Correlation amplitude and entanglement entropy in random spin chains

Hoyos, José A.; Vieira, André P.; Laflorencie, Nicolas; Miranda, E.

doi:10.1103/physrevb.76.174425

Cited by 59 publications

(107 citation statements)

References 53 publications

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“…8 shows a clear difference in the correlation function between even and odd distances. The difference in magnitude is found to be 1/4 as predicted previously [38].…”

Section: B Correlation Functionssupporting

confidence: 70%

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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“…8 shows a clear difference in the correlation function between even and odd distances. The difference in magnitude is found to be 1/4 as predicted previously [38].…”

Section: B Correlation Functionssupporting

confidence: 70%

Self-assembling tensor networks and holography in disordered spin chains

Goldsborough

Römer

2014

Phys. Rev. B

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“…Furthermore, the moments of the reduced density matrix Trρ α A have been also studied 52 , as well as the spectrum 53 , and the entanglement in low-lying excited states 54 . Other disordered spin models [55][56][57][58][59][60][61][62][63][64][65][66][67] have been also considered, obtaining similar results for the scaling of the entanglement entropy. The non-equilibrium features of the entanglement in these random spin chains are also under intensive investigation 51,[68][69][70][71][72][73][74][75] .…”

Section: Introductionmentioning

confidence: 70%

Entanglement negativity in random spin chains

2016

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We investigate the logarithmic negativity in strongly-disordered spin chains in the random-singlet phase. We focus on the spin-1/2 random Heisenberg chain and the random XX chain. We find that for two arbitrary intervals the disorder-averaged negativity and the mutual information are proportional to the number of singlets shared between the two intervals. Using the strong-disorder renormalization group (SDRG), we prove that the negativity of two adjacent intervals grows logarithmically with the intervals length. In particular, the scaling behavior is the same as in conformal field theory, but with a different prefactor. For two disjoint intervals the negativity is given by a universal simple function of the cross ratio, reflecting scale invariance. As a function of the distance of the two intervals, the negativity decays algebraically in contrast with the exponential behavior in clean models. We confirm our predictions using a numerical implementation of the SDRG method. Finally, we also implement DMRG simulations for the negativity in open spin chains. The chains accessible in the presence of strong disorder are not sufficiently long to provide a reliable confirmation of the SDRG results.

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“…It is thus clear that we can write [79] S RSP (ℓ) =n ln 2, (2.70) wheren is the disorder-averaged number of singlets that cross the boundary between the two blocks. It has been shown thatn ∼ (1/3) ln ℓ [79,92,93]. For a factorized state like the RSP, it is also easy to find the cumulants of the total spinŜ z in the subsystem.…”

Section: The Spin-1/2 XX Chainmentioning

confidence: 99%

“…One such quantity is the valence bond (VB) entanglement entropy for SU(2) quantum spin systems [134,135], which generalizes the idea, first used in the context of random spin chains [79,92,93], that for a pure valence bond state whose wave function is a product of disjoint singlet bonds between two spin-1/2s the entanglement entropy of a subsystem is essentially the number of singlet bonds that cross the boundary between the subsystem and the remainder of the system, with each singlet |Ψ s = (|↑ A ↓ B − |↓ A ↑ B )/ √ 2 contributing ln 2 to the entanglement entropy. For more general wave functions which are superpositions of pure VB states the number of such crossings can be averaged to obtain a well-defined (with certain restrictions [134]) measure of entanglement.…”

Section: Concluding Remarks On Bipartite Fluctuations a Comparismentioning

confidence: 99%

Bipartite fluctuations as a probe of many-body entanglement

et al. 2012

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We investigate in detail the behavior of the bipartite fluctuations of particle numberN and spin S z in many-body quantum systems, focusing on systems where such U(1) charges are both conserved and fluctuate within subsystems due to exchange of charges between subsystems. We propose that the bipartite fluctuations are an effective tool for studying many-body physics, particularly its entanglement properties, in the same way that noise and Full Counting Statistics have been used in mesoscopic transport and cold atomic gases. For systems that can be mapped to a problem of non-interacting fermions we show that the fluctuations and higher-order cumulants fully encode the information needed to determine the entanglement entropy as well as the full entanglement spectrum through the Rényi entropies. In this connection we derive a simple formula that explicitly relates the eigenvalues of the reduced density matrix to the Rényi entropies of integer order for any finite density matrix. In other systems, particularly in one dimension, the fluctuations are in many ways similar but not equivalent to the entanglement entropy. Fluctuations are tractable analytically, computable numerically in both density matrix renormalization group and quantum Monte Carlo calculations, and in principle accessible in condensed matter and cold atom experiments. In the context of quantum point contacts, measurement of the second charge cumulant showing a logarithmic dependence on time would constitute a strong indication of many-body entanglement.

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Correlation amplitude and entanglement entropy in random spin chains

Cited by 59 publications

References 53 publications

Self-assembling tensor networks and holography in disordered spin chains

Self-assembling tensor networks and holography in disordered spin chains

Entanglement negativity in random spin chains

Bipartite fluctuations as a probe of many-body entanglement

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