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Entanglement Features of Random Neural Network Quantum States
Restricted Boltzmann machines (RBMs) are a class of neural networks that have
been successfully employed as a variational ansatz for quantum many-body wave
functions. Here, we develop an analytic method to study quantum many-body spin
states encoded by random RBMs with independent and identically distributed
complex Gaussian weights. By mapping the computation of ensemble-averaged
quantities to statistical mechanics models, we are able to investigate the
parameter space of the RBM ensemble in the thermodynamic limit. We discover
qualitatively distinct wave functions by varying RBM parameters, which
correspond to distinct phases in the equivalent statistical mechanics model.
Notably, there is a regime in which the typical RBM states have near-maximal
entanglement entropy in the thermodynamic limit, similar to that of Haar-random
states. However, these states generically exhibit nonergodic behavior in the
Ising basis, and do not form quantum state designs, making them distinguishable
from Haar-random states.Comment: 22 pages, 13 figures, close to published versio
Itinerant quantum critical point with frustration and non-Fermi-liquid
Employing the self-learning quantum Monte Carlo algorithm, we investigate the
frustrated transverse-field triangle-lattice Ising model coupled to a Fermi
surface. Without fermions, the spin degrees of freedom undergoes a second-order
quantum phase transition between paramagnetic and clock-ordered phases. This
quantum critical point (QCP) has an emergent U(1) symmetry and thus belongs to
the (2+1)D XY universality class. In the presence of fermions, spin
fluctuations introduce effective interactions among fermions and distort the
bare Fermi surface towards an interacting one with hot spots and Fermi pockets.
Near the QCP, non-Fermi-liquid behavior are observed at the hot spots, and the
QCP is rendered into a different universality with Hertz-Millis type exponents.
The detailed properties of this QCP and possibly related experimental systems
are also discussed.Comment: 9 pages, 8 figure
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