Accuracy of the microcanonical Lanczos method to compute real-frequency dynamical spectral functions of quantum models at finite temperatures

TL;DR

This paper assesses the microcanonical Lanczos method's accuracy for calculating finite-temperature dynamical spectral functions in quantum models, proposing an improved approach using thermal pure quantum states and demonstrating its effectiveness on 1D Heisenberg chains.

Contribution

It introduces a new procedure combining thermal pure quantum states with the Lanczos method to improve spectral function calculations at finite temperatures.

Findings

Method yields reasonable accuracy for small systems

Effective for 1D antiferromagnetic Heisenberg chains

Combines microcanonical ensemble with thermal pure quantum states

Abstract

We examine the accuracy of the microcanonical Lanczos method (MCLM) developed by Long, {\it et al.} [Phys. Rev. B {\bf 68}, 235106 (2003)] to compute dynamical spectral functions of interacting quantum models at finite temperatures. The MCLM is based on the microcanonical ensemble, which becomes exact in the thermodynamic limit. To apply the microcanonical ensemble at a fixed temperature, one has to find energy eigenstates with the energy eigenvalue corresponding to the internal energy in the canonical ensemble. Here, we propose to use thermal pure quantum state methods by Sugiura and Shimizu [Phys. Rev. Lett. {\bf 111}, 010401 (2013)] to obtain the internal energy. After obtaining the energy eigenstates using the Lanczos diagonalization method, dynamical quantities are computed via a continued fraction expansion, a standard procedure for Lanczos-based numerical methods. Using one-dimensional antiferromagnetic Heisenberg chains with $S=1/2$, we demonstrate that the proposed procedure is reasonably accurate even for relatively small systems.