Luttinger liquid physics from infinite-system DMRG

TL;DR

This paper uses infinite-system DMRG to demonstrate Luttinger liquid behavior in one-dimensional spinless fermions, analyzing static correlations, thermodynamics, and finite-temperature scaling without finite-size effects.

Contribution

It introduces an infinite-system DMRG approach to study Luttinger liquids at finite temperature, capturing power-law behaviors and extracting parameters without finite-size scaling.

Findings

Luttinger liquid power-law suppression of n(k) observed over several orders of magnitude.

Finite-temperature n(k) follows a scaling relation.

Luttinger parameters can be obtained from various response functions without finite-size analysis.

Abstract

We study one-dimensional spinless fermions at zero and finite temperature T using the density matrix renormalization group. We consider nearest as well as next-nearest neighbor interactions; the latter render the system inaccessible by a Bethe ansatz treatment. Using an infinite-system alogrithm we demonstrate the emergence of Luttinger liquid physics at low energies for a variety of static correlation functions as well as for thermodynamic properties. The characteristic power law suppression of the momentum distribution n(k) function at T=0 can be directly observed over several orders of magnitude. At finite temperature, we show that n(k) obeys a scaling relation. The Luttinger liquid parameter and the renormalized Fermi velocity can be extracted from the density response function, the specific heat, and/or the susceptibility without the need to carry out any finite-size analysis. We illustrate that the energy scale below which Luttinger liquid power laws manifest vanishes as the half-filled system is driven into a gapped phase by large interactions.