[Paper Review] Gauge invariance and electron spectral functions in underdoped cuprates

Walter Rantner, Xiao-Gang Wen|arXiv (Cornell University)|May 28, 2001

Spectroscopy and Quantum Chemical Studies2 references3 citations

TL;DR

This paper proposes a gauge-invariant formulation of the electron spectral function in underdoped cuprates using a slave-boson approach with a dynamical U(1) gauge field, showing that gauge fluctuations bind spinons and holons into a coherent entity, explaining the broad but not incoherent spectral lineshapes observed in ARPES experiments. The key result is a physical electron propagator that combines spinon and holon contributions, with non-trivial scaling due to gauge fluctuations.

ABSTRACT

The single particle spectral function for the normal state of underdoped high $T_c$ cuprates is studied within the slave particle framework. We find that the presence of a massless dynamical gauge field - a direct consequence of the quantum order - explains the broad, but not totally incoherent, line-shapes observed in experiments. The issue of the negative anomalous dimension of a recently proposed gauge invariant single particle amplitude is also considered. We show how the anomalous behavior of the single particle amplitude can be incorporated within the slave particle approach and, thus reinterpreted, lead to physical phenomenology.

Motivation & Objective

• To resolve the gauge non-invariance of standard Green's functions in strongly correlated electron systems.
• To understand the origin of the broad, incoherent, yet not fully incoherent spectral functions observed in underdoped high-Tc cuprates.
• To reinterpret the negative anomalous dimension of a gauge-invariant amplitude as a two-particle spinon-holon bound state.
• To construct a physically consistent electron spectral function incorporating both spinon and holon degrees of freedom via gauge fluctuations.

Proposed method

• Formulates a first-quantized path integral for a gauge-invariant Green's function involving a particle coupled to a dynamical U(1) gauge field.
• Uses a 2+1 dimensional effective theory of massless Dirac spinons coupled to a dynamical gauge field, modeling the Algebraic Spin Liquid (ASL) state.
• Introduces a gauge-invariant single-particle amplitude that is reinterpreted as a two-particle spinon-holon propagator due to anomalous scaling.
• Performs explicit path integral calculations involving Bessel functions and confluent hypergeometric functions to evaluate the physical hole Green's function.
• Solves the Green's function in momentum-frequency space using series expansions and integral identities involving Gamma and hypergeometric functions.
• Derives the full electron spectral function as a sum of spinon and holon contributions, with vertex corrections mediated by the gauge field.

Experimental results

Research questions

• RQ1 How can a gauge-invariant single-particle Green's function be consistently defined in a strongly correlated electron system with a dynamical gauge field?
• RQ2 Why does the gauge-invariant amplitude for the spinon exhibit a negative anomalous dimension, and what is its physical interpretation?
• RQ3 Can the broad, incoherent spectral lineshape in underdoped cuprates be explained by gauge fluctuations without quasiparticle peaks?
• RQ4 How do spinons and holons combine to form a coherent physical electron despite being distinct in the mean-field slave-boson description?

Key findings

• The gauge-invariant Green's function is derived using a first-quantized path integral, explicitly incorporating the Wilson loop for gauge invariance.
• The negative anomalous dimension of the gauge-invariant amplitude is reinterpreted as a two-particle spinon-holon bound state, not a physical single-particle excitation.
• The physical electron spectral function is found to be non-perturbative and exhibits a power-law scaling due to the dynamical gauge field, with critical exponent α ≈ 1.5.
• The resulting spectral function shows a broad, incoherent background with a weak, non-peak-like structure, consistent with ARPES observations in underdoped cuprates.
• The holon contribution is essential for coherence, as gauge fluctuations bind holons to spinons, forming a more coherent composite object.
• The full Green's function is expressed as a series involving confluent hypergeometric functions, with explicit dependence on frequency, momentum, and the gauge field's dynamical mass scale.