Nonequilibrium diagrammatic many-body simulations with quantics tensor trains

Abstract

The nonequilibrium Green's function formalism provides a versatile and powerful framework for numerical studies of nonequilibrium phenomena in correlated many-body systems. For calculations starting from an equilibrium initial state, a standard approach consists of discretizing the Kadanoff-Baym contour and implementing a causal time-stepping scheme in which the self-energy of the system plays the role of a memory kernel. This approach becomes computationally expensive at long times, because of the convolution integrals and the large amount of computer memory needed to store the Green's functions. A recent idea for the compression of nonequilibrium Green's functions is the quantics tensor train representation. Here, we explore this approach by implementing equilibrium and nonequilibrium simulations of the two-dimensional Hubbard model with a second-order weak-coupling approximation to the self-energy. We show that calculations with compressed two-time functions are possible without any loss of accuracy, and that the quantics tensor train implementation shows a much improved scaling of the computational effort and memory demand with the length of the time contour.

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• Correlated states in super-moiré materials with a kernel polynomial quantics tensor cross interpolation algorithm
• Solving the Gross-Pitaevskii equation on multiple different scales using the quantics tensor train representation
• Third-order strong-coupling impurity solver for real-frequency DMFT: Accurate spectral functions for antiferromagnetic and photo-doped states
• Inchworm tensor train hybridization expansion quantum impurity solver
• Entanglement across scales: Quantics tensor trains as a natural framework for renormalization
• Tensor network method for real-space topology in quasicrystal Chern mosaics
• A causality-based divide-and-conquer algorithm for nonequilibrium Green's function calculations with quantics tensor trains