Density Matrix Renormalization Group of Gapless Systems

TL;DR

This paper analyzes the convergence and properties of the DMRG method in gapless systems, revealing how correlation length scales with kept states and exploring excitation spectra and ground state overlaps.

Contribution

It provides new insights into DMRG convergence in gapless systems, including correlation length scaling, symmetry properties of excitation spectra, and a method for computing ground state overlaps.

Findings

Correlation length scales as ξ ∼ m^{1.3} in DMRG fixed points.

The excitation spectrum symmetry E(k)=E(π−k) is proven for certain systems.

A method to compute overlaps between different DMRG ground states is introduced.

Abstract

We investigate convergence of the density matrix renormalization group (DMRG) in the thermodynamic limit for gapless systems. Although the DMRG correlations always decay exponentially in the thermodynamic limit, the correlation length at the DMRG fixed-point scales as $\xi \sim m^{1.3}$, where $m$ is the number of kept states, indicating the existence of algebraic order for the exact system. The single-particle excitation spectrum is calculated, using a Bloch-wave ansatz, and we prove that the Bloch-wave ansatz leads to the symmetry $E(k)=E(\pi -k)$ for translationally invariant half-integer spin-systems with local interactions. Finally, we provide a method to compute overlaps between ground states obtained from different DMRG calculations.