Entanglement-Guided Search for Parent Hamiltonians

Area of Science:

• Quantum Information Theory
• Condensed Matter Physics
• Quantum Field Theory

Background:

• Identifying the parent Hamiltonian for a given quantum state is crucial for understanding its properties and dynamics.
• Existing methods often struggle with complex or strongly correlated systems.
• The entanglement structure of wave functions encodes significant information about their underlying physics.

Purpose of the Study:

• To develop a systematic and efficient method for reconstructing parent Hamiltonians from wave functions.
• To demonstrate the applicability of the method to various nontrivial quantum states and phases.
• To highlight the role of entanglement in simplifying Hamiltonian reconstruction.

Main Methods:

• Utilizing an ansatz relating the reduced density matrix to the parent Hamiltonian, exact at the field theory level.
• Employing a convex minimization procedure in the space of relative entropies.
• Testing the method on diverse ground state wave functions, including conformal and symmetry-protected topological phases.

Main Results:

• Successfully reconstructed parent Hamiltonians for several nontrivial quantum states.
• Demonstrated the method's effectiveness for quantum critical points in 2D antiferromagnets.
• Confirmed that the entanglement structure of wave functions significantly aids in finding parent Hamiltonians.

Conclusions:

• The proposed method offers a powerful tool for Hamiltonian reconstruction.
• Entanglement properties are key to simplifying the search for parent Hamiltonians.
• This approach is applicable to strongly coupled field theories and various quantum phases.