Correlations in topological states of matter provide a rich phenomenology, including a reduction in the topological classification of the interacting system compared to its noninteracting counterpart. This happens when two phases that are topologically distinct on the noninteracting level become adiabatically connected once interactions are included. Here, we use a numerically exact quantum Monte Carlo method to study such a topological reduction. We consider a two-dimensional charge-conserving analog of the Levin-Gu superconductor whose classification is reduced from $\mathbb{Z}$ to ${\mathbb{Z}}_4$. We may expect any symmetry-preserving interaction that leads to a symmetric gapped ground state at strong coupling, and consequently a gapped symmetric surface, to be sufficient for such reduction. Here, we provide a counterexample by considering an interaction that (i) leads to a symmetric gapped ground state at sufficient strength, and (ii) does not allow for any adiabatic path connecting the trivial phase to the topological phase with $w=4$. The latter statement is established by numerically mapping the phase diagram as a function of the interaction strength and a parameter tuning the topological invariant. Instead of the adiabatic connection, the system exhibits an extended region of spontaneous symmetry breaking separating the topological sectors. Upon the inclusion of frustration, the size of this long-range-ordered region is reduced until it gives way to a first-order phase transition. Within the investigated range of parameters, there is no adiabatic path deforming the formerly distinct free-fermion states into each other. We conclude that an interaction that trivializes the surface of a gapped topological phase is a necessary but not sufficient condition to establish an adiabatic path within the interaction-reduced classification. In other words, the class of interactions that trivializes the surface is different (likely larger) from the class of interactions that establishes an adiabatic connection in the bulk.

• Received 31 December 2019
• Accepted 6 May 2020

DOI:https://doi.org/10.1103/PhysRevResearch.2.023390

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Published by the American Physical Society