Quantum many-body physics II: Models and methods

We continue our previous investigation of the properties of a system of either fermions or bosons interacting in one dimension by a two-body potential $V(\mathcal{r})=\frac{g}{{\mathcal{r}}^{2}}$ with periodic boundary conditions. A method is introduced which provides a physically intuitive description of the excited states. The energies are given explicitly for finite and infinite systems, including all corrections due to quasiparticle interaction. The method is shown to apply to other one-dimensional systems as well. In particular, the results are applied to a classical one-dimensional $N$ -body model of Dyson---the Coulomb gas in a Brownian medium.We continue our previous investigation of the properties of a system of either fermions or bosons interacting in one dimension by a two-body potential $V(\mathcal{r})=\frac{g}{{\mathcal{r}}^{2}}$ with periodic boundary conditions. A method is introduced which provides a physically intuitive description of the excited states. The energies are given explicitly for finite and infinite systems, including all corrections due to quasiparticle interaction. The method is shown to apply to other one-dimensional systems as well. In particular, the results are applied to a classical one-dimensional $N$-body model of Dyson---the Coulomb gas in a Brownian medium.

Physical Review AMar 1, 1972706 citations

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Ferreira, Lidia S, A. C. Fonseca, Ludwig Streit

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Sparse Modeling in Quantum Many-Body Problems

Junya Otsuki, Masayuki Ohzeki, Hiroshi Shinaoka +1 more

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 explain a given dataset. This concept reminds us physics, where the goal is to find a small number of physical laws that are hidden behind complicated phenomena. Sparse modeling extends the target of physics from natural phenomena to data, and may be interpreted as "physics for data". The first half of this review introduces sparse modeling for physicists. It is assumed that readers have physics background but no expertise in data science. The second half reviews applications. Matsubara Green's function, which plays a central role in descriptions of correlated systems, has been found to be sparse, meaning that it contains little information. This leads to (i) a new method for solving the ill-conditioned inverse problem for analytical continuation, and (ii) a highly compact representation of Matsubara Green's function, which enables efficient calculations for quantum many-body systems.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 explain a given dataset. This concept reminds us physics, where the goal is to find a small number of physical laws that are hidden behind complicated phenomena. Sparse modeling extends the target of physics from natural phenomena to data, and may be interpreted as "physics for data". The first half of this review introduces sparse modeling for physicists. It is assumed that readers have physics background but no expertise in data science. The second half reviews applications. Matsubara Green's function, which plays a central role in descriptions of correlated systems, has been found to be sparse, meaning that it contains little information. This leads to (i) a new method for solving the ill-conditioned inverse problem for analytical continuation, and (ii) a highly compact representation of Matsubara Green's function, which enables efficient calculations for quantum many-body systems.

arXiv:1911.04116Journal of the Physical Society of JapanDec 12, 201948 citations

We continue our previous investigation of the properties of a system of either fermions or bosons interacting in one dimension by a two-body potential

V(\mathcal{r})=\frac{g}{{\mathcal{r}}^{2}}

with periodic boundary conditions. A method is introduced which provides a physically intuitive description of the excited states. The energies are given explicitly for finite and infinite systems, including all corrections due to quasiparticle interaction. The method is shown to apply to other one-dimensional systems as well. In particular, the results are applied to a classical one-dimensional

N

-body model of Dyson---the Coulomb gas in a Brownian medium.