Topological Phases and Phase Transitions in Clean and Disordered Systems

Roderich Moessner, Joel E. Moore

Jan Borchmann, Aaron Farrell, T. Pereg-Barnea

In this paper we study the phase diagram of a disordered, spin-orbit coupled superconductor with $s$-wave or $d+id$-wave pairing symmetry in symmetry class $D$. We analyze the topological phase transitions by applying three different methods which include a disorder averaged entanglement entropy, a disorder averaged real-space Chern number, and an evaluation of the momentum space Chern number in a disorder averaged effective model. We find evidence for a disorder-induced topological state. While in the clean limit there is a single phase transition from a trivial phase with a Chern number $C=4$ to a topological phase with $C=1$, in the disordered system there is an intermediate phase with $C=3$. The phase transition from the trivial $C=4$ phase into the intermediate phase with $C=3$ is seen in the real-space calculation of the Chern number. In spite of this, this phase transition is not detectable in the entanglement entropy. A second phase transition from the disorder induced $C=3$ into the $C=1$ phase is seen in all three quantities.

Saikat Mondal, Adhip Agarwala

In clean and weakly disordered systems, topological and trivial phases having a finite bulk energy gap can transit to each other via a quantum critical point. In presence of strong disorder, both the nature of the phases and the associated criticality can fundamentally change. Here we investigate topological properties of a strongly disordered fermionic chain where the bond couplings are drawn from normal probability distributions which are defined by characteristic standard deviations. Using numerical strong disorder renormalization group methods along with analytical techniques, we show that the competition between fluctuation scales renders both the trivial and topological phases gapless with Griffiths like rare regions. Moreover, the transition between these phases is solely governed by the fluctuation scales, rather than the means, rendering the critical behavior to be determined by an infinite randomness fixed point with an irrational central charge. Our work points to a host of novel topological phases and atypical topological phase transitions which can be realized in systems under strong disorder.

Emmanuel V. C. Lopes

Henry Ling, Philip Richard, Saeed Rahmanian Koshkaki +4 more

We study a periodically driven one-dimensional Kitaev model in the presence of disorder. In the clean limit our model exhibits four topological phases corresponding to the existence or nonexistence of edge modes at zero and $\ensuremath{\pi}$ quasienergy. When potential disorder is added, the system parameters get renormalized and the system may exhibit a topological phase transition. When starting from the Majorana $\ensuremath{\pi}$ mode (MPM) phase, which hosts only edge Majoranas with quasienergy $\ensuremath{\pi}$, disorder induces a transition into a neighboring phase with both $\ensuremath{\pi}$ and zero modes on the edges. We characterize the disordered system using (i) exact diagonalization, (ii) Arnoldi mapping onto an effective tight-binding chain, and (iii) topological entanglement entropy.

M. A. Contínentino