One Dimensional Chain with Long Range Hopping

Abstract

The one-dimensional (1D) tight binding model with random nearest neighbor hopping is known to have a singularity of the density of states and of the localization length at the band center. We study numerically the effects of random long range (power-law) hopping with an ensemble averaged magnitude $\expectation{|t_{ij}|} \propto |i-j|^{-σ}$ in the 1D chain, while maintaining the particle-hole symmetry present in the nearest neighbor model. We find, in agreement with results of position space renormalization group techniques applied to the random XY spin chain with power-law interactions, that there is a change of behavior when the power-law exponent $\sigma$ becomes smaller than 2.

References in corpus (3)

• Multifractality and critical fluctuations at the Anderson transition
• Exact results for quantum phase transitions in random XY spin chains
• Quantum percolation in power-law diluted chains

Cited by in corpus (12)

• Interplay between long range hopping and disorder in topological systems
• Many-Body Localization Transition in Random Quantum Spin Chains with Long-Range Interactions
• Disordered Quantum Spin Chains with Long-Range Antiferromagnetic Interactions
• Perturbative instability towards delocalization at phase transitions between MBL phases
• From Disordered Quantum Walk to Physics of Off-diagonal Disorder
• Beyond universal behavior in the one-dimensional chain with random nearest neighbor hopping
• Effects of large disorder on the Hofstadter butterfly
• Beyond the universal Dyson singularity for 1-D chains with hopping disorder
• Connecting bright and dark states through accidental degeneracy caused by lack of symmetry
• Effect of Hilbert space truncation on Anderson localization
• Testing the validity of random-singlet state for long-range hopping models through the scaling of entanglement entropy
• Anderson transition of the plasma oscillations of 1D disordered Wigner lattices