Negativity spectrum in 1D gapped phases of matter

Mbeng, Glen Bigan; Alba, Vincenzo; Calabrese, Pasquale

doi:10.1088/1751-8121/aa6734

Cited by 35 publications

(40 citation statements)

References 87 publications

(188 reference statements)

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“…As for the von Neumann entropy, the mutual information is dominated by the regular part (cf. (70)). More precisely, although the singular term in (70) gives a universal crossing, this is not visible because it is suppressed as L −2 in the limit L → ∞.…”

Section: Mutual Informationmentioning

confidence: 99%

Entanglement and classical fluctuations at finite-temperature critical points

Wald¹,

Arias²,

Alba³

2020

J. Stat. Mech.

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We investigate several entanglement-related quantities at finite-temperature criticality in the three-dimensional quantum spherical model, both as a function of temperature T and of the quantum parameter g, which measures the strength of quantum fluctuations. While the von Neumann and the Rényi entropies exhibit the volume-law for any g and T , the mutual information obeys an area law. The prefactors of the volume-law and of the area-law are regular across the transition, reflecting that universal singular terms vanish at the transition. This implies that the mutual information is dominated by nonuniversal contributions. This hampers its use as a witness of criticality, at least in the spherical model. We also study the logarithmic negativity. For any value of g, T , the negativity exhibits an area-law. The negativity vanishes deep in the paramagnetic phase, it is larger at small temperature, and it decreases upon increasing the temperature. For any g, it exhibits the so-called sudden death, i.e., it is exactly zero for large enough T . The vanishing of the negativity defines a "death line", which we characterise analytically at small g. Importantly, for any finite T the area-law prefactor is regular across the transition, whereas it develops a cusp-like singularity in the limit T → 0. Finally, we consider the single-particle entanglement and negativity spectra. The vast majority of the levels are regular across the transition. Only the larger ones exhibit singularities. These are related to the presence of a zero mode, which reflects the symmetry breaking. This implies the presence of sub-leading singular terms in the entanglement entropies. Interestingly, since the larger levels do not contribute to the negativity, sub-leading singular corrections are expected to be suppressed for the negativity.

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Section: Mutual Informationmentioning

confidence: 99%

Entanglement and classical fluctuations at finite-temperature critical points

Wald¹,

Arias²,

Alba³

2020

J. Stat. Mech.

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“…In this case, the largest eigenvalue of the RDM is doubly degenerate, and the same is true for all the spectrum, as a consequence of the zero mode with j = 0. Following [12,51,66], the entanglement spectrum is obtained by filling in all the possible ways the single particle levels j in (31) (i.e., setting alln j equal either to 0 or 1). The resulting eigenvalues of the reduced density matrix, with n = j j (cf.…”

Section: The Anisotropic Heisenberg Spin-chainmentioning

confidence: 99%

“…Finally, we will show that the degeneracy in the spectrum of ρ A has non-trivial effects also on the distribution of the eigenvalues of the partial transpose of ρ A , i.e., the negativity spectrum of Refs. [50,51]. This paper is organised as follows.…”

Section: Introductionmentioning

confidence: 99%

Entanglement spectrum degeneracy and the Cardy formula in 1+1 dimensional conformal field theories

Alba¹,

Calabrese²,

Tonni³

2017

J. Phys. A: Math. Theor.

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Abstract.We investigate the effect of a global degeneracy in the distribution of entanglement spectrum in conformal field theories in one spatial dimension. We relate the recently found universal expression for the entanglement hamiltonian to the distribution of the entanglement spectrum. The main tool to establish this connection is the Cardy formula. It turns out that the Affleck-Ludwig noninteger degeneracy, appearing because of the boundary conditions induced at the entangling surface, can be directly read from the entanglement spectrum distribution. We also clarify the effect of the non-integer degeneracy on the spectrum of the partial transpose, which is the central object for quantifying the entanglement in mixed states. We show that the exact knowledge of the entanglement spectrum in some integrable spin-chains provides strong analytical evidences corroborating our results.arXiv:1707.07532v1 [hep-th]

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“…(3) may be obtained as the replica limit 66,67 ρ T2 A = lim α→1/2 M T2 2α . The negativity spectrum so far has been investigated only for clean systems [101][102][103] . On the other hand, when considering quenched disorder, static and dynamic properties of a system drastically change compared to the clean case.…”

Section: Introductionmentioning

confidence: 99%

Negativity spectrum in the random singlet phase

2020

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Entanglement features of the ground state of disordered quantum matter are often captured by an infinite randomness fixed point that, for a variety of models, is the random singlet phase. Although a copious number of studies covers bipartite entanglement in pure states, at present, less is known for mixed states and tripartite settings. Our goal is to gain insights in this direction by studying the negativity spectrum in the random singlet phase. Through the strong disorder renormalization group technique, we derive analytic formulas for the universal scaling of the disorder averaged moments of the partially transposed reduced density matrix. Our analytic predictions are checked against a numerical implementation of the strong disorder renormalization group and against exact computations for the XX spin chain (a model in which free fermion techniques apply). Importantly, our results show that the negativity and logarithmic negativity are not trivially related after the average over the disorder. arXiv:1910.09571v1 [cond-mat.stat-mech]

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Negativity spectrum in 1D gapped phases of matter

Cited by 35 publications

References 87 publications

Entanglement and classical fluctuations at finite-temperature critical points

Entanglement and classical fluctuations at finite-temperature critical points

Entanglement spectrum degeneracy and the Cardy formula in 1+1 dimensional conformal field theories

Negativity spectrum in the random singlet phase

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