Tomonaga-Luttinger parameters for doped Mott insulators

TL;DR

This paper introduces a numerical method to accurately compute the Tomonaga-Luttinger parameter $K_{\rho}$ in doped Mott insulators, confirming theoretical predictions and analyzing critical behavior in extended Hubbard models.

Contribution

The authors develop a density-matrix renormalization group approach to determine $K_{\rho}$, validating it against exact models and applying it to the extended Hubbard model at quarter filling.

Findings

Confirmed $K_{\rho}=1/4$ on the critical line.

Found $K_{\rho}^{\rm CDW}=1/8$ at infinitesimal doping.

Identified conditions for exponents $\alpha>1$ in doped CDW insulators.

Abstract

The Tomonaga--Luttinger parameter $K_{\rho}$ determines the critical behavior in quasi one-dimensional correlated electron systems, e.g., the exponent $\alpha$ for the density of states near the Fermi energy. We use the numerical density-matrix renormalization group method to calculate $K_{\rho}$ from the slope of the density-density correlation function in momentum space at zero wave vector. We check the accuracy of our new approach against exact results for the Hubbard and XXZ Heisenberg models. We determine $K_{\rho}$ in the phase diagram of the extended Hubbard model at quarter filling, $n_{\rm c}=1/2$, and confirm the bosonization results $K_{\rho}=n_{\rm c}^2=1/4$ on the critical line and $K_{\rho}^{\rm CDW}=n_{\rm c}^2/2=1/8$ at infinitesimal doping of the charge-density-wave (CDW) insulator for all interaction strengths. The doped CDW insulator exhibits exponents $\alpha>1$ only for small doping and strong correlations.