Scattering at the Anderson transition: Power-law banded random matrix model

Méndez-Bermúdez, J. A.; Varga, Imre

doi:10.1103/physrevb.74.125114

Cited by 22 publications

(19 citation statements)

References 57 publications

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“…To compute τ W we use the effective Hamiltonian approach described in Refs. [19,24]. For statistical processing a large number of disorder realizations is used.…”

Section: B Wigner Delay Timesmentioning

confidence: 99%

On the generalized dimensions of multifractal eigenstates

2014

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Recently, based on heuristic arguments, it was conjectured that an intimate relation exists between any multifractal dimensions, Dq and D q ′ , of the eigenstates of critical random matrix ensembles:Here, we verify this relation by extensive numerical calculations on critical random matrix ensembles and extend its applicability to q < 1/2 but also to deterministic models producing multifractal eigenstates and to generic multifractal structures. We also demonstrate, for the scattering version of the power-law banded random matrix model at criticality, that the scaling exponents σq of the inverse moments of Wigner delay times, τ

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“…To compute τ W we use the effective Hamiltonian approach described in Refs. [19,24]. For statistical processing a large number of disorder realizations is used.…”

Section: B Wigner Delay Timesmentioning

confidence: 99%

On the generalized dimensions of multifractal eigenstates

2014

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“…It would be interesting to further explore the connection between the PRBM ensemble and the truncated Anderson models to shed more light on the role of randomness and symmetry-breaking in driving a metal-insulator transition in 1 dimension, in a similar spirit to previous works [98,99].…”

Section: Appendix B: Link Between Trs Broken Model and Long-range Hopmentioning

confidence: 86%

Effect of Hilbert space truncation on Anderson localization

Krishna¹,

Bhatt²

2018

Phys. Rev. B

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The 1-D Anderson model possesses a completely localized spectrum of eigenstates for all values of the disorder. We consider the effect of projecting the Hamiltonian to a truncated Hilbert space, destroying time reversal symmetry. We analyze the ensuing eigenstates using different measures such as inverse participation ratio and sample-averaged moments of the position operator. In addition, we examine amplitude fluctuations in detail to detect the possibility of multifractal behavior (characteristic of mobility edges) that may arise as a result of the truncation procedure.

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“…This model has attracted much attention and has been used in several recent studies (see for example Ref. [32][33][34][35] We calculate the SPEE of the MEM and |E F by Eq. (7).…”

Section: Single-particle Entanglement Entropy Of Memmentioning

confidence: 99%

Single-particle entanglement of the entanglement Hamiltonian eigenmodes

Pouranvari

2018

Mod. Phys. Lett. A

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Single-particle entanglement entropy (SPEE) is calculated for entanglement Hamiltonian eigenmode in a one-dimensional free fermion model that undergoes a delocalized-localized phase transition. In this numerical study, we show that SPEE of entanglement Hamiltonian eigen-mode has the same behavior as EPEE of Hamiltonian eigen-mode at the Fermi level: as we go from delocalized phase toward localized phase, SPEE of both modes decreases in the same manner. Furthermore, fluctuations of SPEE of entanglement Hamiltonian eigen-mode -which can be obtained through the calculation of moments of SPEE -signature very sharply the phase transition point. These two modes are also compared by calculation of single particle Réyni entropy (SPRE). We show that SPEE and SPRE of entanglement Hamiltonian eigen-mode can be used as a phase detection parameter.

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Scattering at the Anderson transition: Power-law banded random matrix model

Cited by 22 publications

References 57 publications

On the generalized dimensions of multifractal eigenstates

On the generalized dimensions of multifractal eigenstates

Effect of Hilbert space truncation on Anderson localization

Single-particle entanglement of the entanglement Hamiltonian eigenmodes

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