Ginzberg-Landau-Wilson theory for Flat band, Fermi-arc and surface states of strongly correlated systems

TL;DR

This paper develops a holographic Ginzburg-Landau framework to analyze strongly correlated systems near quantum criticality, revealing spectral features like gaps, flat bands, and Fermi-arcs linked to zero modes and symmetries.

Contribution

It introduces a holographic approach modeling strongly interacting systems with order parameters, classifying spectral features and exploring 'order without symmetry breaking' phenomena.

Findings

Spectral features such as gaps, pseudo-gaps, flat bands, and Fermi-arcs are identified.

Zero modes linked to discrete symmetries influence the system's Fermi-liquid or flat band behavior.

Some bulk order parameters lack boundary symmetry-breaking interpretations.

Abstract

We consider a holographic theory as a Ginzberg-Landau theory working for strongly interacting system near the quantum critical point: we take the bulk matter field $\Phi^I(r,x)$, the dual of the fermion bilinear, as the order parameter. We calculate and classify the fermion spectral functions in the presence of such orders. Depending on the symmetry, we found spectral features like the gap, pseudo-gap, flat disk bands and the Fermi-arc connecting the two Dirac cones, which are familiar in Dirac material and Kondo lattice. Many of above features are associated with the zero modes whose presence is tied with a discrete symmetry of the interaction. The interaction induced zero modes either makes the strongly correlated system fermi-liquid like, or creates a disk-like flat band. Some of the order parameters in the bulk theory do not have an interpretation of symmetry breaking in terms of the boundary space, which opens the possibility of 'an order without symmetry breaking'.