Mott Transition and Volume Law Entanglement with Neural Quantum States

Area of Science:

• Condensed matter physics
• Quantum mechanics
• Computational physics

Background:

• The Mott transition signifies a phase change in electronic systems from metal to insulator, driven by delocalization and repulsion.
• Dynamical mean-field theory (DMFT) offers exact solutions for bulk properties but is limited to the thermodynamic limit.
• Accurate simulation of finite-sized systems is crucial for understanding complex electronic behaviors.

Purpose of the Study:

• To introduce and validate neural network hidden fermion determinantal states (HFDS) for studying the Mott transition.
• To overcome limitations of existing methods like exact diagonalization and matrix product states (MPS) for finite systems.
• To gain novel insights into the wave function's behavior near the metal-insulator transition.

Main Methods:

• Implementation of neural network hidden fermion determinantal states (HFDS) to model the disordered, fully connected Hubbard model.
• Comparison of HFDS accuracy against dynamical mean-field theory (DMFT) and matrix product state (MPS) ansatz.
• Calculation of key physical observables including energy, double occupancy, quasiparticle weight, and energy gap.

Main Results:

• HFDS provide more accurate results in the metallic regime and near the Mott transition compared to MPS.
• The method successfully accesses wave function properties for finite system sizes beyond exact diagonalization limits.
• Novel insights into the wave function amplitudes were obtained, elucidating the transition mechanism.

Conclusions:

• HFDS represent a powerful new tool for simulating strongly correlated electron systems.
• This approach overcomes entanglement limitations that hinder other methods like MPS.
• The study opens new avenues for exploring quantum phenomena in condensed matter using neural quantum states.