Andreas Feuerpfeil
Condensed matter physics and NISQ
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Field-theoretic analysis has predicted that the edge of a double quantum spin Hall insulator (DQSHI) can undergo an interaction-driven transition from a phase with fermionic edge modes into one with only bosonic modes. All single-fermion edge excitations are gapped in this bosonic edge phase, but fermion pairs remain gapless, leading to distinct experimental signatures. We numerically simulate the interacting DQSHI edge and verify the existence of the bosonic edge phase. This calculation requires an explicit bulk embedding of the DQSHI edge, due to its mixed anomaly between charge and Sz conservation. We hence employ segment DMRG on an infinite two-dimensional cylinder, where the DQSHI bulk is modeled in terms of two copies of the spin-up lowest Landau level, combined with their time-reversed counterparts. We find that interactions can open a single-fermion gap at the DQSHI edge while fermion pairs remain gapless, matching the predictions for the bosonic edge phase. We find the scaling of the single-fermion gap with interaction strength to be consistent with field-theoretic calculations, and discuss the relevance of the bosonic edge phase to twisted homobilayers of WSe2 and MoTe2. We elaborate on the methodological extension of the segment geometry used here to other topological phases with edge anomalies.
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We compare two time-reversal-symmetric triangular-lattice Hubbard models at half filling: the zero-flux model and a staggered π-flux model with zero and π flux through oppositely oriented triangles. Although both reduce to the same Heisenberg model at leading order in the strong-coupling limit, their distinct charge fluctuation profiles yield different quantum paramagnetic regimes. Combining a strong-coupling expansion with infinite density matrix renormalization group (iDMRG) calculations, we find that the positive ring-exchange of the zero-flux model promotes spontaneous chirality, consistent with its notion of a chiral spin liquid at intermediate coupling. In the staggered-π-flux model, whose noninteracting limit is a Dirac semimetal, the ring exchange changes sign and disfavors chiral order and we find no resolvable scalar chirality. This renders flux-tuned ring-exchange an efficient discriminator between chiral and non-chiral quantum paramagnets at finite coupling.
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