Chebyshev matrix product state approach for spectral functions

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.