1. Restricted Boltzmann machine representation for the groundstate and excited states of Kitaev Honeycomb model
- Author
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Babak Haghighat, Mohammadreza Noormandipour, Youran Sun, Noormandipour, Mohammadreza [0000-0001-9294-2035], and Apollo - University of Cambridge Repository
- Subjects
High Energy Physics - Theory ,Paper ,Focus on Machine Learning for Quantum Physics ,conformal blocks ,Lattice (group) ,Boltzmann machine ,FOS: Physical sciences ,Topological quantum computer ,Theoretical physics ,Condensed Matter - Strongly Correlated Electrons ,topological field theory ,46 Information and Computing Sciences ,Artificial Intelligence ,4611 Machine Learning ,Periodic boundary conditions ,4601 Applied Computing ,Quantum computer ,Physics ,Kitaev honeycomb model ,Strongly Correlated Electrons (cond-mat.str-el) ,Disordered Systems and Neural Networks (cond-mat.dis-nn) ,Condensed Matter - Disordered Systems and Neural Networks ,Human-Computer Interaction ,machine learning ,High Energy Physics - Theory (hep-th) ,Excited state ,Ising model ,Ground state ,Software ,restricted Boltzmann machine - Abstract
In this work, the capability of restricted Boltzmann machines (RBMs) to find solutions for the Kitaev honeycomb model with periodic boundary conditions is investigated. The measured groundstate (GS) energy of the system is compared and, for small lattice sizes (e.g. $3 \times 3$ with $18$ spinors), shown to agree with the analytically derived value of the energy up to a deviation of $0.09\%$. Moreover, the wave-functions we find have $99.89\%$ overlap with the exact ground state wave-functions. Furthermore, the possibility of realizing anyons in the RBM is discussed and an algorithm is given to build these anyonic excitations and braid them for possible future applications in quantum computation. Using the correspondence between topological field theories in (2+1)d and 2d CFTs, we propose an identification between our RBM states with the Moore-Read state and conformal blocks of the $2$d Ising model., Comment: (15+5) pages, 11 figures, 5 tables: Minor journal revisions and additions. + Journal ref
- Published
- 2022
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