Abstract
The study of symmetry-protected topological states in presence of electron correlations has recently aroused great interest as rich and exotic phenomena can emerge. Here, we report a concrete example by employing large-scale unbiased quantum Monte Carlo study of the Kane-Mele model with cluster charge interactions. The ground-state phase diagram for the model at half filling is established. Our simulation identifies the coexistence of a symmetry-protected topological order with a symmetry-breaking Kekul$\acute{e}$ valence bond order and shows that the spontaneous symmetry-breaking is accompanied by an interaction-driven topological phase transition (TPT). This TPT features appearance of zeros of single-particle Green's function and gap closing in spin channel rather than single-particle excitation spectrum, and thus has no mean-field correspondence.
Highlights
The marriage of two ingredients, symmetry and topology, has significantly promoted the developments in topological phases of matter in the past decades [1,2]
We mainly demonstrate the projector QMC (PQMC) results for λ/t = 0.05 and 0.2 cases as the only difference for the λ/t = 0.4 case is the net shift in the phase boundary
This can be taken as the indication of a first-order disordered-ordered phase transition, as the magnitude of the Kekulé valence bond solid (KVBS) order can be evaluated as mVBS =
Summary
The marriage of two ingredients, symmetry and topology, has significantly promoted the developments in topological phases of matter in the past decades [1,2]. Unlike the TPT in the noninteracting limit that is driven by closing the single-particle excitation gap, the TPT in interacting systems can involve bosonic degrees of freedom with the spin gap closing, which allows the phase transition described by the bosonic field theory [26] With these in mind, it will be of great interest to demystify whether topological symmetry protection and spontaneous symmetry breaking can coexist in a single quantum phase in fermion systems, namely, an SPT phase with symmetry breaking and long-range order. The corresponding TPT and disordered-ordered phase transition in such a system should be quite different from the conventional ones mentioned above Such exotic phases have already been studied in bosonic systems [40], termed symmetry-breaking topological insulators, while the fermionic counterpart is missing. The spin channel becomes critical while the single-particle gap remains finite across this exotic phase transition, which makes this
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