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.

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Cited by in corpus (12)

• 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
• 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
• Energy-filtered excited states and real-time dynamics served in a contour integral
• Nonunitary gates using measurements only