Journal
ANNALS OF PHYSICS
Volume 356, Issue -, Pages 383-416Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.aop.2015.02.031
Keywords
Topological insulators; K-theory; Phase transitions; Algorithms
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Funding
- Simons Foundation [208723]
- Erwin Schrodinger International Institute for Mathematical Physics
- Fields Institute for Research in Mathematical Sciences
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We derive formulas and algorithms for Kitaev's invariants in the periodic table for topological insulators and superconductors for finite disordered systems on lattices with boundaries. We find that K-theory arises as an obstruction to perturbing approximately compatible observables into compatible observables. We derive formulas in all symmetry classes up to dimension two, and in one symmetry class in dimension three, that can be computed with sparse matrix algorithms. We present algorithms in two symmetry classes in 2D and one in 3D and provide illustrative studies regarding how these algorithms can detect the scaling properties of phase transitions. (C) 2015 Elsevier Inc. All rights reserved.
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