[Paper Review] Current Algebra Approach to 2d Chiral Metals

Chao-Jung Lee, Michael Mulligan|arXiv (Cornell University)|Apr 11, 2022

Physics of Superconductivity and Magnetism74 references4 citations

TL;DR

This paper proposes that two-dimensional chiral metals with non-Fermi liquid behavior can be described by U(N) Wess-Zumino-Witten (WZW) models at integer level k ≥ 1, where k = 1 corresponds to the free chiral metal of Balents and Fisher. The theory maintains U(N) symmetry and translation invariance at k > 1, and the level k rescales the amplitude of U(1) density and current two-point correlation functions without altering their functional form.

ABSTRACT

We reinterpret Balents and Fisher's free 2d chiral metal [Phys. Rev. Lett. 76, 2782 (1996)] as a chiral $U(N)$ Wess-Zumino-Witten model at level $k = 1$. Here, the $U(N)$ symmetry relates the $N ightarrow \infty$ low-energy excitations about the chiral Fermi surface. We obtain non-Fermi liquid generalizations of the free chiral metal that maintain the $U(N)$ symmetry of the $k=1$ theory by taking the level to be a positive integer $k>1$. We calculate two-point correlation functions of the $U(1)$ number density and current operators in these theories for general $k$. We find $k$ to provide an overall rescaling of the amplitude of these correlation functions. This construction illustrates the ersatz Fermi liquid proposal of Else, Thorgren, and Senthil [Phys. Rev. X 11, 021005 (2021)].

Motivation & Objective

• To provide an effective field theory description of non-Fermi liquid metals in two spatial dimensions that preserve the enhanced infrared symmetries of Fermi liquids.
• To generalize Balents and Fisher’s free 2d chiral metal to interacting, non-Fermi liquid states while maintaining the same global symmetries.
• To illustrate the ersatz Fermi liquid proposal by Else, Thorgren, and Senthil through a solvable, symmetry-preserving construction.
• To compute and analyze the two-point correlation functions of U(1) number density and current operators in these theories for arbitrary k ≥ 1.

Proposed method

• Reinterpret the free 2d chiral metal as a U(N) WZW model at level k = 1, with N representing the number of points on the Fermi surface.
• Construct interacting generalizations by elevating the level to integer k > 1, preserving the U(N) symmetry and translation invariance.
• Use the perturbed WZW model framework, where single-fermion hopping between wires corresponds to perturbation by SU(N) symmetry currents.
• Compute two-point correlation functions using the free fermion representation at k = 1 and extend the result to general k via rescaling.
• Employ the free field representation of WZW models to explore potential non-Fermi liquid behavior in single-particle correlation functions.
• Utilize the nonlocal SU(N) symmetry to argue for robustness against nonuniform hopping and quenched disorder in the k > 1 theories.

Experimental results

Research questions

• RQ1 Can the U(N) symmetry and translation invariance of the free 2d chiral metal be preserved in interacting, non-Fermi liquid generalizations?
• RQ2 How does the level k of the U(N) WZW model affect the low-energy correlation functions of U(1) density and current operators?
• RQ3 What is the role of the k = 1 theory as a fixed point for a family of interacting non-Fermi liquid metals with the same global symmetries?
• RQ4 Can the ersatz Fermi liquid proposal be concretely realized through a solvable effective field theory with exact symmetries?
• RQ5 Is there a microscopic mechanism to tune the level k from 1 to higher integers, and can this be achieved via local interactions?

Key findings

• The k = 1 U(N) WZW model is equivalent to Balents and Fisher’s free 2d chiral metal, with the U(N) symmetry arising from nonlocal fermion transformations across spatially separated wires.
• For k > 1, the theory describes interacting non-Fermi liquid metals that preserve the same U(N) and translation symmetries as the k = 1 theory.
• The two-point correlation function of the U(1) current operator scales as ⟨J^y_I(x)J^y_K(x')⟩_k = k⟨J^y_I(x)J^y_K(x')⟩_{k=1}, showing a universal amplitude rescaling by k.
• The density correlation function exhibits the same k-dependent rescaling, indicating that k controls the strength of correlations without altering their functional form.
• The absence of non-Fermi liquid scaling in these U(1) correlation functions is consistent with similar behavior in the spinon-gauge problem, suggesting a universal feature in symmetry-preserving non-Fermi liquids.
• The nonlocal SU(N) symmetry remains intact under nonuniform hopping and quenched disorder, implying robustness against such perturbations in the k > 1 models.