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arXiv:2602.23477

Signatures of Green's function zeros and their topology using impurity spectroscopy

Sayan Mitra, Fang Xie, Marek Kolmer, Qimiao Si A, Chandan Setty

Published Feb 26, 2026• 0 citations
arXivHTMLPDF

Abstract

Topology without quasiparticles has emerged as a key framework for understanding Mott insulators, where Green's-function zeros encode nontrivial topological structure. Yet, experimental detection of these zeros represents a challenge. Using exact diagonalization of the one-dimensional Hubbard model with an impurity and Zeeman field, supported by exact analytic results, we show that Green's-function zeros manifest as an in-gap spectral weight in the unitary scattering regime. In this limit, we map the impurity problem onto a doped Mott insulator and identify the resulting in-gap state as a "zeron" excitation which is a localized doublon (holon) for an attractive (repulsive) potential. The zeron spectral weight and its associated zero vanish above a critical Zeeman field. Our results imply that Green's function zeros have in fact already been observed in experiments, and establish impurity and magnetic-field tuning as practical tools for controlling their topology.

DOI
10.48550/arxiv.2602.23477

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Topology without quasiparticles has emerged as a key framework for understanding Mott insulators, where Green's-function zeros encode nontrivial topological structure. Yet, experimental detection of these zeros represents a challenge. Using exact diagonalization of the one-dimensional Hubbard model with an impurity and Zeeman field, supported by exact analytic results, we show that Green's-function zeros manifest as an in-gap spectral weight in the unitary scattering regime. In this limit, we map the impurity problem onto a doped Mott insulator and identify the resulting in-gap state as a "zeron" excitation which is a localized doublon (holon) for an attractive (repulsive) potential. The zeron spectral weight and its associated zero vanish above a critical Zeeman field. Our results imply that Green's function zeros have in fact already been observed in experiments, and establish impurity and magnetic-field tuning as practical tools for controlling their topology.
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.
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The local density of states near dopants or impurities has recently been probed by scanning tunneling microscopy in both the parent and very lightly doped compounds of the high-Tc{T}_{c}Tc​ cuprate superconductors. We use a slave-rotor representation of the Hubbard model to compute the local density of states on impurities in a Mott insulator. Our calculation accounts for the following key features of the experimental observation: (i) positions and amplitudes of the in-gap spectral weights of a single impurity; (ii) the spectral weight transfer from the upper Hubbard band to the lower Hubbard band; (iii) the difference between the cases of single and multiple impurities. For multiple impurities, our study explains the complete suppression of spectral weight observed at precisely the Fermi energy and links this property to zeros of the underlying bulk Green's function of the Mott insulating phase.
Many strongly correlated electron systems fall outside the conventional quasiparticle paradigm. Their low-energy fermionic excitations need not be adiabatically connected to the bare electrons or appear as poles of the physical electron single-particle Green's function. This thesis investigates to what extent an effective quasiparticle description can nevertheless survive, and which emergent degrees of freedom provide the appropriate low-energy structure. First, the interaction-driven evolution from a quantum spin Hall insulator to a Mott insulator is studied using the dynamical cluster approximation. Dispersive zeros of the single-particle Green's function emerge near the Mott transition and retain a nontrivial topological character. When symmetry breaking is allowed, a nontopological excitonic insulator is found to intrude between quantum spin Hall and Mott insulators. Encoding both poles and zeros within a low-energy quasiparticle Hamiltonian provides a continuous one-body description of the three phases. On the Mott side, its gap evolution supports interpreting the soft excitonic mode as a bound state of quasiparticle and quasihole excitations tied to the Green's function zeros, rather than to the widely separated Hubbard bands. Second, the intrinsic anomalous Hall conductivity of a topological metal is analyzed within a multiband extension of Landau Fermi-liquid theory. Residual interactions among quasiparticles at the Fermi surface dress the dynamic current vertex and generate corrections to the Berry-curvature contribution obtained from the quasiparticle bands alone. Our result supports recent claims that the correct expressions for topological observables include vertex corrections besides the topological invariants built just upon the Green's function. It also demonstrates that such corrections are naturally accounted for by Landau Fermi-liquid theory. Extracting the relevant ingredients for an effective description of material-relevant correlated systems requires computational tools that remain reliable at low temperatures. To this end, a deterministic strong-coupling impurity solver for dynamical mean-field theory is discussed. By providing static, dynamical, and thermodynamic observables without stochastic sampling, it offers a promising route toward multiorbital and spin-orbit coupled problems where conventional Monte Carlo methods currently struggle. Finally, the auxiliary quasiparticle framework underlying the ghost-Gutzwiller Ansatz is investigated. On a model for correlated quantum spin Hall insulators, we show that the topology of the interacting state is encoded in the auxiliary one-body Hamiltonian. The resulting band-structure reveals topological Hubbard bands whose topological character can be tuned through a finite magnetization. When applied to the single-band t-J model, the same framework yields a fractionalized Fermi liquid (FL*). In this phase, dispersive neutral spinons, with vanishing physical-electron spectral weight, coexist with conventional quasiparticles forming a small hole-like Fermi surface, thus violating Luttinger's theorem. The corresponding temperature--doping phase diagram contains a low-doping FL*, a d-wave superconducting dome, and an overdoped conventional Fermi liquid, thereby reproducing key qualitative features of cuprate phenomenology.
Quantum tunneling experiments have provided deep insights into basic excitations occurring as Green's function poles in the realm of complex quantum matter. However, strongly correlated quantum materials also allow for Green's functions zeros (GFZs) that may be seen as an antidote to the familiar poles and have so far largely eluded direct experimental study. Here, we propose and investigate theoretically how cotunneling through Mott insulators enables direct access to the shadow band structure of GFZs. In particular, we derive an effective Hamiltonian for the GFZ that is shown to govern the cotunneling amplitude and reveal fingerprints of many-body correlations clearly distinguishing the GFZ structure from the underlying free Bloch band structure of the system. Our perturbative analytical results are corroborated by numerical data in the framework of both exact diagonalization and matrix product state simulations for a one-dimensional model system consisting of a Su-Schrieffer-Heeger-Hubbard model coupled to two single-level quantum dots.
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.