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Exact projected entangled pair ground states with topological Euler invariant
Thorsten B Wahl1, Wojciech J Jankowski2, Adrien Bouhon2,3
1TCM Group, Cavendish Laboratory, Department of Physics, Cambridge, UK. tw344@cam.ac.uk.
Nature Communications
|January 2, 2025
Summary
We introduce gapped Projected Entangled Pair States (PEPS) with Euler topology, representing the first tensor network for a 2D topological phase. These states offer new avenues for quantum spin liquids and quantum information.
Area of Science:
- Condensed Matter Physics
- Quantum Information Theory
- Topological Phases of Matter
Background:
- Projected Entangled Pair States (PEPS) are crucial tensor network states for simulating quantum many-body systems.
- Topological phases of matter exhibit properties robust against local perturbations, characterized by topological invariants.
- Band geometry and quantum geometrical bounds offer insights into the properties of quantum states.
Purpose of the Study:
- To construct gapped Projected Entangled Pair States (PEPS) exhibiting non-trivial Euler topology.
- To explore the connection between band geometry, quantum geometrical bounds, and the realization of topological phases in PEPS.
- To develop interacting variants of these topological PEPS and investigate their properties.
Main Methods:
- Utilizing optimal conditions related to quantum geometrical bounds for non-interacting systems.
- Constructing gapped parent Hamiltonians with flat bands and PEPS as unique ground states.
- Employing unitary circuits to formulate interacting PEPS and their parent Hamiltonians.
Main Results:
- Demonstrated gapped PEPS with non-trivial Euler topology, protected by crystalline symmetries.
- Established these PEPS as the first tensor network representation of a non-interacting, gapped two-dimensional topological phase.
- Identified characteristic entanglement features shared between free-fermionic and interacting topological PEPS.
- Revealed that these PEPS unexpectedly possess a finite topological invariant.
Conclusions:
- The developed PEPS models provide a novel platform for studying topological phases in a tensor network framework.
- These findings pave the way for new research in quantum spin liquids, quantum Hall physics, and quantum information.
- The study bridges concepts from band geometry, tensor networks, and topological phases of matter.
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