Breakdown of Fermi liquid behavior near the hot spots in a two-dimensional model: A two-loop renormalization group analysis

TL;DR

This study uses a two-loop renormalization group analysis to investigate the breakdown of Fermi liquid behavior near hot spots in a 2D model, revealing vanishing quasiparticle weight and suppressed susceptibilities.

Contribution

It provides a detailed two-loop RG analysis of a 2D hot spot model, showing non-divergent order parameters but vanishing quasiparticle weight, indicating non-Fermi liquid behavior.

Findings

Quasiparticle weight vanishes at low energy

Spin and charge susceptibilities are suppressed

Order-parameter susceptibilities do not diverge

Abstract

Motivated by a recent experimental observation of a nodal liquid on both single crystals and thin films of Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ by Chatterjee \emph{et al.} [Nature Physics \textbf{6}, 99 (2010)], we perform a field-theoretical renormalization group (RG) analysis of a two-dimensional model consisting of eight points located near the "hot spots" on the Fermi surface which are directly connected by spin density wave ordering wave vector. We derive RG equations up to two-loop order describing the flow of renormalized couplings, quasiparticle weight, several order-parameter response functions, and uniform spin and charge susceptibilities of the model. We find that while the order-parameter susceptibilities investigated here become non-divergent at two loops, the quasiparticle weight vanishes in the low-energy limit, indicating a breakdown of Fermi liquid behavior at this RG level. Moreover, both uniform spin and charge susceptibilities become suppressed in the scaling limit which indicate gap openings in both spin and charge excitation spectra of the model.