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Topological order in an entangled SU(2) ⊗ XY spin-orbital ring
Wojciech Brzezicki1, Jacek Dziarmaga1, Andrzej M Oleś2
1Marian Smoluchowski Institute of Physics, Jagellonian University, Reymonta 4, PL-30059 Kraków, Poland.
Physical Review Letters
|April 8, 2014
Summary
Closing a one-dimensional spin-orbital model chain reveals novel topological order. Spins become interdependent on the ring topology, unlike in open chains, leading to unique ground state properties and excitations.
Area of Science:
- Condensed Matter Physics
- Quantum Materials
- Topological Phases of Matter
Background:
- One-dimensional spin-orbital models with SU(2) spin and XY orbital interactions typically separate spin and orbital degrees of freedom on open chains.
- The concept of topological order describes exotic phases of matter characterized by robust ground state degeneracies and fractionalized excitations.
- Ring topology in condensed matter systems can lead to unique phenomena not observed in linear or open chain configurations.
Purpose of the Study:
- To investigate the emergence of topological order in a one-dimensional spin-orbital model when transitioning from an open to a ring (periodic) topology.
- To analyze the interdependence of spin and orbital degrees of freedom under different topological constraints.
- To characterize the ground state properties and low-energy excitations of the model on a closed ring.
Main Methods:
- Utilized a unitary transformation to analyze the spin and orbital interactions.
- Investigated the model's behavior on both open and closed (ring) chain topologies.
- Examined ground state degeneracy and excitation spectra as a function of total quasimomentum.
Main Results:
- On a closed ring, spins become interdependent and form two half-rings with opposite quasimomenta, unlike their separation on an open chain.
- Transitioning from open to periodic topology partially lifts the ground state degeneracy.
- Low-energy excitations exhibit a novel quadratic dispersion relation with respect to the total quasimomentum.
Conclusions:
- The ring topology induces a novel type of topological order in the spin-orbital model, breaking the independent behavior of spins and orbitals.
- This emergent topological order, characterized by specific ground state and excitation properties, is reminiscent of the behavior seen in the infinite-U Hubbard chain.
- Topology plays a crucial role in dictating the quantum phases and emergent phenomena in one-dimensional interacting systems.
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