A Field Theory for Fermionic Ladder with Generic Intrachain Interactions

TL;DR

This paper develops a low energy field theory for a two-chain fermionic system with arbitrary intrachain interactions, revealing different regimes and incoherent spectral features relevant to ladder and stripe phases.

Contribution

It introduces a novel effective field theory that handles generic intrachain interactions and distinguishes multiple doping regimes in fermionic ladders.

Findings

Identifies three doping regimes with distinct velocity ratios.

Derives highly incoherent electron spectral functions.

Analyzes excitation spectrum and effects of ladder array configurations.

Abstract

An effective low energy field theory is developed for a system of two chains. The main novelty of the approach is that it allows to treat generic intrachain repulsive interactions of arbitrary strength. The chains are coupled by a direct tunneling and four-fermion interactions. At low energies the individual chains are described as Luttinger liquids with an arbitrary ratio of spin $v_s$ and charge $v_c$ velocities. A judicious choice of the basis for the decoupled chains greatly simplifies the description and allows one to separate high and low energy degrees of freedom. In a direct analogy to the bulk cuprates the resulting effective field theory distinguishes between three qualitatively different regimes: (i) small doping ($v_c << v_s$), (ii) optimal doping ($v_s \approx v_c$) and (iii) large doping ($v_s << v_c$). I discuss the excitation spectrum and derive expressions for the electron spectral function which turns out to be highly incoherent. The degree of incoherence increases when one considers an array of ladders (stripe phase).