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Register a new userSparse sampling and tensor network representation of two-particle Greens functions
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Many-body calculations at the two-particle level require a compact representation of two-particle Greens functions. In this paper, we introduce a sparse sampling scheme in the Matsubara frequency domain as well as a tensor network representation for two-particle Greens functions. The sparse sampling is based on the intermediate representation basis and allows an accurate extraction of the generalized susceptibility from a reduced set of Matsubara frequencies. The tensor network representation provides a system independent way to compress the information carried by two-particle Greens functions. We demonstrate efficiency of the present scheme for calculations of static and dynamic susceptibilities in single- and two-band Hubbard models in the framework of dynamical mean-field theory.
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Two-particle Greens functions and the vertex functions play a critical role in theoretical frameworks for describing strongly correlated electron systems. However, numerical calculations at two-particle level often suffer from large computation time and massive memory consumption. We derive a general expansion formula for the two-particle Greens functions in terms of an overcomplete representation based on the recently proposed intermediate representation basis. The expansion formula is obtained by decomposing the spectral representation of the two-particle Greens function. We demonstrate that the expansion coefficients decay exponentially, while all high-frequency and long-tail structures in the Matsubara-frequency domain are retained. This representation therefore enables efficient treatment of two-particle quantities and opens a route to the application of modern many-body theories to realistic strongly correlated electron systems.
Recently, a class of tensor networks called isometric tensor network states (isoTNS) was proposed which generalizes the canonical form of matrix product states to tensor networks in higher dimensions. While this ansatz allows for efficient numerical computations, it remained unclear which phases admit an isoTNS representation. In this work, we show that two-dimensional string-net liquids, which represent a wide variety of topological phases including discrete gauge theories, admit an exact isoTNS representation. We further show that the isometric form can be preserved after applying a finite depth local quantum circuit. Taken together, these results show that long-range entanglement by itself is not an obstruction to isoTNS representation and suggest that all two-dimensional gapped phases with gappable edges admit an isoTNS representation.
We present SpM, a sparse modeling tool for the analytic continuation of imaginary-time Greens function, licensed under GNU General Public License version 3. In quantum Monte Carlo simulation, dynamic physical quantities such as single-particle and magnetic excitation spectra can be obtained by applying analytic continuation to imaginary-time data. However, analytic continuation is an ill-conditioned inverse problem and thus sensitive to noise and statistical errors. SpM provides stable analytic continuation against noise by means of a modern regularization technique, which automatically selects bases that contain relevant information unaffected by noise. This paper details the use of this program and shows some applications.
Efficient ab initio calculations of correlated materials at finite temperature require compact representations of the Greens functions both in imaginary time and Matsubara frequency. In this paper, we introduce a general procedure which generates sparse sampling points in time and frequency from compact orthogonal basis representations, such as Chebyshev polynomials and intermediate representation (IR) basis functions. These sampling points accurately resolve the information contained in the Greens function, and efficient transforms between different representations are formulated with minimal loss of information. As a demonstration, we apply the sparse sampling scheme to diagrammatic $GW$ and GF2 calculations of a hydrogen chain, of noble gas atoms and of a silicon crystal.
We propose a generalized Lanczos method to generate the many-body basis states of quantum lattice models using tensor-network states (TNS). The ground-state wave function is represented as a linear superposition composed from a set of TNS generated by Lanczos iteration. This method improves significantly both the accuracy and the efficiency of the tensor-network algorithm and allows the ground state to be determined accurately using TNS with very small virtual bond dimensions. This state contains significantly more entanglement than each individual TNS, reproducing correctly the logarithmic size dependence of the entanglement entropy in a critical system. The method can be generalized to non-Hamiltonian systems and to the calculation of low-lying excited states, dynamical correlation functions, and other physical properties of strongly correlated systems.
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