Instanton sector of correlated electron systems as the origin of populated pseudo-gap and flat "band" behavior: analytic solution

TL;DR

This paper analytically solves finite temperature instantons in a quasi-1D Hubbard model, revealing their role in pseudo-gap formation, flat-band behavior, and symmetry breaking, with implications for high-Tc cuprate experiments.

Contribution

It provides an analytical solution for instantons in correlated electron systems, linking instanton dynamics to pseudo-gap and flat-band phenomena in high-Tc cuprates.

Findings

Instantons induce dynamic symmetry breaking between SC and SDW states.

Spectral properties show pseudo-gap with finite density of states at the center.

Inverse temperature scaling of pseudo-gap matches experimental data.

Abstract

Finite temperature instantons between meta-stable vacua of correlated electronic system are solved analytically for quasi one-dimensional Hubbard model. The instantons produce dynamic symmetry breaking and connect metallic state with the dual vacua: superconducting (SC) and spin-density wave (SDW) states. The instantons spread along the Matsubara's imaginary time and possess the structure similar to the coordinate-space solitonic lattices previously discovered in quasi one-dimensional Peierls model. On the microscopic level the inter-vacua excursion is described by mutual transformations between the "resonating quartets" of the couples of electron-hole and Cooper pairs. Spectral properties of the electrons in the "instantonic crystal" reveal pseudo-gap (PG) behavior, with finite fermionic density of states in the center of the PG and ``flat-band'' outside of it. Analytically derived inverse temperature scaling of the pseudo-gap and the densities of the SC and SDW condensates is discussed in the context of ARPES and STM data in high-Tc cuprates.