Autocorrelations from the transfer matrix DMRG method

TL;DR

This paper extends the transfer matrix DMRG algorithm to accurately compute imaginary time spin autocorrelations across a wide temperature range, enabling the extraction of real frequency spectra for various spin models.

Contribution

The authors develop an improved transfer matrix DMRG method to calculate autocorrelations and spectra with high precision, including analytic continuation techniques for real frequency analysis.

Findings

High accuracy autocorrelation calculations over broad temperature range

Effective analytic continuation for real frequency spectra

Method identifies low temperature gaps and peak positions

Abstract

Extending the transfer matrix DMRG algorithm, we are able to calculate imaginary time spin autocorrelations with high accuracy (absolute error $<10^{-6}$) over a wide temperature range ($0<\beta J<20$). After analytic continuation using the rules of probability theory along with the entropic prior (MaxEnt), we obtain real frequency spectra for the XY model, the isotropic Heisenberg and the gaped Heisenberg-Ising model. Available exact results in some limits allow for a critical evaluation of the quality of answers expected from this procedure. We find that high precision data are still insufficient for resolving specific lineshapes such as low frequency divergences. However, the method is appropriate for identifying low temperature gaps and peak positions.