On the Validity of the Tomonaga Luttinger Liquid Relations for the One-dimensional Holstein Model

TL;DR

This paper investigates the finite size effects on Tomonaga Luttinger liquid relations in the 1D Holstein model, revealing slow decay of corrections and challenging previous interpretations of its metallic phase.

Contribution

It provides analytical expressions for finite size corrections to LL relations and re-evaluates the metallic phase without relying on these relations.

Findings

Finite size corrections decay slowly with system size.

Re-examination of the metallic phase challenges previous claims of dominant singlet pairing.

Quantum Monte Carlo results do not support a dominant singlet pairing state.

Abstract

For the one-dimensional Holstein model, we show that the relations among the scaling exponents of various correlation functions of the Tomonaga Luttinger liquid (LL), while valid in the thermodynamic limit, are significantly modified by finite size corrections. We obtain analytical expressions for these corrections and find that they decrease very slowly with increasing system size. The interpretation of numerical data on finite size lattices in terms of LL theory must therefore take these corrections into account. As an important example, we re-examine the proposed metallic phase of the zero-temperature, half-filled one-dimensional Holstein model without employing the LL relations. In particular, using quantum Monte Carlo calculations, we study the competition between the singlet pairing and charge ordering. Our results do not support the existence of a dominant singlet pairing state.