Curvature function renormalization, topological phase transitions, and multicriticality

Abstract

A recently proposed curvature renormalization group scheme for topological phase transitions defines a generic “curvature function” as a function of the parameters of the theory and shows that topological phase transitions are signaled by the divergence of this function at certain parameter values, called critical points, in analogy with usual phase transitions. A renormalization group procedure was also introduced as a way of flowing away from the critical point toward a fixed point, where an appropriately defined correlation function goes to zero and topological quantum numbers characterizing the phase are easy to compute. In this paper, using two independent models, a model in the AIII symmetry class and a model in the BDI symmetry class, in one dimension as examples, we show that there are cases where the fixed-point curve and the critical-point curve appear to intersect, which turn out to be multicritical points, and focus on understanding its implications.