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Traversing Quantum Many-Body Hilbert...

Hendry, Douglas,

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Traversing Quantum Many-Body Hilbert Spaces with Neural Networks /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Traversing Quantum Many-Body Hilbert Spaces with Neural Networks // Douglas Hendry.
作者:	Hendry, Douglas,
面頁冊數:	1 electronic resource (103 pages)
附註:	Source: Dissertations Abstracts International, Volume: 84-10, Section: B.
Contained By:	Dissertations Abstracts International84-10B.
標題:	Condensed matter physics. -
電子資源:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=30421497
ISBN:	9798379421908

Traversing Quantum Many-Body Hilbert Spaces with Neural Networks /
Hendry, Douglas,

Traversing Quantum Many-Body Hilbert Spaces with Neural Networks /Douglas Hendry. - 1 electronic resource (103 pages)

Source: Dissertations Abstracts International, Volume: 84-10, Section: B.

Understanding strongly correlated quantum many-body systems requires dealing with a large configuration space comprised of a set of all possible measurable configurations. The total number of configurations grows exponentially with the size of the system, which makes exact numerical calculations impossible for even moderately sized systems. Since the advent of high-temperature superconductivity and the subsequent interest in strongly correlated phases of matter, progress in the field has been marked by ingenuity of the field to overcome these computational limitations. The first techniques to emerge were inspired by quantum chemistry and based on exact diagonalization, which is limited to small clusters, and different variants of quantum Monte Carlo, that suffers from the sign problem in fermionic and frustrated systems. Circa 1992, the density matrix renormalization group (DMRG) became one of the major breakthroughs of the past few decades. Despite the success of DMRG for one-dimensional(1D) and quasi-one-dimensional geometries, extensions to actual two-dimensional systems remain challenging and applications are constrained to long cylinders and strips. One promising alternative is to combine one the oldest methods, variational wave functions (VWFs), with neural networks, which have been used to recently with great success in machine learning.The focus of this dissertation is on developing novel variational Monte Carlo algorithms to make neural network variational wave functions applicable to many problems in quantum many-body physics. These algorithms draw from existing variational wave-function, tensor network, and machine learning methods. We calculate dynamical spectral functions using the vector correction and Chebyshev expansion method. We do finite temperature calculations with minimally entangled thermal states. Finally, we do ground state calculations for the frustrated J1−J2 Heisenberg model. We benchmark these results using restricted Boltzmann machines as the neural network for the the variational wave-functions.

English

ISBN: 9798379421908Subjects--Topical Terms:

3173567
Condensed matter physics.
Subjects--Index Terms:

Machine learning

Traversing Quantum Many-Body Hilbert Spaces with Neural Networks /
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653 $a Quantum many-body
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653 $a Variatational monte carlo
653 $a Variational wave function
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