function on a Riemann surface with the insertion of an Aharonov-Bohm flux α, such that the field acquires a total phase α when moving on the entire worldsheet. Similar charged moments have been already considered in the context of free field theories [39][40][41], in holographic settings [42,43], as well as in the study of entanglement in mixed states [44,45]. The Fourier transforms of the charged moments are just the moments of the RDM restricted to the sector of fixed charge [28], i.e.…”

Section: Symmetry Resolution Flux Insertion and Corner Transfer Matrixmentioning

confidence: 69%

Symmetry resolved entanglement in gapped integrable systems: a corner transfer matrix approach

2020

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We study the symmetry resolved entanglement entropies in gapped integrable lattice models. We use the corner transfer matrix to investigate two prototypical gapped systems with a U (1) symmetry: the complex harmonic chain and the XXZ spin-chain. While the former is a free bosonic system, the latter is genuinely interacting. We focus on a subsystem being half of an infinitely long chain. In both models, we obtain exact expressions for the charged moments and for the symmetry resolved entropies. While for the spin chain we found exact equipartition of entanglement (i.e. all the symmetry resolved entropies are the same), this is not the case for the harmonic system where equipartition is effectively recovered only in some limits. Exploiting the gaussianity of the harmonic chain, we also develop an exact correlation matrix approach to the symmetry resolved entanglement that allows us to test numerically our analytic results. arXiv:1911.09588v2 [cond-mat.stat-mech]

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“…However, for fermionic systems this is not any more the case. Indeed, in contrast to partial time reversal [34], the partial transpose in general does not lead to a Gaussian operator [42]. However, it has been proved that the definition based on partial time reversal also yields a proper measure of entanglement [43].…”

Section: B Entanglement Negativitymentioning

confidence: 99%

Time evolution of entanglement negativity across a defect

Gruber¹,

Eisler²

2020

J. Phys. A: Math. Theor.

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We consider a quench in a free-fermion chain by joining two homogeneous half-chains via a defect. The time evolution of the entanglement negativity is studied between adjacent segments surrounding the defect. In case of equal initial fillings, the negativity grows logarithmically in time and essentially equals one-half of the Rényi mutual information with index α = 1/2 in the limit of large segments. In sharp contrast, in the biased case one finds a linear increase followed by the saturation at an extensive value for both quantities, which is due to the backscattering from the defect and can be reproduced in a quasiparticle picture. Furthermore, a closer inspection of the subleading corrections reveals that the negativity and the mutual information have a small but finite difference in the steady state. Finally, we also study a similar quench in the XXZ spin chain via density-matrix renormalization group methods and compare the results for the negativity to the fermionic case.

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Partial time-reversal transformation and entanglement negativity in fermionic systems

Cited by 157 publications

References 85 publications

Exact zero modes in twisted Kitaev chains

Exact zero modes in twisted Kitaev chains

Symmetry resolved entanglement in gapped integrable systems: a corner transfer matrix approach

Time evolution of entanglement negativity across a defect

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