Interacting surface topological matter: conformal manifolds and entanglement entropy

Synopsis

Symmetry-protected topological (SPT) phases host gapless surface states that are stable against weak symmetry-preserving interactions, while sufficiently strong interactions can drive symmetry-breaking ordered phases. The phase boundary separating these regimes can host exotic conformal field theory states that are not typically encountered in conventional quantum phase transitions. We refer to such critical points as surface topological quantum critical points (sTQCPs).

In this talk, I discuss attractive interaction-driven quantum criticality on the surface of three-dimensional topological insulators hosting multiple Dirac cones. In the multidimensional interaction parameter space, the phase boundary separating the gapless and ordered phases forms a continuous manifold. In the limit of suppressed quantum fluctuations, the universality of this phase boundary is governed by conformal manifolds, continuous families of interacting conformal field theories characterized by exactly marginal operators.

Higher-order quantum fluctuations, however, break these conformal manifolds into isolated fixed points with varying infrared stability. Remarkably, we find that along the RG flow within the manifold, an EPR-like entanglement entropy in fermion flavor space always increases. Infrared-stable conformal field theories correspond to maximally entangled interaction operators, whereas weakly entangled fixed points are unstable. These results highlight the role of entangled conformal operators and their entropy in shaping the universality classes of surface topological quantum critical points.