Entanglement spectrum of the Heisenberg XXZ chain near the ferromagnetic point

Alba, Vincenzo; Haque, Masudul; Läuchli, Andreas M.

doi:10.1088/1742-5468/2012/08/p08011

Cited by 39 publications

(58 citation statements)

References 42 publications

(70 reference statements)

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“…The same assumption has been used in deriving the entanglement spectrum distribution in Ref. 51 (and the accuracy of the tail distribution function showed in numerical works [66][67][68] is a further confirmation of the plausibility of this assumption).…”

Section: T2mentioning

confidence: 58%

Negativity spectrum of one-dimensional conformal field theories

2016

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The partial transpose ρ T 2 A of the reduced density matrix ρA is the key object to quantify the entanglement in mixed states, in particular through the presence of negative eigenvalues in its spectrum. Here we derive analytically the distribution of the eigenvalues of ρA , that we dub negativity spectrum, in the ground sate of gapless one-dimensional systems described by a Conformal Field Theory (CFT), focusing on the case of two adjacent intervals. We show that the negativity spectrum is universal and depends only on the central charge of the CFT, similarly to the entanglement spectrum. The precise form of the negativity spectrum depends on whether the two intervals are in a pure or mixed state, and in both cases, a dependence on the sign of the eigenvalues is found. This dependence is weak for bulk eigenvalues, whereas it is strong at the spectrum edges. We also investigate the scaling of the smallest (negative) and largest (positive) eigenvalues of ρ T 2 A . We check our results against DMRG simulations for the critical Ising and Heisenberg chains, and against exact results for the harmonic chain, finding good agreement for the spectrum, but showing that the smallest eigenvalue is affected by very large scaling corrections.

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Section: T2mentioning

confidence: 58%

Negativity spectrum of one-dimensional conformal field theories

2016

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“…[39,40]. In particular, for attractive ∆ < 0, n(λ) underestimates the analytical prediction [40]. Conversely for repulsive interaction ∆ > 0, n(λ) overestimates the CL-curve.…”

Section: Reduced Density Matrix and Entanglement Hamiltonian For Critmentioning

confidence: 86%

Spin-resolved entanglement spectroscopy of critical spin chains and Luttinger liquids

Laflorencie¹,

Rachel²

2014

J. Stat. Mech.

122

141

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Abstract. Quantum critical chains are well described and understood by virtue of conformal field theory. Still the meaning of the real space entanglement spectrumthe eigenvalues of the reduced density matrix -of such systems remains in general elusive, even when there is an additional quantum number available such as spin or particle number. In this paper we explore in details the properties and the structure of the reduced density matrix of critical XXZ spin-1 2 chains. We investigate the quantum/thermal correspondence between the reduced density matrix of a T = 0 pure quantum state and the thermal density matrix of an effective entanglement Hamiltonian. Using large scale DMRG and QMC simulations, we investigate the conformal structure of the spectra, the entanglement Hamiltonian and temperature. We then introduce the notion of spin-resolved entanglement entropies which display interesting scaling features.

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“…An example is the string order parameter [48] that is used to find a hidden topological order in the ground state [49]. If the entanglement entropy can be found, so too can the entanglement spectrum, which has become a popular means of characterizing many-body wave functions [50][51][52][53][54][55][56], for better or for worse [57]. Excited states can be found by diagonalizing the top tensor and instead of keeping the lowest energy eigenvector, one keeps a suitable set of higher energy eigenvectors.…”

Section: Discussionmentioning

confidence: 99%

Self-assembling tensor networks and holography in disordered spin chains

Goldsborough

Römer

2014

Phys. Rev. B

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We show that the numerical strong disorder renormalization group algorithm of Hikihara et al. [Phys. Rev. B 60, 12116 (1999)] for the one-dimensional disordered Heisenberg model naturally describes a tree tensor network (TTN) with an irregular structure defined by the strength of the couplings. Employing the holographic interpretation of the TTN in Hilbert space, we compute expectation values, correlation functions, and the entanglement entropy using the geometrical properties of the TTN. We find that the disorder-averaged spin-spin correlation scales with the average path length through the tensor network while the entanglement entropy scales with the minimal surface connecting two regions. Furthermore, the entanglement entropy increases with both disorder and system size, resulting in an area-law violation. Our results demonstrate the usefulness of a self-assembling TTN approach to disordered systems and quantitatively validate the connection between holography and quantum many-body systems.

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Entanglement spectrum of the Heisenberg XXZ chain near the ferromagnetic point

Cited by 39 publications

References 42 publications

Negativity spectrum of one-dimensional conformal field theories

Negativity spectrum of one-dimensional conformal field theories

Spin-resolved entanglement spectroscopy of critical spin chains and Luttinger liquids

Self-assembling tensor networks and holography in disordered spin chains

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