2018
DOI: 10.1103/physrevb.98.085153
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Schmidt gap in random spin chains

Abstract: We numerically investigate the low-lying entanglement spectrum of the ground state of random one-dimensional spin chains obtained after partition of the chain into two equal halves. We consider two paradigmatic models: the spin-1/2 random transverse field Ising model, solved exactly, and the spin-1 random Heisenberg model, simulated using the density matrix renormalization group. In both cases we analyze the mean Schmidt gap, defined as the difference between the two largest eigenvalues of the reduced density … Show more

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Cited by 6 publications
(7 citation statements)
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“…4 we show the average string order parameters as functions of L for various disorder parameters δ near the transition point. From the decay behavior of the curves in the log-log plot and a comparison of the exponent η st with the theoretical conjecture (η st ≈ 0.5093), it seems reasonable to fix δ c = 1 for our results, which is also consistent with previous numerical results obtained by the density matrix renormalization group (DMRG) [26,29]. At δ c = 1 we obtain η st ≈ 0.52, slightly larger than the theoretical value.…”
Section: A String Order Parametersupporting
confidence: 90%
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“…4 we show the average string order parameters as functions of L for various disorder parameters δ near the transition point. From the decay behavior of the curves in the log-log plot and a comparison of the exponent η st with the theoretical conjecture (η st ≈ 0.5093), it seems reasonable to fix δ c = 1 for our results, which is also consistent with previous numerical results obtained by the density matrix renormalization group (DMRG) [26,29]. At δ c = 1 we obtain η st ≈ 0.52, slightly larger than the theoretical value.…”
Section: A String Order Parametersupporting
confidence: 90%
“…8; here the broad distributions of the logarithmic energy gaps can be rescaled using the same form in Eq. (27), but with [29] 0.21(4) 0.24 (5) With weaker disorder δ < 1, the width of the gap distribution becomes saturated for L → ∞. Fig.…”
Section: B Energy Gapsmentioning
confidence: 89%
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“…Other entanglement measures have been also studied in random quantum chains, like the entanglement [122,123] or the concurrence [124] between distant pairs of q-bits, the full entanglement spectrum of random singlet critical points [125], the Rényi entropies [126], the fluctuations of the entanglement entropy [127], the full probability distribution of the entanglement entropy [128], the Schmidtgap ( i.e. the difference between the two largest eigenvalues of the entanglement spectrum) for the RTIM and for the S = 1 random spin chain [129]. Using the SDRG method the entanglement negativity in random singlet phases are shown to scale logarithmically with the size of the system [130].…”
Section: A Random Quantum Chainsmentioning
confidence: 99%
“…Hence, the choice of exponential dependence of the second term, appropriate for the topological phase, is sufficient for our purposes (compare with Ref. [61]). The resulting δ ∞ is plotted as a function of disorder in Figure 3b, and shows nicely the topological-to-trivial transition.…”
Section: Phase Diagram From Entanglementmentioning
confidence: 99%