Motivated by the recent synthesis of Li beta -Li sub(2) IrO sub(3) -a spin-orbit entangled j = 1/2 Mott insulator with a three-dimensional lattice structure of the Ir super(4+) ions-we consider ...generalizations of the Kitaev model believed to capture some of the microscopic interactions between the iridium moments on various trivalent lattice structures in three spatial dimensions. Of particular interest is the so-called hyperoctagon lattice-the premedial lattice of the hyperkagome lattice, for which the ground state is a gapless quantum spin liquid where the gapless Majorana modes form an extended two-dimensional Majorana Fermi surface. We demonstrate that this Majorana Fermi surface is inherently protected by lattice symmetries and discuss possible instabilities. We thus provide the first example of an analytically tractable microscopic model of interacting SU(2) spin-1/2 degrees of freedom in three spatial dimensions that harbors a spin liquid with a two-dimensional spinon Fermi surface.
Weyl spin liquids Hermanns, M; O'Brien, K; Trebst, S
Physical review letters,
2015-Apr-17, Volume:
114, Issue:
15
Journal Article
Peer reviewed
Open access
The fractionalization of quantum numbers in interacting quantum many-body systems is a central motif in condensed-matter physics with prominent examples including the fractionalization of the ...electron in quantum Hall liquids or the emergence of magnetic monopoles in spin-ice materials. Here, we discuss the fractionalization of magnetic moments in three-dimensional Kitaev models into Majorana fermions (and a Z_{2} gauge field) and their emergent collective behavior. We analytically demonstrate that the Majorana fermions form a Weyl superconductor for the Kitaev model on the recently synthesized hyperhoneycomb structure of β-Li_{2}IrO_{3} when applying a magnetic field. We characterize the topologically protected bulk and surface features of this state, which we dub a Weyl spin liquid, including thermodynamic and transport signatures.
A thermal signatureAlthough the material α-ruthenium chloride exhibits some of the physics associated with Kitaev spin liquids, it is not a perfect representation of this model. Yokoi et al. probed ...the limits of the Kitaev description by studying the thermal Hall response in this material. Applying an external magnetic field both in the plane of the sample and at an angle to it, the researchers observed a half-integer quantization of the thermal Hall signal. The findings suggest the formation of a topological state consistent with the Kitaev model.Science, aay5551, this issue p. 568Half-integer thermal quantum Hall conductance has recently been reported for the two-dimensional honeycomb material α-RuCl3. We found that the half-integer thermal Hall plateau appears even for a magnetic field with no out-of-plane components. The measured field-angular variation of the quantized thermal Hall conductance has the same sign structure as the topological Chern number of the pure Kitaev spin liquid. This observation suggests that the non-Abelian topological order associated with fractionalization of the local magnetic moments persists even in the presence of non-Kitaev interactions in α-RuCl3.
Topological phases in frustrated quantum spin systems have fascinated researchers for decades. One of the earliest proposals for such a phase was the chiral spin liquid, a bosonic analogue of the ...fractional quantum Hall effect, put forward by Kalmeyer and Laughlin in 1987. Elusive for many years, recent times have finally seen this phase realized in various models, which, however, remain somewhat artificial. Here we take an important step towards the goal of finding a chiral spin liquid in nature by examining a physically motivated model for a Mott insulator on the Kagome lattice with broken time-reversal symmetry. We discuss the emergent phase from a network model perspective and present an unambiguous numerical identification and characterization of its universal topological properties, including ground-state degeneracy, edge physics and anyonic bulk excitations, by using a variety of powerful numerical probes, including the entanglement spectrum and modular transformations.
In quantum mechanics, stringnet condensed states-a family of prototypical states exhibiting nontrivial topological order-can be classified via their long-range entanglement properties, in particular, ...topological corrections to the prevalent area law of the entanglement entropy. Here we consider classical analogs of such string-net models whose partition function is given by an equal-weight superposition of classical stringnet configurations. Our analysis of the Shannon and Renyi entropies for a bipartition of a given system reveals that the prevalent volume law for these classical entropies is augmented by subleading topological corrections that are intimately linked to the anyonic theories underlying the construction of the classical models. We determine the universal values of these topological corrections for a number of underlying anyonic theories including SU(2)k, SU(N) sub(1), and SU(N) sub(2) theories.
Galois conjugates of topological phases Freedman, M. H.; Gukelberger, J.; Hastings, M. B. ...
Physical review. B, Condensed matter and materials physics,
01/2012, Volume:
85, Issue:
4
Journal Article
Peer reviewed
Open access
Galois conjugation relates unitary conformal field theories and topological quantum field theories (TQFTs) to their nonunitary counterparts. Here we investigate Galois conjugates of quantum double ...models, such as the Levin-Wen model. While these Galois-conjugated Hamiltonians are typically non-Hermitian, we find that their ground-state wave functions still obey a generalized version of the usual code property (local operators do not act on the ground-state manifold) and hence enjoy a generalized topological protection. The key question addressed in this paper is whether such nonunitary topological phases can also appear as the ground states of Hermitian Hamiltonians. Specific attempts at constructing Hermitian Hamiltonians with these ground states lead to a loss of the code property and topological protection of the degenerate ground states. Beyond this, we rigorously prove that no local change of basis can transform the ground states of the Galois-conjugated doubled Fibonacci theory into the ground states of a topological model whose Hermitian Hamiltonian satisfies Lieb-Robinson bounds. These include all gapped local or quasilocal Hamiltonians. A similar statement holds for many other nonunitary TQFTs. One consequence is that these nonunitary TQFTs do not describe physical realizations of topological phases. In particular, this implies that the "Gaffnian" wave function can not be the ground state of a gapped fractional quantum Hall state.
We establish the double perovskite Ba2CeIrO6 as a nearly ideal model system for j=1/2 moments, with resonant inelastic x-ray scattering indicating that the ideal j=1/2 state contributes by more than ...99% to the ground-state wave function. The local j=1/2 moments form an fcc lattice and are found to order antiferromagnetically at TN=14K, more than an order of magnitude below the Curie-Weiss temperature. Model calculations show that the geometric frustration of the fcc Heisenberg antiferromagnet is further enhanced by a next-nearest neighbor exchange, and a significant size of the latter is indicated by ab initio theory. Our theoretical analysis shows that magnetic order is driven by a bond-directional Kitaev exchange and by local distortions via a strong magnetoelastic effect. Both, the suppression of frustration by Kitaev exchange and the strong magnetoelastic effect are typically not expected for j=1/2 compounds making Ba2CeIrO6 a riveting example for the rich physics of spin-orbit entangled Mott insulators.
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