Quantum Criticality of Quasi-One-Dimensional Topological Anderson Insulators

Abstract

We present an analytic theory of quantum criticality in the quasi one-dimensional topological Anderson insulators of class AIII and BDI. We describe the systems in terms of two parameters (g, χ) representing localization and topological properties, respectively. Surfaces of half-integer valued χ define phase boundaries between distinct topological sectors. Upon increasing system size, the two parameters exhibit flow similar to the celebrated two parameter flow describing the class A quantum Hall insulator. However, unlike the quantum Hall system, an exact analytical description of the entire phase diagram can be given. We check the quantitative validity of our theory by comparison to numerical transfer matrix computations.

Planck’s Quantum-Driven Integer Quantum Hall Effect in Chaos

“…In addition, are there any relations between the present rotor insulator and the Floquet topological insulator found in driven but non-chaotic systems [46]? Finally, the rotor insulator, lack of translation symmetry, resembles the topological Anderson insulator in disordered systems [47]. Our findings may bring a new angle to this currently active subject.…”

Exact zero modes in twisted Kitaev chains

“…The existence of Majorana zero modes is of special interest because it can be applied to the physical construction of qubits for topological quantum computing [13][14][15] . From an experimental point of view, it is essential to investigate the effects of disorder [16][17][18][19][20] and interactions [21][22][23][24][25][26][27][28][29][30][31][32] . Furthermore, various theoretical aspects have been revealed, including the connection with supersymmetry 30,31,[33][34][35] , the generalization to parafermion modes [36][37][38][39][40][41][42][43] , and the construction of topologically invariant defects 44 .…”

Topological order in the Kitaev/Majorana chain in the presence of disorder and interactions

“…Two of the most relevant experimental influences are disorder [10][11][12][13][14][15][16][17] and interactions [11,16,[18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33]. Concerning the effects of disorder, it has been observed that moderate disorder supports the topological phase by pinning down quasiparticles associated with the phase transition, which has been investigated in particular for the two-dimensional toric code [34][35][36].…”

“…Specifically, we consider a onedimensional chain of spinless fermions in the presence of pwave superconducting pairing, nearest-neighbor interactions, and a disordered chemical potential. While the special cases of the interacting model without disorder [20,23,24,30] as well as the noninteracting, disordered [12,13,15] model have been studied previously and can be investigated using analytical methods, the combined effect of interactions and disorder is not amenable to analytic methods. Thus we employ the density-matrix renormalization-group (DMRG) method [37] to calculate several observables from which we determine the phase boundary between the topological and trivial phases.…”