Exploring large-scale entanglement in quantum simulation

Area of Science:

• Quantum Information Science
• Condensed Matter Physics
• Quantum Simulation

Background:

• Entanglement is crucial in quantum many-body systems, but its structure is challenging to uncover in large systems.
• The entanglement Hamiltonian (EH) offers an effective description of reduced density operators for large subsystems.
• Experimental verification of theoretical predictions regarding entanglement structure is a key goal.

Purpose of the Study:

• To experimentally investigate the entanglement structure of quantum many-body systems using the entanglement Hamiltonian.
• To test fundamental predictions of quantum field theory in the context of lattice models.
• To explore the scaling of entanglement entropy in ground and excited states.

Main Methods:

• Utilized a 51-ion programmable quantum simulator to prepare ground and excited states of a 1D XXZ Heisenberg chain.
• Employed sample-efficient 'learning' techniques to determine the entanglement Hamiltonian for subsystems up to 20 lattice sites.
• Analyzed the structure of the entanglement Hamiltonian and the scaling of von Neumann entanglement entropies.

Main Results:

• Provided compelling experimental evidence for a local structure of the entanglement Hamiltonian.
• Confirmed fundamental predictions of quantum field theory (Bisognano-Wichmann theorems) adapted to lattice models.
• Observed a transition from area-law to volume-law scaling of entanglement entropies between ground and excited states.
• Demonstrated that the reduced quantum state forms a Gibbs ensemble with a spatially varying temperature profile, a signature of entanglement.

Conclusions:

• The experimental confirmation of local entanglement Hamiltonian structure validates theoretical predictions in quantum matter.
• The observed entanglement entropy scaling transitions offer insights into the nature of entanglement in different quantum states.
• The developed methods and findings are broadly applicable to studying entanglement in complex many-body systems, potentially aiding in the pursuit of quantum advantage.