Non-Landau Quantum Phase Transitions and nearly-Marginal non-Fermi Liquid

TL;DR

This paper constructs a nearly-marginal non-Fermi liquid state by coupling electrons to unconventional quantum critical points with large anomalous dimensions, revealing new non-Landau quantum phases.

Contribution

It introduces a controlled method to realize non-Fermi liquids based on unconventional QCPs with large anomalous dimensions, extending beyond Landau's paradigm.

Findings

A state with fermion self-energy scaling as |ω|^α with α close to 1 is demonstrated.

Unconventional QCPs with anomalous dimension η near 1 are identified as key to this mechanism.

The approach provides a framework for exploring non-Landau quantum criticality.

Abstract

Non-fermi liquid and unconventional quantum critical points (QCP) with strong fractionalization are two exceptional phenomena beyond the classic condensed matter doctrines, both of which could occur in strongly interacting quantum many-body systems. This work demonstrates that using a controlled method one can construct a non-Fermi liquid within a considerable energy window based on the unique physics of unconventional QCPs. We will focus on the "nearly-marginal non-Fermi liquid", defined as a state whose fermion self-energy scales as $\Sigma_f(i \omega) \sim i \mathrm{sgn}(\omega)|\omega|^{\alpha}$ with $\alpha$ close to $1$ in a considerable energy window. The nearly-marginal non-fermi liquid is obtained by coupling an electron fermi surface to unconventional QCPs that are beyond the Landau's paradigm. This mechanism relies on the observation that the anomalous dimension $\eta$ of the order parameter of these unconventional QCPs can be close to $1$, which is significantly larger than conventional Landau phase transitions, for example the Wilson-Fisher fixed points. The fact that $\eta \sim 1$ justifies a perturbative renormalization group calculation proposed earlier. Various candidate QCPs that meet this desired condition are proposed.