Spectral representation of Matsubara n-point functions: Exact kernel functions and applications

Abstract

In the field of quantum many-body physics, the spectral (or Lehmann) representation simplifies the calculation of Matsubara n-point correlation functions if the eigensystem of a Hamiltonian is known. It is expressed via a universal kernel function and a system- and correlator-specific product of matrix elements. Here we provide the kernel functions in full generality, for arbitrary n, arbitrary combinations of bosonic or fermionic operators and an arbitrary number of anomalous terms. As an application, we consider bosonic 3- and 4-point correlation functions for the fermionic Hubbard atom and a free spin of length S, respectively.

close to published version

References in corpus (3)

• Exact evolution equation for the effective potential
• Superperturbation solver for quantum impurity models
• Highly nonperturbative nature of the Mott metal-insulator transition: Two-particle vertex divergences in the coexistence region

Cited by in corpus (9)

• Pseudo-fermion functional renormalization group for spin models
• Phase diagram of the $J_1$-$J_2$ quantum Heisenberg model for arbitrary spin
• Analytic continuation of multipoint correlation functions
• Dipolar ordering transitions in many-body quantum optics: Analytical diagrammatic approach to equilibrium quantum spins
• Recursive algorithm for generating high-temperature expansions for spin systems and the chiral non-linear susceptibility
• Overcomplete intermediate representation of two-particle Green's functions and its relation to partial spectral functions
• High-temperature series expansion of the dynamic Matsubara spin correlator
• Computation Kernel for Feynman Diagrams
• Imaginary Time Formalism for Causal Nonlinear Response Functions