Boundary criticality in quantum spin Hall insulators with bosonic degrees of freedom

Exotic boundary physics is a hallmark of interacting topological systems. Specifically, interactions can drive symmetry-protected topological materials to undergo unique boundary phase transitions that are typically characterized as either ordinary or extraordinary, depending on the relative ordering of the bulk. In the case of (2+1)D topological insulators, field-theoretical analysis predicts a multicritical point with the special Berezinskii–Kosterlitz–Thouless transition for helical edge fermions [1]. However, this special transition has yet to be realized in a microscopic lattice model. In this work, we present a new model for studying boundary criticality in topological materials, based on the well-known Kane-Mele model for quantum spin Hall insulators. The bulk order is represented by a Z2 boson field, with dynamics governed by the quantum Ising model. Meanwhile, edge Yukawa coupling between the bosons and fermions enables the special transition. To simulate our model, we formulate a sign problem-free determinant quantum Monte Carlo calculation that also includes a computationally tractable cluster algorithm for boson updates. We then map out the phase diagram and extract the boundary critical exponents. Various characterizations of the boundary phase transition will be presented.

[1] X. Shen, Z. Wu, and S.-K. Jian, New boundary criticality in topological phases, arXiv:2407.15916.