Interactions and Green's functions

W.T.M. Caspers

Chen Ren

The Green functions and the anomalous Green functions of the systems with the unsymmetrical interactions are calculated by using the stochastic quantization. By the correct treatment, the Dyson equations including the Green functions and the anomalous Green functions are obtained.

Heinrich Saller

Elio J. König, Aditi Mitra

Motivated by recent advances in digital quantum emulation using noisy intermediate-scale quantum (NISQ) devices and an increased interest in topological Green's function zeros in condensed matter systems, we here study Green's function zeros in topological Floquet systems. We concentrate on interacting Kitaev-like Floquet chains (or equivalently transverse field Ising circuits) and introduce Floquet Green's-function-based topological invariants for the corresponding symmetry class BDI. In the vicinity of special points in the free fermion phase diagram and using tailor-made interactions which lead to the Floquet version of symmetric mass generation, we analytically calculate both edge and bulk Green's functions. Just as in the case of continuum time evolution, topological bands of Green's function zeros may also contribute to the topological invariant. However, contrary to the case of continuum time evolution, Floquet Green's functions can have zeros even in the absence of interactions. Finally, we also discuss an implementation of this Floquet system in a digital quantum emulator: We present a circuit which encodes the interaction under consideration and pinpoint the observables carrying information about the topological Green's function boundary zeros.

Norman J. M. Horing

Abstract Chapter 11 employs variational differential techniques and the Schwinger Action Principle to derive coupled-field Green’s function equations for a multi-component system, modeled as an interacting electron-hole-phonon system. The coupled Fermion Green’s function equations involve five interactions (electron-electron, hole-hole, electron-hole, electron-phonon, and hole-phonon). Starting with quantum Hamilton equations of motion for the various electron/hole creation/annihilation operators and their nonequilibrium average/expectation values, variational differentiation with respect to particle sources leads to a chain of coupled Green’s function equations involving differing species of Green’s functions. For example, the 1-electron Green’s function equation is coupled to the 2-electron Green’s function (as earlier), also to the 1-electron/1-hole Green’s function, and to the Green’s function for 1-electron propagation influenced by a nontrivial phonon field. Similar remarks apply to the 1-hole Green’s function equation, and all others. Higher order Green’s function equations are derived by further variational differentiation with respect to sources, yielding additional couplings. Chapter 11 also introduces the 1-phonon Green’s function, emphasizing the role of electron coupling in phonon propagation, leading to dynamic, nonlocal electron screening of the phonon spectrum and hybridization of the ion and electron plasmons, a Bohm-Staver phonon mode, and the Kohn anomaly. Furthermore, the single-electron Green’s function with only phonon coupling can be rewritten, as usual, coupled to the 2-electron Green’s function with an effective time-dependent electron-electron interaction potential mediated by the 1-phonon Green’s function, leading to the polaron as an electron propagating jointly with its induced lattice polarization. An alternative formulation of the coupled Green’s function equations for the electron-hole-phonon model is applied in the development of a generalized shielded potential approximation, analysing its inverse dielectric screening response function and associated hybridized collective modes. A brief discussion of the (theoretical) origin of the exciton-plasmon interaction follows.

John J. Quinn, Kyung-Soo Yi