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Keyword: conformal invariance ×Clear all

3 claims from 1 paper

1. Physics and Astronomy › Quantum many-body systems

   Simulating disordered quantum Ising chains via dense and sparse restricted Boltzmann machines

   Pilati and Pieri · Physical review. E · 2020

   The paper uses sparse restricted Boltzmann machines as variational wave functions for disordered quantum spin chains, comparing them with dense versions and using them to guide quantum Monte Carlo simulations.

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   1. UncheckedIn tests on pure and random quantum Ising chains, sparse restricted Boltzmann machines trained more easily and outperformed dense ones.“We find that the sparse connectivity facilitates the training process and allows sparse RBMs to outperform the dense counterparts.”
   2. UncheckedUsing sparse restricted Boltzmann machines to guide projective quantum Monte Carlo is said to cut computational cost and avoid biases from finite walker populations.“Furthermore, the use of sparse RBMs as guiding functions for PQMC simulations allows us to perform PQMC simulations at a reduced computational cost, avoiding possible biases due to finite random-walker populations.”
   3. UncheckedMagnetisation profiles from the simulations match the Fisher-de Gennes scaling relation, including the scaling dimension predicted by renormalisation-group analysis.“The magnetization profiles agree with the Fisher-de Gennes scaling relation for conformally invariant systems, including the scaling dimension predicted by the renormalization-group analysis.”