Finite-temperature density-matrix renormalization group method for electron-phonon systems: Thermodynamics and Holstein-polaron spectral functions

TL;DR

This paper develops an efficient finite-temperature DMRG method with local basis optimization to study thermodynamics and spectral functions of the Holstein polaron, revealing temperature-induced spectral shifts and broadening.

Contribution

It introduces a combined purification and local basis optimization approach for finite-temperature DMRG applied to electron-phonon systems, enabling accurate spectral analysis in the crossover regime.

Findings

Spectral weight shifts to lower frequencies and larger momenta with increasing temperature.

Phonon spectral function broadens and the polaron peak flattens at high temperatures.

Method simplifies calculations of thermodynamics and spectral functions in electron-phonon models.

Abstract

We investigate the thermodynamics and finite-temperature spectral functions of the Holstein polaron using a density-matrix renormalization group method. Our method combines purification and local basis optimization (LBO) as an efficient treatment of phonon modes. LBO is a scheme which relies on finding the optimal local basis by diagonalizing the local reduced density matrix. By transforming the state into this basis, one can truncate the local Hilbert space with a negligible loss of accuracy for a wide range of parameters. In this work, we focus on the crossover regime between large and small polarons of the Holstein model. Here, no analytical solution exists and we show that the thermal expectation values at low temperatures are independent of the phonon Hilbert space truncation provided the basis is chosen large enough. We then demonstrate that we can extract the electron spectral function and establish consistency with results from a finite-temperature Lanczos method. We additionally calculate the electron emission spectrum and the phonon spectral function and show that all the computations are significantly simplified by the local basis optimization. We observe that the electron emission spectrum shifts spectral weight to both lower frequencies and larger momenta as the temperature is increased. The phonon spectral function experiences a large broadening and the polaron peak at large momenta gets significantly flattened and merges almost completely into the free-phonon peak.