Strong-disorder renormalization-group study of the one-dimensional tight-binding model

Abstract

We formulate a strong-disorder renormalization-group (SDRG) approach to study the beta function of the tight-binding model in one dimension with both diagonal and off-diagonal disorder for states at the band center. We show that the SDRG method, when used to compute transport properties, yields exact results since it is identical to the transfer matrix method. The beta function is shown to be universal when only off-diagonal disorder is present even though single-parameter scaling is known to be violated. A different single-parameter scaling theory is formulated for this particular (particle-hole symmetric) case. Upon breaking particle-hole symmetry (by adding diagonal disorder), the beta function is shown to crossover from the universal behavior of the particle-hole symmetric case to the conventional non-universal one in agreement with the two-parameter scaling theory. We finally draw an analogy with the random transverse-field Ising chain in the paramagnetic phase. The particle-hole symmetric case corresponds to the critical point of the quantum Ising model while the generic case corresponds to the Griffiths paramagnetic phase.

includes 12 pages, 4 figures

References in corpus (5)

• Band-center anomaly of the conductance distribution in one-dimensional Anderson localization
• Correlation amplitude and entanglement entropy in random spin chains
• Scaling and the center of band anomaly in a one-dimensional Anderson model with diagonal disorder
• Strong disorder renormalization group on fractal lattices: Heisenberg models and magnetoresistive effects in tight binding models
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Cited by in corpus (4)

• Critical properties of the Anderson localization transition and the high dimensional limit
• Critical Properties of the Superfluid - Bose Glass Transition in Two Dimensions
• The correlation functions of certain random antiferromagnetic spin-1/2 critical chains
• Beyond the universal Dyson singularity for 1-D chains with hopping disorder