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Variational Neural and Tensor Network Approximations of Thermal States

MPS-Authors
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Lu,  Sirui
Theory, Max Planck Institute of Quantum Optics, Max Planck Society;
MCQST - Munich Center for Quantum Science and Technology, External Organizations;
IMPRS (International Max Planck Research School), Max Planck Institute of Quantum Optics, Max Planck Society;

/persons/resource/persons232821

Giudice,  Giacomo
Theory, Max Planck Institute of Quantum Optics, Max Planck Society;
MCQST - Munich Center for Quantum Science and Technology, External Organizations;

/persons/resource/persons60441

Cirac,  J. Ignacio       
Theory, Max Planck Institute of Quantum Optics, Max Planck Society;
MCQST - Munich Center for Quantum Science and Technology, External Organizations;

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2401.14243.pdf
(Preprint), 4MB

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Citation

Lu, S., Giudice, G., & Cirac, J. I. (submitted). Variational Neural and Tensor Network Approximations of Thermal States.


Cite as: https://hdl.handle.net/21.11116/0000-000E-A830-E
Abstract
We introduce a variational Monte Carlo algorithm for approximating
finite-temperature quantum many-body systems, based on the minimization of a
modified free energy. We employ a variety of trial states -- both tensor
networks as well as neural networks -- as variational ans\"atze for our
numerical optimization. We benchmark and compare different constructions in the
above classes, both for one- and two-dimensional problems, with systems made of
up to \(N=100\) spins. Despite excellent results in one dimension, our results
suggest that the numerical ans\"atze employed have certain expressive
limitations for tackling more challenging two-dimensional systems.