Spectral functions and time evolution from the Chebyshev recursion

Abstract

We link linear prediction of Chebyshev and Fourier expansions to analytic continuation. We push the resolution in the Chebyshev-based computation of $T=0$ many-body spectral functions to a much higher precision by deriving a modified Chebyshev series expansion that allows to reduce the expansion order by a factor $\sim \frac{1}{6}$. We show that in a certain limit the Chebyshev technique becomes equivalent to computing spectral functions via time evolution and subsequent Fourier transform. This introduces a novel recursive time evolution algorithm that instead of the group operator $e^{-iHt}$ only involves the action of the generator $H$. For quantum impurity problems, we introduce an adapted discretization scheme for the bath spectral function. We discuss the relevance of these results for matrix product state (MPS) based DMRG-type algorithms, and their use within dynamical mean-field theory (DMFT). We present strong evidence that the Chebyshev recursion extracts less spectral information from $H$ than time evolution algorithms when fixing a given amount of created entanglement.

12 pages + 6 pages appendix, 11 figures

References in corpus (15)

• The density-matrix renormalization group in the age of matrix product states
• Thermalization and its mechanism for generic isolated quantum systems
• The numerical renormalization group method for quantum impurity systems
• The Kernel Polynomial Method
• General entanglement scaling laws from time evolution
• Spectral functions in one-dimensional quantum systems at T>0
• Spectral Function for the S=1 Heisenberg Antiferromagetic Chain
• Chebyshev matrix product state approach for spectral functions
• Solving nonequilibrium dynamical mean-field theory using matrix product states
• Real-space calculation of the conductivity tensor for disordered topological matter
• Chebyshev Matrix Product State Impurity Solver for the Dynamical Mean-Field Theory
• Chebyshev expansion for Impurity Models using Matrix Product States
• Lanczos algorithm with Matrix Product States for dynamical correlation functions
• High Energy Dynamics of the Single Impurity Anderson Model
• Real-time dynamics in the one-dimensional Hubbard model

Cited by in corpus (9)

• Quantum dynamics of thermalizing systems
• Spectral Functions with the Density Matrix Renormalization Group: Krylov-space Approach for Correction Vectors
• Time-step targeting time-dependent and dynamical density matrix renormalization group algorithms with ab initio Hamiltonians
• Fully Algebraic and Self-consistent Effective Dynamics in a Static Quantum Embedding
• Approximating the long time average of the density operator: Diagonal ensemble
• The spectral function of Mott-insulating Hubbard ladders: From fractionalized excitations to coherent quasi-particles
• Dynamical topological excitations in parafermion chains
• Chebyshev Polynomial Method to Landauer-Büttiker Formula of Quantum Transport in Nanostructures
• Many-body Majorana-like zero modes without gauge symmetry breaking