Gauge Invariant and Anyonic Symmetric Transformer and RNN Quantum States for Quantum Lattice Models

Understand

Symmetries such as gauge invariance and anyonic symmetry play a crucial role in quantum many-body physics.

• We develop a general approach to constructing gauge invariant or anyonic symmetric autoregressive neural network quantum states, including a wide range of architectures such as Transformer and recurrent neural network (RNN), for quantum lattice models.
• These networks can be efficiently sampled and explicitly obey gauge symmetries or anyonic constraint.
• We prove that our methods can provide exact representation for the ground and excited states of the 2D and 3D toric codes, and the X-cube fracton model.