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Entanglement in 3D Kitaev spin liquids

Matern, S., Maria Hermanns

Published Jan 1, 2018• 7 citations
OpenAlex

Abstract

Quantum spin liquids are highly fascinating quantum liquids in which the spin degrees of freedom fractionalize. An interesting class of spin liquids axe the exactly solvable, three-dimensional Kitaev spin liquids. Their fractionalized excitations are Majonara fermions, which may exhibit a variety of topological band structures-ranging from topologically protected Weyl semimetals over nodal semi-metals to systems with Majorana Fermi surfaces. We study the entanglement spectrum of such Kitaev spin liquids and verify that it is closely related to the topologically protected edge spectrum. Moreover, we find that in some cases the entanglement spectrum contains even more information about the topological features than the surface spectrum, and thus provides a simple and reliable tool to probe the topology of a system.

Related papers

Entanglement in 3D Kitaev spin liquids

Stephanie Matern, Maria Hermanns

Abstract Quantum spin liquids are highly fascinating quantum liquids in which the spin degrees of freedom fractionalize. An interesting class of spin liquids are the exactly solvable, three-dimensional Kitaev spin liquids. Their fractionalized excitations are Majonara fermions, which may exhibit a variety of topological band structures—ranging from topologically protected Weyl semi-metals over nodal semi-metals to systems with Majorana Fermi surfaces. We study the entanglement spectrum of such Kitaev spin liquids and verify that it is closely related to the topologically protected edge spectrum. Moreover, we find that in some cases the entanglement spectrum contains even more information about the topological features than the surface spectrum, and thus provides a simple and reliable tool to probe the topology of a system.

arXiv:1712.07715•Journal of Statistical Mechanics Theory and Experiment•Jun 1, 2018•6 citations

Crystalline Kitaev spin liquids

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Three-dimensional Kitaev models -- generalizations of the well known exactly solvable Kitaev honeycomb model -- exhibit a rich variety of quantum spin liquid phases. Their fractionalized excitations are Majorana fermions that may form topological band structures. These can be enriched by lattice symmetries, as shown in the present work. In particular, the authors propose two new instances of Kitaev spin liquids that exhibit nodal chains and 3D Dirac nodes in the bulk. Such crystalline Kitaev spin liquids are direct generalizations of crystalline topological insulators, albeit in an interacting spin system. A potential material realization in metal-organic frameworks is also discussed.

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Three-Dimensional Kitaev Spin Liquids

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The formation of quantum spin liquids in frustrated magnets represents an exciting possibility due to the rather exotic features they harbor, including fractionalized excitations and emergent gauge fields. \nUnfortunately, they are notoriously difficult to study as there are often no good analytical methods available and quantum Monte Carlo simulations are hindered by the negative sign problem. \nThe Kitaev honeycomb model is a notable exception of a frustrated quantum model which is exactly solvable and which hosts a number of distinct quantum spin liquid ground states. \nAs such, it allows for a rare opportunity to study the physics of spin liquids with full analytical control. \n \nIn this thesis, we study the fractionalization of spin-1/2 moments into Majorana fermions and an emergent Z2 gauge field in a generalization of the Kitaev honeycomb model to a number of three-dimensional lattices. \nWhile the excitations of the gauge field are always gapped, the fermionic quasiparticles may exhibit a gapless dispersion, forming fully two-dimensional Fermi surfaces, symmetry protected nodal lines, or topological Weyl nodes. \nWe show that one can deduce rather general constraints on the possible gapless excitations by making use of an object called the projective symmetry group. \nIn doing so we provide a scheme for classifying the various gapless Kitaev spin liquids. \nA thorough analysis is carried out for a number of these spin liquids, primarily investigating the stability of the gapless modes and the novel features resulting from their sometimes non-trivial topology, as well as their effects on certain equal-time correlation functions.

