Entanglement Hamiltonian of Interacting Fermionic Models.

Area of Science:

• Condensed Matter Physics
• Quantum Many-Body Systems
• Computational Physics

Background:

• Calculating entanglement Hamiltonians for interacting fermionic systems is challenging.
• Numerical methods for strongly correlated electron systems have advanced, enabling entanglement spectrum and entropy calculations.
• Few explicit determinations of entanglement (modular) Hamiltonians exist.

Purpose of the Study:

• To introduce a novel technique for directly determining the entanglement Hamiltonian of interacting fermionic models.
• To implement and test this method on specific physical systems.
• To investigate the influence of physical temperature on the entanglement Hamiltonian.

Main Methods:

• Utilizing auxiliary field quantum Monte Carlo (AFQMC) simulations.
• Applying the method to a one-dimensional Hubbard chain divided into two segments.
• Implementing the technique on a Hubbard two-leg ladder partitioned into two chains.

Main Results:

• Successfully determined the entanglement Hamiltonian for the studied fermionic models.
• Observed the evolution of the entanglement Hamiltonian with varying physical temperatures.
• Demonstrated the applicability of the AFQMC-based technique for entanglement Hamiltonian calculations.

Conclusions:

• The developed AFQMC technique provides a direct route to calculating entanglement Hamiltonians.
• The study offers insights into the temperature dependence of entanglement in correlated fermionic systems.
• This method opens new avenues for exploring entanglement properties in complex quantum systems.