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A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference

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Gapless Hamiltonians for the toric code using the projected entangled pair state formalism.

Carlos Fernández-González¹, Norbert Schuch, Michael M Wolf

¹Departamento de Física de los Materiales, Universidad Nacional de Educación a Distancia (UNED), 28040 Madrid, Spain.

Physical Review Letters

|February 2, 2013

Summary

Researchers created a new Hamiltonian that shares the ground state of Kitaev's toric code but exhibits continuous spectrum gapless excitations. This method, using projected entangled pair states, offers a way to design novel Hamiltonians for 2D systems.

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Area of Science:

Condensed Matter Physics
Quantum Information Theory

Background:

Kitaev's toric code is a key model in topological quantum computation, known for its ground state degeneracy.
Understanding Hamiltonians with unique ground states is crucial for developing new quantum materials and algorithms.

Purpose of the Study:

To construct a Hamiltonian that preserves the ground space of Kitaev's toric code.
To introduce gapless excitations with a continuous spectrum into such a system.

Main Methods:

Utilizing the framework of projected entangled pair states (PEPS).
Developing a general construction applicable to a broad range of 2D quantum systems.

Main Results:

Successfully constructed a Hamiltonian sharing the toric code's ground space.
Demonstrated the emergence of gapless excitations with a continuous spectrum in the thermodynamic limit.
Introduced the concept of "uncle Hamiltonians" as a class of such systems.

Conclusions:

The construction provides a method to engineer Hamiltonians with tunable properties, moving beyond the gapped nature of the original toric code.
This work opens avenues for exploring novel quantum phases of matter and their excitations.