Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userOvercomplete compact representation of two-particle Greens functions
84
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
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.
rate research
Read More
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.
We show how few-particle Greens functions can be calculated efficiently for models with nearest-neighbor hopping, for infinite lattices in any dimension. As an example, for one dimensional spinless fermions with both nearest-neighbor and second nearest-neighbor interactions, we investigate the ground states for up to 5 fermions. This allows us not only to find the stability region of various bound complexes, but also to infer the phase diagram at small but finite concentrations.
Bayesian parametric analytic continuation (BPAC) is proposed for the analytic continuation of noisy imaginary-time Greens function data as, e.g., obtained by continuous-time quantum Monte Carlo simulations (CTQMC). Within BPAC, the spectral function is inferred from a suitable set of parametrized basis functions. Bayesian model comparison then allows to assess the reliability of different parametrizations. The required evidence integrals of such a model comparison are determined by nested sampling. Compared to the maximum entropy method (MEM), routinely used for the analytic continuation of CTQMC data, the presented approach allows to infer whether the data support specific structures of the spectral function. We demonstrate the capability of BPAC in terms of CTQMC data for an Anderson impurity model (AIM) that shows a generalized Kondo scenario and compare the BPAC reconstruction to the MEM as well as to the spectral function obtained from the real-time fork tensor product state impurity solver where no analytic continuation is required. Furthermore, we present a combination of MEM and BPAC and its application to an AIM arising from the ab initio treatment of SrVO$_3$.
Cluster Perturbation Theory (CPT) is a computationally economic method commonly used to estimate the momentum and energy resolved single-particle Greens function. It has been used extensively in direct comparisons with experiments that effectively measure the single-particle Greens function, e.g., angle-resolved photoemission spectroscopy. However, many experimental observables are given by two-particle correlation functions. CPT can be extended to compute two-particle correlation functions by approximately solving the Bethe-Salpeter equation. We implement this method and focus on the transverse spin-susceptibility, measurable via inelastic neutron scattering or with optical probes of atomic gases in optical lattices. We benchmark the method with the one-dimensional Fermi-Hubbard model at half filling by comparing with known results.
The imaginary-time Greens function is a building block of various numerical methods for correlated electron systems. Recently, it was shown that a model-independent compact orthogonal representation of the Greens function can be constructed by decomposing its spectral representation. We investigate the performance of this so-called textit{intermedaite representation} (IR) from several points of view. First, for two simple models, we study the number of coefficients necessary to achieve a given tolerance in expanding the Greens function. We show that the number of coefficients grows only as $O(log beta)$ for fermions, and converges to a constant for bosons as temperature $T=1/beta$ decreases. Second, we show that this remarkable feature is ascribed to the properties of the physically constructed basis functions. The fermionic basis functions have features in the spectrum whose width is scaled as $O(T)$, which are consistent with the low-$T$ properties of quasiparticles in a Fermi liquid state. On the other hand, the properties of the bosonic basis functions are consistent with those of spin/orbital susceptibilities at low $T$. These results demonstrate the potential wide application of the IR to calculations of correlated systems.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
