Luttinger liquid physics from infinite-system DMRG

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.

References in corpus (9)

• The density-matrix renormalization group in the age of matrix product states
• Real time evolution using the density matrix renormalization group
• Classical simulation of infinite-size quantum lattice systems in one spatial dimension
• Scaling of entanglement support for Matrix Product States
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• Time evolution of correlations in strongly interacting fermions after a quantum quench
• Exact edge singularities and dynamical correlations in spin-1/2 chains
• Spectral function of spinless fermions on a one-dimensional lattice
• Tomonaga-Luttinger parameters for doped Mott insulators

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