Transformer Wave Function for the Shastry-Sutherland Model: emergence of a Spin-Liquid Phase
arxiv(2023)
摘要
Quantum magnetism in two-dimensional systems represents a lively branch of
modern condensed-matter physics. In the presence of competing super-exchange
couplings, magnetic order is frustrated and can be suppressed down to zero
temperature, leading to exotic ground states. The Shastry-Sutherland model,
describing S=1/2 degrees of freedom interacting in a two-dimensional lattice,
portrays a simple example of highly-frustrated magnetism, capturing the
low-temperature behavior of SrCu_2(BO_3)_2 with its intriguing
properties. Here, we investigate this problem by using a Vision Transformer to
define an extremely accurate variational wave function. From a technical side,
a pivotal achievement relies on using a deep neural network with real-valued
parameters, parametrized with a Transformer, to map physical spin
configurations into a high-dimensional feature space. Within this abstract
space, the determination of the ground-state properties is simplified,
requiring only a single output layer with complex-valued parameters. From the
physical side, we supply strong evidence for the stabilization of a spin-liquid
between the plaquette and antiferromagnetic phases. Our findings underscore the
potential of Neural-Network Quantum States as a valuable tool for probing
uncharted phases of matter, opening opportunities to establish the properties
of many-body systems.
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