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arXiv:1311.0991 · Physical Review Letters

Topological Order in an Entangled SU(2) ⊗XY Spin-Orbital Ring

Wojciech Brzezicki, Jacek Dziarmaga, Andrzej M. Oleś

Published Mar 18, 2014• 29 citations
arXivHTMLPDF

Abstract

We present rigorous topological order which emerges in a one-dimensional spin-orbital model due to the ring topology. Although this model with SU(2) spin and XY orbital interactions is known to exactly separate spins from orbitals by means of a unitary transformation on the open chain, we find that they are not quite independent when the chain is closed, and the spins form two half-rings carrying opposite quasimomenta. We show that on changing the topology from an open to a periodic chain, the degeneracy of the ground state is partially lifted while the low-energy excitations have a quadratic dispersion as a function of the total quasimomentum. This novel type of topological order which emerges from changing the topology from an open to a periodic chain is reminiscent of the infinite-U Hubbard chain.

DOI
10.1103/physrevlett.112.117204

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We show that a wide class of spin chains with topological frustration cannot develop any local order. In particular, we consider translational-invariant one-dimensional chains with frustrated boundary conditions, i.e. periodic boundary conditions and an odd number of sites, which possess a global SU(2) symmetry. This condition implies, even at a finite sizes, an exact degeneracy of the ground state and is quite general in absence of external fields. We directly evaluate the expectation value of operators with support over a finite range of lattice sites and show that, except for some precise conditions, they all decay algebraically, or faster, with the chain length and vanish in the thermodynamic limit. The exceptions that admit a finite order are cases with a higher ground state degeneracy in which the translational symmetry is broken by the ground state choice.
A one-dimensional model of coupled spin-1/2 spins and pseudospin-1/2 orbitals with nearest-neighbor interaction is rigorously shown to exhibit spin-orbital separation by means of a nonlocal unitary transformation. On an open chain, this transformation completely decouples the spins from the orbitals in such a way that the spins become paramagnetic while the orbitals form the soluble XXZ Heisenberg model. The nature of various correlations is discussed. The more general cases, which allow spin-orbital separation by the same method, are pointed out. A generalization for the orbital pseudospin greater than 1/2 is also discussed. Some qualitative connections are drawn with the recently observed spin-orbital separation in Sr2{}_{2}2​CuO3{}_{3}3​.
Motivated by the duality between site-centered spin and bond-centered spin in one-dimensional system, which connects two different constructions of fermions from the same set of Majorana fermions, we show that two-dimensional models with topological orders can be constructed from certain well-known models with classical orders characterized by symmetry breaking. Topology-dependent ground state degeneracy, vanishing two-point correlation functions, and unpaired Majorana fermions on boundaries emerge naturally from such construction. The approach opens a different way to construct and characterize topological orders.
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