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Kevin M. O'Brien, Maria Hermanns, Simon Trebst

In quantum magnetism, Kitaev's honeycomb model is well known for its gapped and gapless spin liquid ground states in which the elementary spin degrees of freedom fractionalize into Majorana fermions and a ${\mathbb{Z}}_{2}$ gauge field. In this paper, the authors discuss the gapless spin liquids arising in three-dimensional Kitaev models and show that the gapless Majorana fermions form metallic states which, depending on the underlying lattice structure, exhibit Fermi surfaces, nodal lines, or Weyl points.

arXiv:1511.05569•Physical review. B./Physical review. B•Feb 1, 2016•159 citations
Quantum spin liquids are highly fascinating quantum liquids in which the spin degrees of freedom fractionalize. An interesting class of spin liquids axe the exactly solvable, three-dimensional Kitaev spin liquids. Their fractionalized excitations are Majonara fermions, which may exhibit a variety of topological band structures-ranging from topologically protected Weyl semimetals over nodal semi-metals to systems with Majorana Fermi surfaces. We study the entanglement spectrum of such Kitaev spin liquids and verify that it is closely related to the topologically protected edge spectrum. Moreover, we find that in some cases the entanglement spectrum contains even more information about the topological features than the surface spectrum, and thus provides a simple and reliable tool to probe the topology of a system.
Abstract Quantum spin liquids are highly fascinating quantum liquids in which the spin degrees of freedom fractionalize. An interesting class of spin liquids are the exactly solvable, three-dimensional Kitaev spin liquids. Their fractionalized excitations are Majonara fermions, which may exhibit a variety of topological band structures—ranging from topologically protected Weyl semi-metals over nodal semi-metals to systems with Majorana Fermi surfaces. We study the entanglement spectrum of such Kitaev spin liquids and verify that it is closely related to the topologically protected edge spectrum. Moreover, we find that in some cases the entanglement spectrum contains even more information about the topological features than the surface spectrum, and thus provides a simple and reliable tool to probe the topology of a system.
Three-dimensional Kitaev models -- generalizations of the well known exactly solvable Kitaev honeycomb model -- exhibit a rich variety of quantum spin liquid phases. Their fractionalized excitations are Majorana fermions that may form topological band structures. These can be enriched by lattice symmetries, as shown in the present work. In particular, the authors propose two new instances of Kitaev spin liquids that exhibit nodal chains and 3D Dirac nodes in the bulk. Such crystalline Kitaev spin liquids are direct generalizations of crystalline topological insulators, albeit in an interacting spin system. A potential material realization in metal-organic frameworks is also discussed.
The formation of quantum spin liquids in frustrated magnets represents an exciting possibility due to the rather exotic features they harbor, including fractionalized excitations and emergent gauge fields. \nUnfortunately, they are notoriously difficult to study as there are often no good analytical methods available and quantum Monte Carlo simulations are hindered by the negative sign problem. \nThe Kitaev honeycomb model is a notable exception of a frustrated quantum model which is exactly solvable and which hosts a number of distinct quantum spin liquid ground states. \nAs such, it allows for a rare opportunity to study the physics of spin liquids with full analytical control. \n \nIn this thesis, we study the fractionalization of spin-1/2 moments into Majorana fermions and an emergent Z2 gauge field in a generalization of the Kitaev honeycomb model to a number of three-dimensional lattices. \nWhile the excitations of the gauge field are always gapped, the fermionic quasiparticles may exhibit a gapless dispersion, forming fully two-dimensional Fermi surfaces, symmetry protected nodal lines, or topological Weyl nodes. \nWe show that one can deduce rather general constraints on the possible gapless excitations by making use of an object called the projective symmetry group. \nIn doing so we provide a scheme for classifying the various gapless Kitaev spin liquids. \nA thorough analysis is carried out for a number of these spin liquids, primarily investigating the stability of the gapless modes and the novel features resulting from their sometimes non-trivial topology, as well as their effects on certain equal-time correlation functions.
Recently, there has been much effort in understanding topological phases of matter with gapless bulk excitations, which are characterized by topological invariants and protected intrinsic boundary states. Here we show that topological semimetals of Majorana fermions arise in exactly solvable Kitaev spin models on a series of three-dimensional lattices. The ground states of these models are quantum spin liquids with gapless nodal spectra of bulk Majorana fermion excitations. It is shown that these phases are topologically stable as long as certain discrete symmetries are protected. The corresponding topological indices and the gapless boundary states are explicitly computed to support these results. In contrast to previous studies of noninteracting systems, the phases discussed in this work are novel examples of gapless topological phases in interacting spin systems.
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.
In quantum magnetism, Kitaev's honeycomb model is well known for its gapped and gapless spin liquid ground states in which the elementary spin degrees of freedom fractionalize into Majorana fermions and a Z2{\mathbb{Z}}_{2}Z2​ gauge field. In this paper, the authors discuss the gapless spin liquids arising in three-dimensional Kitaev models and show that the gapless Majorana fermions form metallic states which, depending on the underlying lattice structure, exhibit Fermi surfaces, nodal lines, or Weyl points.