Parity-Time Symmetric Holographic Principle

Area of Science:

• Quantum Physics
• Condensed Matter Physics
• Atomic, Molecular, and Optical Physics

Background:

• The avoided level crossing phenomenon is fundamental across physics, appearing in Landau-Zener transitions, condensed matter band structures, and relativistic quantum physics.
• This phenomenon originates from the Hamiltonian of a single qubit system.

Purpose of the Study:

• To revisit the avoided level crossing phenomenon in a spinless relativistic quantum particle in (1+1)-dimensional spacetime.
• To establish a connection between this phenomenon and a spin-1/2 system under a PT-symmetric Hamiltonian.
• To explore the application of PT-symmetric and non-Hermitian physics in quantum simulation.

Main Methods:

• Simulating 1-dimensional eigenvalue problems using a single qubit.
• Generalizing the relation to map N-dimensional bulk eigenvalue problems onto the time evolution of (N-1)-dimensional edge states governed by a non-Hermitian Hamiltonian.
• Analyzing the PT-symmetry of the evolution under parity symmetry conditions.

Main Results:

• A novel relation is established between relativistic quantum particles and PT-symmetric Hamiltonians, enabling qubit-based simulation of eigenvalue problems.
• The eigenvalue problem of bulk systems can be mapped to the edge state evolution of non-Hermitian Hamiltonians, encoding bulk states as edge state holograms.
• The temporal evolution of edge states can decode these holographic bulk states.

Conclusions:

• The study demonstrates the application of PT-symmetric and non-Hermitian physics in quantum simulation.
• It provides insights into fundamental symmetries by linking bulk and edge state properties.
• The findings offer a new perspective on simulating complex quantum systems.