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arXiv:2105.09568 · Scientific Reports

Higher-order topological Mott insulator on the pyrochlore lattice

Yuichi Otsuka, Tsuneya Yoshida, Koji Kudo, Seiji Yunoki, Yasuhiro Hatsugai

Published Oct 12, 2021• 17 citations
arXivHTMLPDF

Abstract

We provide the first unbiased evidence for a higher-order topological Mott insulator in three dimensions by numerically exact quantum Monte Carlo simulations. This insulating phase is adiabatically connected to a third-order topological insulator in the noninteracting limit, which features gapless modes around the corners of the pyrochlore lattice and is characterized by a [Formula: see text] spin-Berry phase. The difference between the correlated and non-correlated topological phases is that in the former phase the gapless corner modes emerge only in spin excitations being Mott-like. We also show that the topological phase transition from the third-order topological Mott insulator to the usual Mott insulator occurs when the bulk spin gap solely closes.

DOI
10.1038/s41598-021-99213-z

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We provide the first unbiased evidence for a higher-order topological Mott insulator in three dimensions by numerically exact quantum Monte Carlo simulations. This insulating phase is adiabatically connected to a third-order topological insulator in the noninteracting limit, which features gapless modes around the corners of the pyrochlore lattice and is characterized by a [Formula: see text] spin-Berry phase. The difference between the correlated and non-correlated topological phases is that in the former phase the gapless corner modes emerge only in spin excitations being Mott-like. We also show that the topological phase transition from the third-order topological Mott insulator to the usual Mott insulator occurs when the bulk spin gap solely closes.
We propose a new correlated topological state, which we call a higher-order topological Mott insulator (HOTMI). This state exhibits a striking bulk-boundary correspondence due to electron correlations. Namely, the topological properties in the bulk, characterized by the Z_{3} spin-Berry phase, result in gapless corner modes emerging only in spin excitations (i.e., the single-particle excitations remain gapped around the corner). We demonstrate the emergence of the HOTMI in a Hubbard model on the kagome lattice, and elucidate how strong correlations change gapless corner modes at the noninteracting case.
We investigate properties of a topological Mott insulator in one dimension by examining the bulk topological invariant and the entanglement spectrum of a correlated electron model. We clarify how gapless edge states in a noninteracting topological band insulator evolve into spinon edge states in a topological Mott insulator. Furthermore, we propose a topological Mott transition, which is a new type of topological phase transition which has never been observed in free fermion systems. This unconventional transition occurs in spin liquid phases in the Mott insulator and is accompanied by zeros of the single-electron Green's function and a gap closing in the spin excitation spectrum.
We study the higher-order topological spin phases based on a spin analogue of Benalcazar-Bernevig-Hughes model in two dimensions using large-scale quantum Monte Carlo simulations. A continuous Néel-valence bond solid quantum phase transition is revealed by tuning the ratio between dimerized spin couplings, namely, the weak and strong exchange couplings. Through the finite-size scaling analysis, we identify the phase critical points, and consequently, map out the full phase diagrams in related parameter spaces. Particularly, we find that the valence bond solid phase can be a higher-order topological spin phase, which has a gap for spin excitations in the bulk while demonstrates characteristic gapless spin modes at corners of open lattices. We further discuss the connection between the higher-order topological spin phases and the electronic correlated higher-order phases, and find both of them possess gapless spin corner modes that are protected by higher-order topology. Our result exemplifies higher-order physics in the correlated spin systems and will contribute to further understandings of the many-body higher-order topological phenomena.
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We investigate the ground-state phase diagram of a modified spinless Haldane-Hubbard model, with broken threefold rotational symmetry, employing exact diagonalization calculations. The interplay of asymmetry, interactions, and topology gives rise to a rich phase diagram. The noninteracting limit of the Hamiltonian exhibits a higher-order topological insulator characterized by the existence of corner modes, in contrast to known chiral edge metallic states of the standard Haldane model. Our investigation demonstrates that these symmetry-protected states are robust to the presence of finite interactions. Furthermore, in certain regimes of parameters, we show that a topological Mott insulator exists in this model, where a nontrivial topological bulk coexists with an interaction-driven charge-density wave, whose emergence is characterized by a Z2{Z}_{2}Z2​-symmetry breaking within the 3d-Ising3d\text{-Ising}3d-Ising universality class.
Topological phase transitions and the phase diagram of Haldane-Hubbard model are investigated using the variational cluster approach. With increasing the interaction strength, there are two successive topological phase transitions. The first is characterized by the closing and reopening of the single particle gap with the Chern number changing its sign, while the second is featured by the divergence of the topological Hamiltonian's spectrum with the Chern number changing from a non-zero integer to zero. The second topological phase transition is not accompanied with the single particle gap closing but is associated with the zeros of the single particle Green's function. Between these two topological phase transitions, there exists a non-magnetic topological Mott insulating phase with no gapless single particle edge states which cannot be adiabatically connected to any non-interacting Chern insulator.