Related papers: Sparse sampling and tensor network representation …
This lecture note reviews recently proposed sparse-modeling approaches for efficient ab initio many-body calculations based on the data compression of Green's functions. The sparse-modeling techniques are based on a compact orthogonal…
We propose the sparse modeling approach for quasiclassical theory of superconductivity, which reduces the computational cost of solving the gap equations. The recently proposed sparse modeling approach is based on the fact that the Green's…
Efficient ab initio calculations of correlated materials at finite temperature require compact representations of the Green's functions both in imaginary time and Matsubara frequency. In this paper, we introduce a general procedure which…
Two-particle Green's 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…
Several recent works have introduced highly compact representations of single-particle Green's functions in the imaginary time and Matsubara frequency domains, as well as efficient interpolation grids used to recover the representations. In…
This review paper describes the basic concept and technical details of sparse modeling and its applications to quantum many-body problems. Sparse modeling refers to methodologies for finding a small number of relevant parameters that well…
We generate the perturbative expansion of the single-particle Green's function and related self-energy for a half-filled single-band Hubbard model on a square lattice. We invoke algorithmic Matsubara integration to evaluate single-particle…
In this paper, we propose a new analytic continuation method to extract real frequency spectral functions from imaginary frequency Green's functions of quantum many-body systems. This method is based on the pole representation of Matsubara…
A Quantum Monte Carlo calculation of dynamical spin susceptibility in the half-filled 2D Hubbard model is presented for temperature $T=0.2t$ and an intermediate on-site repulsion $U=4t$. Using the singular value decomposition technique we…
This paper considers the problem of estimating the channel response (or Green's function) between multiple source-receiver pairs. Typically, the channel responses are estimated one-at-a-time: a single source sends out a known probe signal,…
The popular, stable, robust and computationally inexpensive cubic spline interpolation algorithm is adopted and used for finite temperature Green's function calculations of realistic systems. We demonstrate that with appropriate…
This paper shows how sparse, high-dimensional probability distributions could be represented by neurons with exponential compression. The representation is a novel application of compressive sensing to sparse probability distributions…
By introducing multipe-site correlation functions, we propose a hierarchical Green function approach, and apply it to study the characteristic properties of a 2D square lattice Hubbard model by solving the equation of motions of a…
We present a tensor-network-based method for simulating a weakly-measured quantum circuit. In particular, we use a Markov chain to efficiently sample measurements and contract the tensor network, propagating their effect forward along the…
We present a worm sampling method for calculating one- and two-particle Green's functions using continuous-time quantum Monte Carlo simulations in the hybridization expansion (CT-HYB). Instead of measuring Green's functions by removing…
We study tensor network states defined on an underlying graph which is sparsely connected. Generic sparse graphs are expander graphs with a high probability, and one can represent volume law entangled states efficiently with only polynomial…
Sparse representation has attracted great attention because it can greatly save storage resources and find representative features of data in a low-dimensional space. As a result, it may be widely applied in engineering domains including…
Tensor networks are efficient factorisations of high-dimensional tensors into a network of lower-order tensors. They have been most commonly used to model entanglement in quantum many-body systems and more recently are witnessing increased…
Compressive sensing has been successfully used for optimized operations in wireless sensor networks. However, raw data collected by sensors may be neither originally sparse nor easily transformed into a sparse data representation. This…
Strongly correlated electron systems are challenging to calculate, and entanglement in such systems is not widely analyzed. We present an approach that can be used as a post-processing step for calculating the two-site reduced density…