Chebyshev matrix product states with canonical orthogonalization for spectral functions of strongly correlated systems

07 September 2021, Version 1
This content is a preprint and has not undergone peer review at the time of posting.

Abstract

We propose a method to calculate the spectral functions of strongly correlated systems by Chebyshev expansion in the framework of matrix product states coupled with canonical orthogonalization (coCheMPS). The canonical orthogonalization can improve the accuracy and efficiency significantly because the orthogonalized Chebyshev vectors can provide an ideal basis for constructing the effective Hamiltonian in which the exact recurrence relation can be retained. In addition, not only the spectral function but also the excited states and eigen energies can be directly calculated, which is usually impossible for other MPS-based methods such as time-dependent formalism or correction vector. The remarkable accuracy and efficiency of coCheMPS over other methods are demonstrated by calculating the spectral functions of spin chain and ab initio hydrogen chain. We demonstrate for the first time that Chebyshev MPS can be used in quantum chemistry. We also caution the application for electron-phonon system with densed density of states.

Supplementary materials

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Supplementary materials
Description
Gram-Schimidt orthogonalization formulation, DOS calculated by coCheMPS and Lanczos MPS, finite temperature spectral functions of electron-phonon model.
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