Minimally entangled typical thermal states versus matrix product purifications for the simulation of equilibrium states and time evolution

TL;DR

This paper compares the efficiency and accuracy of purification-based and METTS-based DMRG methods for simulating equilibrium states and dynamics in strongly-correlated quantum systems, finding purifications generally more accurate except at very low temperatures.

Contribution

It provides a detailed comparison of purification and METTS approaches in DMRG, highlighting their relative efficiencies and limitations across different models and temperature regimes.

Findings

Purifications are more accurate than METTS at similar computational costs.

METTS becomes more efficient only at temperatures well below the energy gap.

Both methods face exponential cost growth in response function calculations.

Abstract

For the simulation of equilibrium states and finite-temperature response functions of strongly-correlated quantum many-body systems, we compare the efficiencies of two different approaches in the framework of the density matrix renormalization group (DMRG). The first is based on matrix product purifications. The second, more recent one, is based on so-called minimally entangled typical thermal states (METTS). For the latter, we highlight the interplay of statistical and DMRG truncation errors, discuss the use of self-averaging effects, and describe schemes for the computation of response functions. For critical as well as gapped phases of the spin-1/2 XXZ chain and the one-dimensional Bose-Hubbard model, we assess the computation costs and accuracies of the two methods at different temperatures. For almost all considered cases, we find that, for the same computation cost, purifications yield more accurate results than METTS -- often by orders of magnitude. The METTS algorithm becomes more efficient only for temperatures well below the system's energy gap. The exponential growth of the computation cost in the evaluation of response functions limits the attainable timescales in both methods and we find that in this regard, METTS do not outperform purifications.