Spin-Holstein Models in Trapped-Ion Systems

Area of Science:

• Quantum simulation
• Condensed matter physics
• Quantum information science

Background:

• The Holstein model describes electron-phonon interactions, crucial in condensed matter.
• Simulating complex quantum many-body systems is computationally challenging.
• Trapped-ion systems offer a controllable platform for quantum simulations.

Purpose of the Study:

• To explore the use of trapped-ion quantum systems for studying generalized Holstein models.
• To benchmark advanced numerical calculation methods.
• To investigate the interplay of charge-density wave order, fermion pairing, and phase separation in many-electron systems.

Main Methods:

• Implementation of a spin-Holstein model using arrays of trapped ions.
• Utilizing a hybrid numerical approach combining non-Gaussian variational ansatz states and matrix product states.
• Benchmarking against standard density-matrix renormalization group calculations.

Main Results:

• Demonstrated the feasibility of simulating spin-Holstein models with trapped-ion quantum systems.
• Showcased the superiority of the hybrid simulation approach over standard methods.
• Provided insights into the competition between different emergent orders in many-electron systems.

Conclusions:

• Trapped-ion quantum simulators are effective for studying complex condensed matter models.
• The developed hybrid numerical method offers improved accuracy and efficiency.
• This work paves the way for more sophisticated quantum simulations of electron-phonon interactions.