Root-N Krylov-space correction-vectors for spectral functions with the density matrix renormalization group

Abstract

We propose a method to compute spectral functions of generic Hamiltonians using the density matrix renormalization group (DMRG) algorithm directly in the frequency domain, based on a modified Krylov space decomposition to compute the correction-vectors. Our approach entails the calculation of the root-N (N=2 is the standard square root) of the Hamiltonian propagator using Krylov space decomposition, and repeating this procedure N times to obtain the actual correction-vector. We show that our method greatly alleviates the burden of keeping a large bond dimension at large target frequencies, a problem found with conventional correction-vector DMRG, while achieving better computational performance at large N. We apply our method to spin and charge spectral functions of t-J and Hubbard models in the challenging two-leg ladder geometry, and provide evidence that the root-N approach reaches a much improved resolution compared to conventional correction-vector.

arXiv comment11 pages, 5 figures, Supplementary Material

References in corpus (34)

• The density-matrix renormalization group in the age of matrix product states
• Angle-resolved photoemission spectroscopy of the cuprate superconductors
• Real time evolution using the density matrix renormalization group
• Resonant Inelastic X-ray Scattering Studies of Elementary Excitations
• Time-dependent density-matrix renormalization-group using adaptive effective Hilbert spaces
• Time-evolution methods for matrix-product states
• Dynamical density-matrix renormalization-group method
• Dynamical Correlation Functions using the Density Matrix Renormalization Group
• Density matrix algorithm for the calculation of dynamical properties of low dimensional systems
• Low-Lying Excited States and Low-Temperature Properties of an Alternating Spin-1 / Spin-1/2 Chain : A DMRG study
• Time-step targetting methods for real-time dynamics using DMRG
• Spectral Function for the S=1 Heisenberg Antiferromagetic Chain
• Time Dependent Variational Principle with Ancillary Krylov Subspace
• Variational matrix product state approach to quantum impurity models
• Chebyshev matrix product state approach for spectral functions
• One- and Two-Triplon Spectra of a Cuprate Ladder
• Collective spin excitations in a quantum spin ladder probed by high-resolution Resonant Inelastic X-ray Scattering
• Spectral Functions with the Density Matrix Renormalization Group: Krylov-space Approach for Correction Vectors
• Witnessing entanglement in quantum magnets using neutron scattering
• The Density Matrix Renormalization Group for Strongly Correlated Electron Systems: A Generic Implementation
• Lanczos algorithm with Matrix Product States for dynamical correlation functions
• Spectral functions and time evolution from the Chebyshev recursion
• Adaptive Lanczos-vector method for dynamic properties within the density-matrix renormalization group
• Chebyshev matrix product state approach for time evolution
• Computing Resonant Inelastic X-Ray Scattering Spectra Using The Density Matrix Renormalization Group Method
• Reorthonormalization of Chebyshev matrix product states for dynamical correlation functions
• Density-matrix renormalization group methods for momentum- and frequency-resolved dynamical correlation functions
• Theoretical study of the spin and charge dynamics of two-leg ladders as probed by resonant inelastic x-ray scattering
• Doping evolution of charge and spin excitations in two-leg Hubbard ladders: comparing DMRG and RPA+FLEX results
• Magnetic excitation spectra of strongly correlated quasi-one dimensional systems: Heisenberg versus Hubbard-like behavior
• Matrix product state recursion methods for strongly correlated quantum systems
• Signatures of pairing in the magnetic excitation spectrum of strongly correlated ladders
• Crossover of the high-energy spin fluctuations from collective triplons to localized magnetic excitations in doped Sr14-xCaxCu24O41 cuprate ladders
• Infinite boundary conditions for response functions and limit cycles in iDMRG, demonstrated for bilinear-biquadratic spin-1 chains

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