SciPost Physics

SciPost Phys. 8, 024 (2020) · published 7 February 2020

• doi: 10.21468/SciPostPhys.8.2.024
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Abstract

We present a generalization of the Time Dependent Variational Principle (TDVP) to any finite sized loop-free tensor network. The major advantage of TDVP is that it can be employed as long as a representation of the Hamiltonian in the same tensor network structure that encodes the state is available. Often, such a representation can be found also for long-range terms in the Hamiltonian. As an application we use TDVP for the Fork Tensor Product States tensor network for multi-orbital Anderson impurity models. We demonstrate that TDVP allows to account for off-diagonal hybridizations in the bath which are relevant when spin-orbit coupling effects are important, or when distortions of the crystal lattice are present.

• Kohn et al., Efficient mapping for Anderson impurity problems with matrix product states
  Phys. Rev. B 104, 014303 (2021) [Crossref]
• Secular et al., Parallel time-dependent variational principle algorithm for matrix product states
  Phys. Rev. B 101, 235123 (2020) [Crossref]
• Strand et al., Using tensor network states for multi-particle Brownian ratchets
  156, 221103 (2022) [Crossref]
• Causer et al., Optimal Sampling of Dynamical Large Deviations in Two Dimensions via Tensor Networks
  Phys. Rev. Lett. 130, 147401 (2023) [Crossref]
• Kloss et al., Studying dynamics in two-dimensional quantum lattices using tree tensor network states
  SciPost Phys. 9, 070 (2020) [Crossref]
• Bertrand et al., Quantum quasi Monte Carlo algorithm for out-of-equilibrium Green functions at long times
  Phys. Rev. B 103, 155104 (2021) [Crossref]
• Papić,
  , 341 (2022) [Crossref]
• Kohn et al., Quench dynamics of the Anderson impurity model at finite temperature using matrix product states: entanglement and bath dynamics
  J. Stat. Mech. 2022, 063102 (2022) [Crossref]
• Bañuls, Tensor Network Algorithms: A Route Map
  Annu. Rev. Condens. Matter Phys. 14, 173 (2023) [Crossref]
• Ceruti et al., Time Integration of Tree Tensor Networks
  SIAM J. Numer. Anal. 59, 289 (2021) [Crossref]
• Grundner et al., Complex time evolution in tensor networks and time-dependent Green's functions
  Phys. Rev. B 109, 155124 (2024) [Crossref]
• Ke, Tree tensor network state approach for solving hierarchical equations of motion
  158, 211102 (2023) [Crossref]
• Lindoy et al., Time evolution of ML-MCTDH wavefunctions. I. Gauge conditions, basis functions, and singularities
  155, 174108 (2021) [Crossref]
• Dunnett et al., Efficient bond-adaptive approach for finite-temperature open quantum dynamics using the one-site time-dependent variational principle for matrix product states
  Phys. Rev. B 104, 214302 (2021) [Crossref]
• Weh et al., Spin‐Polarization and Resonant States in Electronic Conduction through a Correlated Magnetic Layer
  Physica Status Solidi (b) 259, 2100157 (2022) [Crossref]
• Weh et al., Spectral properties of heterostructures containing half-metallic ferromagnets in the presence of local many-body correlations
  Phys. Rev. Research 2, 043263 (2020) [Crossref]
• Slagle, Quantum Gauge Networks: A New Kind of Tensor Network
  Quantum 7, 1113 1113 (2023) [Crossref]
• Bauernfeind et al., Minimally entangled typical thermal state algorithms for finite temperature Matsubara Green functions
  Phys. Rev. B 105, 195107 (2022) [Crossref]
• Larsson, Computing vibrational eigenstates with tree tensor network states (TTNS)
  151, 204102 (2019) [Crossref]
• Lindoy et al., Time evolution of ML-MCTDH wavefunctions. II. Application of the projector splitting integrator
  155, 174109 (2021) [Crossref]
• Hikihara et al., Automatic structural optimization of tree tensor networks
  Phys. Rev. Research 5, 013031 (2023) [Crossref]
• Tindall et al., Gauging tensor networks with belief propagation
  SciPost Phys. 15, 222 (2023) [Crossref]
• Banerjee et al., Effect of geometry on magnetism of Hund's metals: Case study of BaRuO3
  Phys. Rev. B 105, 235106 (2022) [Crossref]
• Cao et al., Tree tensor-network real-time multiorbital impurity solver: Spin-orbit coupling and correlation functions in Sr2RuO4
  Phys. Rev. B 104, 115119 (2021) [Crossref]
• Weh et al., Dynamical mean-field theory of the Anderson-Hubbard model with local and nonlocal disorder in tensor formulation
  Phys. Rev. B 104, 045127 (2021) [Crossref]
• Strand et al., Computing time-periodic steady-state currents via the time evolution of tensor network states
  157, 054104 (2022) [Crossref]
• Kohn et al., Superfluid-to-Mott transition in a Bose-Hubbard ring: Persistent currents and defect formation
  Phys. Rev. A 101, 023617 (2020) [Crossref]
• Larsson, A tensor network view of multilayer multiconfiguration time-dependent Hartree methods
  Molecular Physics, e2306881 (2024) [Crossref]
• Felser et al., Efficient Tensor Network Ansatz for High-Dimensional Quantum Many-Body Problems
  Phys. Rev. Lett. 126, 170603 (2021) [Crossref]
• Wietek et al., Stripes, Antiferromagnetism, and the Pseudogap in the Doped Hubbard Model at Finite Temperature
  Phys. Rev. X 11, 031007 (2021) [Crossref]