Friedel Oscillations in the Open Hubbard Chain

TL;DR

This paper uses DMRG and Bethe Ansatz to analyze Friedel oscillations in the open Hubbard chain, validating theoretical predictions and exploring how interaction strength affects oscillation coefficients.

Contribution

It provides the first numerical determination of Friedel oscillation coefficients as a function of Hubbard interaction strength, combining DMRG and Bethe Ansatz methods.

Findings

Good agreement between DMRG and Bethe Ansatz results

Validation of Conformal Field Theory predictions

First numerical characterization of oscillation coefficients

Abstract

Using the Density Matrix Renormalization Group (DMRG), we calculate critical exponents for the one-dimensional Hubbard model with open boundary conditions with and without additional boundary potentials at both ends. A direct comparison with open boundary condition Bethe Ansatz calculations provides a good check for the DMRG calculations on large system sizes. On the other hand, the DMRG calculations provide an independent check of the predictions of Conformal Field Theory, which are needed to obtain the critical exponents from the Bethe Ansatz. From Bethe Ansatz we predict the behaviour of the 1/L-corrected mean value of the Friedel oscillations (for the density and the magnetization) and the characteristic wave vectors, and show numerically that these conjectures are fulfilled with and without boundary potentials. The quality of the numerical results allows us to determine, for the first time, the behaviour of the coefficients of the Friedel oscillations as a function of the the Hubbard interaction.