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arXiv:2301.13870 · Physical Review Research

Symmetry constraints and spectral crossing in a Mott insulator with Green's function zeros

Chandan Setty, Shouvik Sur, Lei Chen, Fang Xie, Haoyu Hu, Silke Buehler Paschen, Jennifer Cano, Qimiao Si A

Published Jul 26, 2024• 23 citations
arXivHTMLPDF

Abstract

Lattice symmetries are central to the characterization of electronic topology. Recently, it was shown that Green's function eigenvectors form a representation of the space group. This formulation has allowed the identification of gapless topological states even when quasiparticles are absent. Here we demonstrate the profundity of the framework in the extreme case, when interactions lead to a Mott insulator, through a solvable model with long-range interactions. We find that both Mott poles and zeros are subject to the symmetry constraints, and relate the symmetry-enforced spectral crossings to degeneracies of the original noninteracting eigenstates. Our results lead to new understandings of topological quantum materials and highlight the utility of interacting Green's functions toward their symmetry-based design. Published by the American Physical Society 2024

DOI
10.1103/physrevresearch.6.l032018

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There is extensive current interest in electronic topology in correlated settings. In strongly correlated systems, contours of Green's function zeros may develop in frequency-momentum space, and their role in correlated topology has increasingly been recognized. However, whether and how the zeros contribute to electronic properties is a matter of uncertainty. Here we address the issue in an exactly solvable model for a Mott insulator. We show that the Green's function zeros contribute to several physically measurable correlation functions in a way that does not run into inconsistencies. In particular, the physical properties remain robust to chemical potential variations up to the Mott gap, as it should be based on general considerations. Our work sets the stage for further understandings of the rich interplay among topology, symmetry, and strong correlations. Published by the American Physical Society 2024
Topology is routinely used to understand the physics of electronic insulators. However, for strongly interacting electronic matter, such as Mott insulators, a comprehensive topological characterization is still lacking. When their ground state only contains short-range entanglement and does not break symmetries spontaneously, they generically realize crystalline fermionic symmetry-protected topological phases (cFSPTs), supporting gapless modes at the boundaries or at the lattice defects. Here, we provide an exhaustive classification of cFSPTs in two dimensions with U ( 1 ) charge-conservation and spinful time-reversal symmetries, namely, those generically present in spin-orbit coupled insulators, for any of the 17 wallpaper groups. It has been shown that the classification of cFSPTs can be understood from appropriate real-space decorations of lower-dimensional subspaces, and we expose how these relate to the Wyckoff positions of the lattice. We find that all nontrivial one-dimensional decorations require electronic interactions. Furthermore, we provide model Hamiltonians for various decorations, and discuss the signatures of cFSPTs. This classification paves the way to further explore topological interacting insulators, providing the backbone information in generic model systems and ultimately in experiments. Published by the American Physical Society 2024
We investigate the emergence of topological features in the charge excitations of Mott insulators in the Chern-Hubbard model. In the strong correlation regime, treating electrons as the sum of holons and doublons excitations, we compute the topological phase diagram of Mott insulators at half-filling using composite operator formalism. The Green function zeros manifest as the tightly bound pairs of such elementary excitations of the Mott insulators. Our analysis examines the winding number associated with the occupied Hubbard bands and the band of Green's function zeros. We show that both the poles and zeros show gapless states and zeros, respectively, in line with bulk-boundary correspondence. The gapless edge states emerge in a junction geometry connecting a topological Mott band insulator and a topological Mott zeros phase. These include an edge electronic state that carries a charge and a charge-neutral gapless zero mode. Our study is relevant to several twisted materials with flat bands where interactions play a dominant role.
We use a real-space slave-rotor theory of the physics of topological Mott insulators, using the Kane-Mele-Hubbard model as an example, and show that a topological gap in the Green function zeros corresponds to a gap in the bulk spinon spectrum and implies a gapless band of edge zeros and a spinon edge mode. We then consider an interface between a topological Mott insulator and a conventional topological insulator showing how the spinon edge mode of the topological Mott insulator combines with the spin part of the conventional electron topological edge state, leaving a non-Fermi liquid edge mode described by a gapless propagating holon and gapped spinon state. Our work demonstrates the physical meaning of Green function zeros and shows that interfaces between conventional and Mott topological insulators are a rich source of new physics.
Green's function zeros, which can emerge only if correlation is strong, have been for long overlooked and believed to be devoid of any physical meaning, unlike Green's function poles. Here, we prove that Green's function zeros instead contribute on the same footing as poles to determine the topological character of an insulator. The key to the proof, worked out explicitly in two dimensions but easily extendable in three dimensions, is to express the topological invariant in terms of a quasiparticlethermal Green's function matrix ${G}_{*}(i\ensuremath{\epsilon},\mathbf{k})=1/[i\ensuremath{\epsilon}\ensuremath{-}{H}_{*}(\ensuremath{\epsilon},\mathbf{k})]$, with Hermitian ${H}_{*}(\ensuremath{\epsilon},\mathbf{k})$, by filtering out the positive-definite quasiparticle residue. In that way, the topological invariant is easily found to reduce to the Thouless, Kohmoto, Nightingale, and den Nijs formula for quasiparticles described by the noninteracting Hamiltonian H∗(0,k){H}_{*}(0,\mathbf{k})H∗​(0,k). Since the poles of the quasiparticle Green's function ${G}_{*}(\ensuremath{\epsilon},\mathbf{k})$ on the real frequency axis correspond to poles and zeros of the physical-particle Green's function $G(\ensuremath{\epsilon},\mathbf{k})$, both of them equally determine the topological character of an insulator.