Curvature function renormalisation, 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 signalled by the divergence of this function at certain parameters 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 towards a fixed point, where an appropriately defined correlation function goes to zero and topological quantum numbers characterising 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 multi-critical points, and focus on understanding its implications.

arXiv comment11 pages, 7 figures, published version

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Cited by in corpus (9)

• Multi-critical topological transition at quantum criticality
• Unification of topological invariants in Dirac models
• Signatures of topological phase transition on a quantum critical line
• Quench dynamics and scaling laws in topological nodal loop semimetals
• A supervised learning algorithm for interacting topological insulators based on local curvature
• Topological phase transition between non-high symmetry critical phases and curvature function renormalization group
• Quantum critical points, lines and surfaces
• Quantum critical fans from critical lines at zero temperature
• Scaling of Quantum Geometry Near the Non-Hermitian Topological Phase Transitions