Infinite size density matrix renormalization group, revisited

TL;DR

This paper revisits the infinite-size DMRG algorithm, introducing a more effective transformation for wavefunction elements, leading to faster convergence and improved calculation of correlation functions and higher moments.

Contribution

The paper introduces a versatile transformation that enhances the efficiency of the infinite-size DMRG algorithm, enabling faster convergence and better access to correlation spectra.

Findings

New transformation significantly improves convergence speed.

Allows direct calculation of correlation length spectra.

Demonstrates advantages of MPO technique for higher moments.

Abstract

I revisit the infinite-size variant of the Density Matrix Renormalization Group (iDMRG) algorithm for obtaining a fixed-point translationally invariant matrix product wavefunction in the context of one-dimensional quantum systems. A crucial ingredient of this algorithm is an efficient transformation for obtaining the matrix elements of the wavefunction as the lattice size is increased, and I introduce here a versatile transformation that is demonstrated to be much more effective than previous versions. The resulting algorithm has a surprisingly close relationship to Vidal's Time Evolving Block Decimation for infinite systems, but allows much faster convergence. Access to a translationally invariant matrix product state allows the calculation of correlation functions based on the transfer matrix, which directly gives the spectrum of all correlation lengths. I also show some advantages of the Matrix Product Operator (MPO) technique for constructing expectation values of higher moments, such as the exact variance $<(H-E)^2>$.