Localization renormalization and quantum Hall systems

Andrews, Bartholomew; Reiss, Dominic; Harper, Fenner; Roy, Rahul

doi:10.1103/physrevb.109.125132

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2024

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“…The most well-known of these is the appearance of a quantised Hall conductance as in Haldane's original model for a Hall effect without Landau levels [3]. The obstruction to constructing localised degrees of freedom in nontrivial insulators has recently been exploited [4] to use the scaling properties of the localisation length to diagnose a topologically nontrivial phase.…”

Section: Introductionmentioning

confidence: 99%

Gapless edge-modes and topology in the Qi-Wu-Zhang model: a real-space analysis

Dasgupta,

Dasgupta

2024

Phys. Scr.

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The topological phase transition in the Qi-Wu-Zhang model is studied using a real-space approach. An effective Hamiltonian for the topologically protected edge-modes in a finite-size system is developed. The topological phase transition is understood in terms of a global perturbation to the system which lifts the degeneracy of the edge-modes. The effective Hamiltonian method is also applied to a one-dimensional system with spatially varying hopping strengths to understand the impact of disorder on the edge-modes.

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Section: Introductionmentioning

confidence: 99%