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Keyword: irreducible representations ×Clear all

2 claims from 1 paper

1. Physics and Astronomy › Quantum many-body systems

   Restricted Boltzmann Machines for Quantum States with Non-Abelian or Anyonic Symmetries

   Vieijra, Casert, Nys et al. · Physical Review Letters · 2020

   The paper shows that sampling in a basis of irreducible representations, not spins, lets a Boltzmann machine respect non-Abelian symmetries, and it applies this to Heisenberg chains and anyonic spin chains.

   Unchecked2 claims
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   1. UncheckedUsing a basis of irreducible representations as input gave much more accurate ground states of 1D spin-half and spin-1 Heisenberg chains than the s_z basis.“We apply our methodology to find the ground states of the one-dimensional antiferromagnetic Heisenberg (AFH) model with spin-half and spin-1 degrees of freedom, and obtain a substantially higher accuracy than when using the $s_z$-basis as input to the neural network.”
   2. UncheckedThe authors' neural-network ansatz can target excited states, shown by calculating the energy gap of the antiferromagnetic Heisenberg (AFH) model.“The proposed ansatz can target excited states, which is illustrated by calculating the energy gap of the AFH model.”