Chebyshev matrix product state approach for spectral functions

TL;DR

This paper introduces Chebyshev matrix product state (CheMPS), a numerically efficient method for calculating spectral functions of 1D lattice models, offering uniform resolution, controlled broadening, and reduced computational cost.

Contribution

The paper develops CheMPS, a novel approach combining Chebyshev expansions with MPS, providing a scalable and accurate way to compute spectral functions with bounded entanglement growth.

Findings

CheMPS achieves spectral resolution comparable to correction vector DMRG.

It agrees well with Bethe Ansatz results for infinite systems.

CheMPS can be applied in the time domain as an alternative to time-dependent DMRG.

Abstract

We show that recursively generated Chebyshev expansions offer numerically efficient representations for calculating zero-temperature spectral functions of one-dimensional lattice models using matrix product state (MPS) methods. The main features of this Chebychev matrix product state (CheMPS) approach are: (i) it achieves uniform resolution over the spectral function's entire spectral width; (ii) it can exploit the fact that the latter can be much smaller than the model's many-body bandwidth; (iii) it offers a well-controlled broadening scheme; (iv) it is based on a succession of Chebychev vectors |t_n>, (v) whose entanglement entropies were found to remain bounded with increasing recursion order n for all cases analyzed here; (vi) it distributes the total entanglement entropy that accumulates with increasing n over the set of Chebyshev vectors |t_n>. We present zero-temperature CheMPS results for the structure factor of spin-1/2 antiferromagnetic Heisenberg chains and perform a detailed finite-size analysis. Making comparisons to three benchmark methods, we find that CheMPS (1) yields results comparable in quality to those of correction vector DMRG, at dramatically reduced numerical cost; (2) agrees well with Bethe Ansatz results for an infinite system, within the limitations expected for numerics on finite systems; (3) can also be applied in the time domain, where it has potential to serve as a viable alternative to time-dependent DMRG (in particular at finite temperatures). Finally, we present a detailed error analysis of CheMPS for the case of the noninteracting resonant level model.