4 research outputs found
Symmetry-protected topological phases, conformal criticalities, and duality in exactly solvable SO() spin chains
We introduce a family of SO()-symmetric spin chains which generalize the
transverse-field Ising chain for . These spin chains are defined with
Gamma matrices and can be exactly solved by mapping to species of itinerant
Majorana fermions coupled to a static gauge field. Their phase
diagrams include a critical point described by the SO()
Wess-Zumino-Witten model as well as two distinct gapped phases. We show that
one of the gapped phases is a trivial phase and the other realizes a
symmetry-protected topological phase when . These two gapped phases
are proved to be related to each other by a Kramers-Wannier duality.
Furthermore, other elegant structures in the transverse-field Ising chain, such
as the infinite-dimensional Onsager algebra, also carry over to our models.Comment: 12 pages, 3 figure
Microscopic models for Kitaev's sixteenfold way of anyon theories
In two dimensions, the topological order described by gauge
theory coupled to free or weakly interacting fermions with a nonzero spectral
Chern number is classified by as predicted by
Kitaev [Ann. Phys. 321, 2 (2006)]. Here we provide a systematic and complete
construction of microscopic models realizing this so-called sixteenfold way of
anyon theories. These models are defined by matrices satisfying the
Clifford algebra, enjoy a global symmetry, and live on
either square or honeycomb lattices depending on the parity of . We show
that all these models are exactly solvable by using a Majorana representation
and characterize the topological order by calculating the topological spin of
an anyonic quasiparticle and the ground-state degeneracy. The possible
relevance of the and models to materials with
Kugel-Khomskii-type spin-orbital interactions is discussed.Comment: 6+9 pages, 2+1 figures, published versio
Fractionalized fermionic quantum criticality in spin-orbital Mott insulators
We study transitions between topological phases featuring emergent
fractionalized excitations in two-dimensional models for Mott insulators with
spin and orbital degrees of freedom. The models realize fermionic quantum
critical points in fractionalized Gross-Neveu universality classes in
(2+1) dimensions. They are characterized by the same set of critical exponents
as their ordinary Gross-Neveu counterparts, but feature a different energy
spectrum, reflecting the nontrivial topology of the adjacent phases. We
exemplify this in a square-lattice model, for which an exact mapping to a
- model of spinless fermions allows us to make use of large-scale
numerical results, as well as in a honeycomb-lattice model, for which we employ
-expansion and large- methods to estimate the critical behavior.
Our results are potentially relevant for Mott insulators with electronic
configurations and strong spin-orbit coupling, or for twisted bilayer
structures of Kitaev materials.Comment: 6+6 pages, 2+3 figures; v3 (minor changes, discussion on
strong-coupling limit
Flux crystals, Majorana metals, and flat bands in exactly solvable spin-orbital liquids
International audienceSpin-orbital liquids are quantum disordered states in systems with entangled spin and orbital degrees of freedom. We study exactly solvable spin-orbital models in two dimensions with selected Heisenberg-, Kitaev-, and Γ-type interactions, as well as external magnetic fields. These models realize a variety of spin-orbital-liquid phases featuring dispersing Majorana fermions with Fermi surfaces, nodal Dirac or quadratic band touching points, or full gaps. In particular, we show that Zeeman magnetic fields can stabilize nontrivial flux patterns and induce metamagnetic transitions between states with different topological character. Solvable nearest-neighbor biquadratic spin-orbital perturbations can be tuned to stabilize zero-energy flat bands. We discuss in detail the examples of SO(2)- and SO(3)-symmetric spin-orbital models on the square and honeycomb lattices, and use group-theoretical arguments to generalize to SO(ν)-symmetric models with arbitrary integer ν>1. These results extend the list of exactly solvable models with spin-orbital-liquid ground states and highlight the intriguing general features of such exotic phases. Our models are thus excellent starting points for more realistic modelling of candidate materials