Machine-learning semilocal density functional theory for many-body lattice models at zero and finite temperature
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Journal ArticleDate:
2021Access:
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Nelson J., Tiwari R., Sanvito S., Machine-learning semilocal density functional theory for many-body lattice models at zero and finite temperature, Physical Review B, 2021, 103, 24Download Item:
Abstract:
We introduce a machine-learning density-functional-theory formalism for the spinless Hubbard model in one
dimension at both zero and finite temperature. In the zero-temperature case this establishes a one-to-one relation
between the site occupation and the total energy, which is then minimized at the ground-state occupation.
In contrast, at finite temperature the same relation is defined between the Helmholtz free energy and the
equilibrium site occupation. Most importantly, both functionals are semilocal, so that they are independent from
the size of the system under investigation and can be constructed over exact data for small systems. These
“exact” functionals are numerically defined by neural networks. We also define additional neural networks for
finite-temperature thermodynamical quantities, such as the entropy and heat capacity. These can be either a
functional of the ground-state site occupation or of the finite-temperature equilibrium site occupation. In the first
case their equilibrium value does not correspond to an extremal point of the functional, while it does in the second
case. Our work gives us access to finite-temperature properties of many-body systems in the thermodynamic
limit.
Sponsor
Grant Number
European Research Council (ERC)
QUEST
Irish Research Council (IRC)
GOIPG/2016/1056
SFI/HEA Irish Centre for High-End Computing (ICHEC)
Author's Homepage:
http://people.tcd.ie/tiwarirhttp://people.tcd.ie/sanvitos
Description:
PUBLISHED
Author: Tiwari, Rajarshi; Sanvito, Stefano
Sponsor:
European Research Council (ERC)Irish Research Council (IRC)
SFI/HEA Irish Centre for High-End Computing (ICHEC)
Type of material:
Journal ArticleCollections
Series/Report no:
Physical Review B;103;
24;
Availability:
Full text availableKeywords:
Machine learning, Lattice models in condensed matter, Hubbard model, Exact solutions for many-body systems, Electron-correlation calculations, Density functional theory, Approximation methods for many-body systems, FermionsSubject (TCD):
Nanoscience & Materials , DENSITY-FUNCTIONAL THEORY , MACHINE LEARNING , MANY-BODY THEORY , NEURAL NETWORKSDOI:
http://dx.doi.org/10.1103/PhysRevB.103.245111ISSN:
24699969 24699950Metadata
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