Edge theories in projected entangled pair state models

Area of Science:

• Condensed Matter Physics
• Quantum Many-Body Systems
• Topological Phases of Matter

Background:

• Low-energy excitations in 2D spin lattice systems are crucial for understanding quantum materials.
• Projected entangled pair state (PEPS) models offer a powerful framework for simulating such systems.
• Edge phenomena in condensed matter systems often exhibit unique properties distinct from the bulk.

Purpose of the Study:

• To analyze low-energy excitations in 2D spin lattice systems at zero temperature.
• To investigate the emergence and properties of physical excitations at the edge of these systems.
• To explore the phase diagram of edge Hamiltonians and their relation to bulk topological order.

Main Methods:

• Utilized projected entangled pair state (PEPS) models for theoretical analysis.
• Investigated perturbations in the bulk to identify edge excitations.
• Developed a procedure to derive the edge Hamiltonian from bulk properties.

Main Results:

• Identified specific degrees of freedom corresponding to edge excitations.
• Demonstrated that the derived edge Hamiltonian can exhibit a rich phase diagram.
• Showcased that topological order in the bulk constrains edge models, leading to unconventional properties.

Conclusions:

• The study reveals a strong connection between bulk topological order and edge physics in 2D spin systems.
• Topologically ordered bulk phases can protect fragile edge states, such as ferromagnetic Ising chains, from symmetry breaking.
• The framework provides a method to construct and analyze edge Hamiltonians with unique characteristics.