Emergent quasiparticles at Luttinger surfaces

Fermi and Luttinger Arcs: Two Concepts, Realized on One Surface

We present an analytically solvable model for correlated electrons, which is able to capture the major Fermi surface modifications occurring in both hole- and electron-doped cuprates as a function of doping. The proposed Hamiltonian qualitatively reproduces the results of numerically demanding many-body calculations, here obtained using the dynamical vertex approximation. Our analytical theory provides a transparent description of a precise mechanism, capable of driving the formation of disconnected segments along the Fermi surface (the highly debated "Fermi arcs"), as well as the opening of a pseudogap in hole and electron doping. This occurs through a specific mechanism: The electronic states on the Fermi arcs remain intact, while the Fermi surface part where the gap opens transforms into a Luttinger arc.

Topological Green's Function Zeros in an Exactly Solved Model and Beyond

The interplay of topological electronic band structures and strong interparticle interactions provides a promising path towards the constructive design of robust, long-range entangled many-body systems. As a prototype for such systems, we here study an exactly integrable, local model for a fractionalized topological insulator. Using a controlled perturbation theory about this limit, we demonstrate the existence of topological bands of zeros in the exact fermionic Green's function and show that in this model they do affect the topological invariant of the system, but not the quantized transport response. Close to (but prior to) the Higgs transition signaling the breakdown of fractionalization, the topological bands of zeros acquire a finite "lifetime." We also discuss the appearance of edge states and edge zeros at real space domain walls separating different phases of the system. This model provides a fertile ground for controlled studies of the phenomenology of Green's function zeros and the underlying exactly solvable lattice gauge theory illustrates the synergetic cross pollination between solid-state theory, high-energy physics, and quantum information science.

Edge Zeros and Boundary Spinons in Topological Mott Insulators

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.

Connecting the Many-Body Chern Number to Luttinger's Theorem through Středa's Formula

Relating the quantized Hall response of correlated insulators to many-body topological invariants is a key challenge in topological quantum matter. Here, we use Středa's formula to derive an expression for the many-body Chern number in terms of the single-particle interacting Green's function and its derivative with respect to a magnetic field. In this approach, we find that this many-body topological invariant can be decomposed in terms of two contributions, N_{3}[G]+ΔN_{3}[G], where N_{3}[G] is known as the Ishikawa-Matsuyama invariant and where the second term involves derivatives of Green's function and the self-energy with respect to the magnetic perturbation. As a by-product, the invariant N_{3}[G] is shown to stem from the derivative of Luttinger's theorem with respect to the probe magnetic field. These results reveal under which conditions the quantized Hall conductivity of correlated topological insulators is solely dictated by the invariant N_{3}[G], providing new insight on the origin of fractionalization in strongly correlated topological phases.

Mott insulators with boundary zeros

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.

Spin-Liquid Insulators Can Be Landau's Fermi Liquids

The long search for insulating materials that possess low-energy quasiparticles carrying electron's quantum numbers except charge-inspired by the neutral spin-1/2 excitations, the so-called spinons, exhibited by Anderson's resonating-valence-bond state-seems to have reached a turning point after the discovery of several Mott insulators displaying the same thermal and magnetic properties as metals, including quantum oscillations in a magnetic field. Here, we show that such anomalous behavior is not inconsistent with Landau's Fermi liquid theory of quasiparticles at a Luttinger surface. That is the manifold of zeros within the Brillouin zone of the single-particle Green's function at zero frequency, and which thus defines the spinon Fermi surface conjectured by Anderson.