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.

22 pages, 13 figures

References in corpus (27)

• The density-matrix renormalization group in the age of matrix product states
• The density-matrix renormalization group
• Efficient simulation of one-dimensional quantum many-body systems
• The numerical renormalization group method for quantum impurity systems
• Real time evolution using the density matrix renormalization group
• Time-dependent density-matrix renormalization-group using adaptive effective Hilbert spaces
• Matrix Product Density Operators: Simulation of finite-T and dissipative systems
• The Kernel Polynomial Method
• DMRG and periodic boundary conditions: a quantum information perspective
• Renormalization algorithms for Quantum-Many Body Systems in two and higher dimensions
• From density-matrix renormalization group to matrix product states
• Dynamical density-matrix renormalization-group method
• Dynamical Correlation Functions using the Density Matrix Renormalization Group
• The Non-Abelian Density Matrix Renormalization Group Algorithm
• Nonequilibrium electron transport using the density matrix renormalization group
• Spectral functions in one-dimensional quantum systems at T>0
• Density matrix algorithm for the calculation of dynamical properties of low dimensional systems
• Equivalence of the Variational Matrix Product Method and the Density Matrix Renormalization Group applied to Spin Chains
• Spectral Function for the S=1 Heisenberg Antiferromagetic Chain
• Two-spinon dynamic structure factor of the one-dimensional S=1/2 Heisenberg antiferromagnet
• Variational matrix product state approach to quantum impurity models
• Exact edge singularities and dynamical correlations in spin-1/2 chains
• The 4-spinon dynamical structure factor of the Heisenberg chain
• Sparse polynomial space approach to dissipative quantum systems: Application to the sub-ohmic spin-boson model
• Adaptive Lanczos-vector method for dynamic properties within the density-matrix renormalization group
• Chebyshev approach to quantum systems coupled to a bath
• Green-Function-Based Monte Carlo Method for Classical Fields Coupled to Fermions

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