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arXiv:2312.13226 · Physical Review Letters

Edge Zeros and Boundary Spinons in Topological Mott Insulators

Niklas Wagner, Daniele Guerci, Andrew J. Millis, Giorgio Sangiovanni

Published Sep 19, 2024• 18 citations
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Abstract

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.

DOI
10.1103/physrevlett.133.126504

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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.
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.
The topological classification of electronic band structures is based on symmetry properties of Bloch eigenstates of single-particle Hamiltonians. In parallel, topological field theory has opened the doors to the formulation and characterization of non-trivial phases of matter driven by strong electron-electron interaction. Even though important examples of topological Mott insulators have been constructed, the relevance of the underlying non-interacting band topology to the physics of the Mott phase has remained unexplored. Here, we show that the momentum structure of the Green's function zeros defining the "Luttinger surface" provides a topological characterization of the Mott phase related, in the simplest description, to the one of the single-particle electronic dispersion. Considerations on the zeros lead to the prediction of new phenomena: a topological Mott insulator with an inverted gap for the bulk zeros must possess gapless zeros at the boundary, which behave as a form of "topological antimatter" annihilating conventional edge states. Placing band and Mott topological insulators in contact produces distinctive observable signatures at the interface, revealing the otherwise spectroscopically elusive Green's function zeros.
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 study the evolution of metals from Mott insulators in the carrier-doped 2D Hubbard model using a cluster extension of the dynamical mean-field theory. While the conventional metal is simply characterized by the Fermi surface (pole of the Green function G), interference of the zero surfaces of G with the pole surfaces becomes crucial in the doped Mott insulators. Mutually interfering pole and zero surfaces are dramatically transferred over the Mott gap, when lightly doped holes synergetically loosen the doublon-holon binding. The heart of the Mott physics such as the pseudogap, hole pockets, Fermi arcs, in-gap states, Lifshitz transitions, and non-Fermi liquids appears as natural consequences of this global interference in the frequency space.
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.
Topological insulators present a bulk gap, but allow for dissipationless spin transport along the edges. These exotic states are characterized by the Z2 topological invariant and are protected by time-reversal symmetry. The Kane–Mele model is one model to realize this topological class in two dimensions, also called the quantum spin Hall state. In this brief review article, we provide a pedagogical introduction to the influence of correlation effects in the quantum spin Hall states, with special focus on the half-filled Kane–Mele–Hubbard model, solved by means of unbiased determinant quantum Monte Carlo (QMC) simulations. We explain the idea of identifying the topological insulator via π-flux insertion, the Z2 invariant and the associated behavior of the zero-frequency Green's function, as well as the spin Chern number in parameter-driven topological phase transitions. The examples considered are two descendants of the Kane–Mele–Hubbard model, the generalized and dimerized Kane–Mele–Hubbard model. From the Z2 index, spin Chern numbers and the Green's function behavior, one can observe that correlation effects induce shifts of the topological phase boundaries. Although the implementation of these topological quantities has been successfully employed in QMC simulations to describe the topological phase transition, we also point out their limitations as well as suggest possible future directions in using numerical methods to characterize topological properties of strongly correlated condensed matter systems.