Complex Time Evolution in Tensor Networks

Abstract

Real-time calculations in tensor networks are strongly limited in time by entanglement growth, restricting the achievable frequency resolution of Green's functions, spectral functions, self-energies, and other related quantities. By extending the time evolution to contours in the complex plane, entanglement growth is curtailed, enabling numerically efficient high-precision calculations of time-dependent correlators and Green's functions with detailed frequency resolution. Various approaches to time evolution in the complex plane and the required post-processing for extracting the pure real-time and frequency information are compared. We benchmark our results on the examples of the single-impurity Anderson model using matrix-product states and of the three-band Hubbard-Kanamori and Dworin-Narath models using a tree tensor network. Our findings indicate that the proposed methods are also applicable to challenging realistic calculations of materials.

References in corpus (59)

• The density-matrix renormalization group in the age of matrix product states
• Entanglement Entropy and Quantum Field Theory
• Electronic Structure Calculations with Dynamical Mean-Field Theory: A Spectral Density Functional Approach
• Efficient classical simulation of slightly entangled quantum computations
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• 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
• Evolution of Entanglement Entropy in One-Dimensional Systems
• Time-dependent density-matrix renormalization-group using adaptive effective Hilbert spaces
• Matrix Product Density Operators: Simulation of finite-T and dissipative systems
• Strong electronic correlations from Hund's coupling
• Time-dependent variational principle for quantum lattices
• Unifying time evolution and optimization with matrix product states
• Time-evolution methods for matrix-product states
• Mixed-state dynamics in one-dimensional quantum lattice systems: a time-dependent superoperator renormalization algorithm
• Entropy scaling and simulability by Matrix Product States
• Entanglement and correlation functions following a local quench: a conformal field theory approach
• Sum-rule Conserving Spectral Functions from the Numerical Renormalization Group
• Dynamical density-matrix renormalization-group method
• Time-evolving a matrix product state with long-ranged interactions
• Dynamical Correlation Functions using the Density Matrix Renormalization Group
• Energy resolution and discretization artefacts in the numerical renormalization group
• Non-abelian symmetries in tensor networks: a quantum symmetry space approach
• A Numerical Renormalization Group approach to Green's Functions for Quantum Impurity Models
• General entanglement scaling laws from time evolution
• Density matrix algorithm for the calculation of dynamical properties of low dimensional systems
• The Dynamics of 1D Quantum Spin Systems Can Be Approximated Efficiently
• Variational matrix product state approach to quantum impurity models
• DMFT+NRG study of spin-orbital separation in a three-band Hund's metal
• Chebyshev matrix product state approach for spectral functions
• Chebyshev Matrix Product State Impurity Solver for the Dynamical Mean-Field Theory
• Reducing the numerical effort of finite-temperature density matrix renormalization group transport calculations
• Spectral Functions with the Density Matrix Renormalization Group: Krylov-space Approach for Correction Vectors
• How to discretize a quantum bath for real-time evolution
• Fork Tensor Product States - Efficient Three Orbital Real Time DMFT Solver
• Chebyshev expansion for Impurity Models using Matrix Product States
• Efficient DMFT impurity solver using real-time dynamics with Matrix Product States
• Strongly correlated materials from a numerical renormalization group perspective: How the Fermi-liquid state of Sr${}_2$RuO${}_4$ emerges
• Tensor networks and the numerical renormalization group
• Lanczos algorithm with Matrix Product States for dynamical correlation functions
• Precise evaluation of thermal response functions by optimized density matrix renormalization group schemes
• Imaginary-time matrix product state impurity solver for dynamical mean-field theory
• Spectral functions and time evolution from the Chebyshev recursion
• Upper bounds on entangling rates of bipartite Hamiltonians
• T3NS: three-legged tree tensor network states
• Generalized Wilson Chain for solving multichannel quantum impurity problems
• Time Dependent Variational Principle for Tree Tensor Networks
• Orbital differentiation in Hund metals
• Doublon-holon origin of the subpeaks at the Hubbard band edges
• Interleaved numerical renormalization group as an efficient multiband impurity solver
• Imaginary-time matrix product state impurity solver in a real material calculation: Spin-orbit coupling in Sr${}_2$RuO${}_4$
• Adaptive broadening to improve spectral resolution in the numerical renormalization group
• Spectral Densities from Dynamic Density-Matrix Renormalization
• Low-energy physics of three-orbital impurity model with Kanamori interaction
• Renormalized parameters and perturbation theory for an n-channel Anderson model with Hund's rule coupling: Asymmetric case
• Time propagation and spectroscopy of Fermionic systems using a stochastic technique
• BaOsO${}_3$: A Hund's metal in the presence of strong spin-orbit coupling
• Spin-orbit coupling in three-orbital Kanamori impurity model and its relevance for transition-metal oxides

Cited by in corpus (13)

• Exactly solvable non-unitary time evolution in quantum critical systems I: Effect of complex spacetime metrics
• Dynamical correlation functions from complex time evolution
• Loschmidt echo, emerging dual unitarity and scaling of generalized temporal entropies after quenches to the critical point
• Stabilizing the calculation of the self-energy in dynamical mean-field theory using constrained residual minimization
• Semi-group influence matrices for non-equilibrium quantum impurity models
• Low-temperature transport in high-conductivity correlated metals: a density-functional plus dynamical mean-field study of cubic perovskites
• Efficient and systematic calculation of arbitrary observables for the matrix product state excitation ansatz
• A comprehensive study of out-of-equilibrium Kondo effect and Coulomb blockade
• Spectroscopy and complex-time correlations using minimally entangled typical thermal states
• Bath parameterization in multi-band cluster Dynamical Mean-Field Theory
• Multi-orbital dynamical mean-field theory with a complex-time solver
• Nonunitary gates using measurements only
• Energy-filtered excited states and real-time dynamics served in a contour integral