2019/10/29 by Huan He, He, Huan, Yunqin Zheng +5 · 1 citation
Physics and Astronomy · #FOS: Physical sciences #Physics of Superconductivity and Magnetism #Quantum Physics (quant-ph) #Quantum and electron transport phenomena #Quantum many-body systems #Strongly Correlated Electrons (cond-mat.str-el)
paper · pdf · doi:10.48550/arxiv.1910.13454
openalex publication_date 2019/10/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider representing two classes of 1D quantum wave functions of spin systems, including the AKLT and CFT correlator wave functions, in terms of multi-layer restricted Boltzmann machines. In our prescription, the AKLT wave function can be exactly represented by a 2-layer restricted Boltzmann machine with five hidden spins per visible spin. The construction can be generalized to prove that any MPS wave function on N unit cells with finite bond dimension can be approximated by a 2-layer restricted Boltzmann machine with O(N) hidden spins within an error which scales linearly with N. The Haldane-Shastry wave function or a chiral boson CFT correlator wave function, as any Jastrow type of wave functions, can be exactly written as a 1-layer Boltzmann machine with O(N2) hidden spins and N visible spins. Applying the cumulant expansion, we further find that the chiral boson CFT correlator wave function (with small vertex operator conformal dimension α, i.e., α<0.1) can be approximated, within 99.9% accuracy up to 22 visible spins, by a 1-layer RBM with O(N) hidden spins. The cumulant expansion also leads us to a physically inspiring result in which the hidden spins of the restricted Boltzmann machine can be interpreted as the conformal tower of the chiral boson CFT on the cylinder.