13,017 research outputs found
Vison excitations in near-critical quantum dimer models
We study vison excitations in a quantum dimer model interpolating between the
Rokhsar-Kivelson models on the square and triangular lattices. In the
square-lattice case, the model is known to be critical and characterized by
U(1) topological quantum numbers. Introducing diagonal dimers brings the model
to a Z_2 resonating-valence-bond phase. We study variationally the emergence of
vison excitations at low concentration of diagonal dimers, close to the
critical point. We find that, in this regime, vison excitations are large in
size and their structure resembles vortices in type-II superconductors.Comment: 6 pages, 2 figures, minor corrections corresponding to the published
versio
Single hole and vortex excitations in the doped Rokhsar-Kivelson quantum dimer model on the triangular lattice
We consider the doped Rokhsar-Kivelson quantum dimer model on the triangular
lattice with one mobile hole (monomer) at the Rokhsar-Kivelson point. The
motion of the hole is described by two branches of excitations: the hole may
either move with or without a trapped Z2 vortex (vison). We perform a study of
the hole dispersion in the limit where the hole hopping amplitude is much
smaller than the interdimer interaction. In this limit, the hole without vison
moves freely and has a tight-binding spectrum. On the other hand, the hole with
a trapped vison is strongly constrained due to interference effects and can
only move via higher-order virtual processes.Comment: 4 pages, 4 figures; minor changes, replaced by published versio
The nature of visons in the perturbed ferromagnetic and antiferromagnetic Kitaev honeycomb models
The Kitaev honeycomb model hosts a fascinating fractionalized state of matter
featuring emergent Majorana fermions and a vison particle that carries the flux
of an emergent gauge field. In the exactly solvable model these visons are
static but certain perturbations can induce their motion. We show that the
nature of the vison motion induced by a Zeeman field is sharply distinct in the
ferromagnetic vs the antiferromagnetic Kitaev models. Namely, in the
ferromagnetic model the vison has a trivial non-projective translational
symmetry, whereas in the antiferromagnetic Kitaev model it has a projective
translational symmetry with -flux per unit cell. The vison band of the
ferromagnetic case has zero Berry curvature, and no associated intrinsic
contribution to the thermal Hall effect. In contrast, in the antiferromagnetic
case there are two gapped vison bands with opposite Chern numbers and an
associated intrinsic vison contribution to the thermal Hall effect. We discuss
these findings in the light of the physics of the spin liquid candidate
-RuCl.Comment: 15 pages, 14 figure
Crystallization of the resonating valence bond liquid as vortex condensation
We show that the liquid-to-crystal quantum phase transition in the
Rokhsar--Kivelson dimer model on the two-dimensional triangular lattice occurs
as a condensation of vortex-like excitations called ``visons''. This conclusion
is drawn from the numerical studies of the vison spectrum in the liquid phase
by using the Green's function Monte Carlo method. We find that visons remain
the lowest excitation throughout the liquid phase and that their gap decreases
continuously to zero at the phase transition. The nature of the crystal phase
and the second order of the phase transition are in agreement with the earlier
prediction of Moessner and Sondhi [Phys. Rev. B 63, 224401 (2001)].Comment: 4 pages, 4 figure
Fractionalization, topological order, and cuprate superconductivity
This paper is concerned with the idea that the electron is fractionalized in
the cuprate high- materials. We show how the notion of topological order
may be used to develop a precise theoretical characterization of a
fractionalized phase in spatial dimension higher than one. Apart from the
fractional particles into which the electron breaks apart, there are
non-trivial gapped topological excitations - dubbed "visons". A cylindrical
sample that is fractionalized exhibits two disconnected topological sectors
depending on whether a vison is trapped in the "hole" or not. Indeed, "vison
expulsion" is to fractionalization what the Meissner effect ("flux expulsion")
is to superconductivity. This understanding enables us to address a number of
conceptual issues that need to be confronted by any theory of the cuprates
based on fractionalization ideas. We argue that whether or not the electron
fractionalizes in the cuprates is a sharp and well-posed question with a
definite answer. We elaborate on our recent proposal for an experiment to
unambiguously settle this issue.Comment: 18 pages, 7 figure
Extending Luttinger's theorem to Z(2) fractionalized phases of matter
Luttinger's theorem for Fermi liquids equates the volume enclosed by the
Fermi surface in momentum space to the electron filling, independent of the
strength and nature of interactions. Motivated by recent momentum balance
arguments that establish this result in a non-perturbative fashion [M.
Oshikawa, Phys. Rev. Lett. {\bf 84}, 3370 (2000)], we present extensions of
this momentum balance argument to exotic systems which exhibit quantum number
fractionalization focussing on fractionalized insulators, superfluids and
Fermi liquids. These lead to nontrivial relations between the particle filling
and some intrinsic property of these quantum phases, and hence may be regarded
as natural extensions of Luttinger's theorem. We find that there is an
important distinction between fractionalized states arising naturally from half
filling versus those arising from integer filling. We also note how these
results can be useful for identifying fractionalized states in numerical
experiments.Comment: 24 pages, 5 eps figure
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