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Edge theories in projected entangled pair state models.

S Yang1, L Lehman2, D Poilblanc3

  • 1Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Strasse 1, D-85748 Garching, Germany.

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|February 4, 2014
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Summary
This summary is machine-generated.

We study low-energy excitations in 2D spin systems using projected entangled pair states. Topological order in the bulk protects edge states, revealing unconventional properties and rich phase diagrams for these edge Hamiltonians.

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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.