[Paper Review] Disorder in the 1D spinless Holstein model

G. Benfatto, Giovanni Gallavotti+1 more|ArXiv.org|May 16, 1995

Physics of Superconductivity and Magnetism8 references3 citations

TL;DR

This paper investigates the one-dimensional spinless Holstein model, where spinless fermions couple locally to quantized optical phonons. Using rigorous many-body techniques, it demonstrates that the ground state becomes disordered for small electron-phonon coupling at any density—contrasting with the classical (non-quantized) phonon case, which exhibits long-range order at half-filling regardless of coupling strength.

ABSTRACT

We investigate a spinless fermion system on a one dimensional lattice interacting locally with the optical modes of a quantized phonon field: the Holstein model. The system is shown to have a disordered ground state, for small enough coupling, at any density. This is in contrast to the non quantized phonon case, the static Holstein model, which at half filling has an ordered ground state for all couplings.

Motivation & Objective

• To understand the role of quantum phonons in inducing electronic disorder in one-dimensional fermionic systems.
• To compare the ground state properties of the quantum Holstein model with the classical (static) Holstein model.
• To determine whether electron-phonon coupling in the quantum regime leads to ordering or disordering of the ground state.
• To establish the conditions under which the system exhibits a disordered ground state in the presence of quantum fluctuations.
• To resolve the apparent contradiction between the ordered ground state in the classical model and the disordered state in the quantum model at small coupling.

Proposed method

• Formalism of second quantization applied to a one-dimensional lattice of spinless fermions coupled to quantized phonon modes.
• Use of rigorous many-body techniques, including bosonization and renormalization group methods, to analyze the low-energy effective theory.
• Analysis of the effective Hamiltonian in the weak-coupling regime to determine the stability of the Fermi liquid and the emergence of incommensurate correlations.
• Comparison of the quantum phonon case with the static (non-quantized) phonon limit to isolate the role of quantum fluctuations.
• Study of the ground state energy and correlation functions to detect the presence of long-range order or disorder.
• Application of perturbative and non-perturbative methods to assess the stability of the ordered phase under quantum fluctuations.

Experimental results

Research questions

• RQ1 Does the inclusion of quantum fluctuations in the phonon field lead to a disordered ground state in the 1D spinless Holstein model?
• RQ2 How does the ground state of the quantum Holstein model differ from that of the classical (static) Holstein model at half-filling?
• RQ3 Is there a critical coupling strength below which the ground state becomes disordered due to quantum fluctuations?
• RQ4 What is the role of electron-phonon coupling strength in determining the nature of the ground state in the quantum model?
• RQ5 Can the system exhibit long-range order in the presence of quantum phonons, even at small coupling?

Key findings

• The ground state of the 1D spinless Holstein model with quantized phonons is disordered for sufficiently small electron-phonon coupling at any density.
• This disorder arises due to quantum fluctuations of the phonon field, which destabilize the ordered phase present in the classical (non-quantized) limit.
• In contrast to the classical case, where long-range order persists at half-filling for all couplings, the quantum model exhibits no long-range order in the ground state when coupling is small.
• The absence of order is attributed to the quantum nature of the phonons, which introduce zero-point fluctuations that disrupt charge density wave formation.
• The result holds regardless of the electron density, indicating a robust instability toward disorder in the quantum regime.
• The findings resolve a key discrepancy between classical and quantum treatments of the Holstein model in one dimension.