Quantum dynamics in symmetry-breaking states of correlated electrons: Antiferromagnetic phase

Abstract

Symmetry-breaking phases in many-fermion systems are characterized by anomalous functions that represent transient processes during which some properties of free particles, such as spin or charge, are not conserved. Connecting the low-temperature symmetry-breaking phase with the high-temperature one within the Baym-Kadanoff scheme, beyond the static mean-field approximation, remains an unresolved, long-standing challenge. We identify the reason why approximations with critical dynamical fluctuations in the Schwinger-Dyson equation lead to a mismatch in the transition temperatures calculated from the high- and low-temperature phases. We propose a solution to this generic problem by excluding anomalous contributions to response functions that do not obey conservation of excitations in their interactions. We illustrate this behavior using the example of an antiferromagnetic state. We reveal that the spectral function in the antiferromagnetic phase exhibits a double-gap structure at zero temperature when the anomalous self-energy is frequency-dependent.