Dynamical Signature of Symmetry Fractionalization in Frustrated Magnets

The nontrivialness of quantum spin liquid (QSL) typically manifests in the non-local observables that signifies their existence, however, this fact actually casts shadow on detecting QSL with experimentally accessible probes. Here, we provide a solution by unbiasedly demonstrating dynamical signature of anyonic excitations and symmetry fractionalization in QSL. Employing large-scale quantum Monte Carlo simulation and stochastic analytic continuation, we investigate the extended XXZ model on the kagome lattice, and find out that across the phase transitions from Z2 QSLs to different symmetry breaking phases, spin spectral functions can reveal the presence and condensation of emergent anyonic spinon and vison excitations, in particular the translational symmetry fractionalization of the latter, which can be served as the unique dynamical signature of the seemingly ephemeral QSLs in spectroscopic techniques such as inelastic neutron or resonance (inelastic) X-ray scatterings.Comment: 8 pages,6 figure

Fractionalization in an Easy-axis Kagome Antiferromagnet

We study an antiferromagnetic spin-1/2 model with up to third nearest-neighbor couplings on the Kagome lattice in the easy-axis limit, and show that its low-energy dynamics are governed by a four site XY ring exchange Hamiltonian. Simple ``vortex pairing'' arguments suggest that the model sustains a novel fractionalized phase, which we confirm by exactly solving a modification of the Hamiltonian including a further four-site interaction. In this limit, the system is a featureless ``spin liquid'', with gaps to all excitations, in particular: deconfined S^z=1/2 bosonic ``spinons'' and Ising vortices or ``visons''. We use an Ising duality transformation to express vison correlators as non-local strings in terms of the spin operators, and calculate the string correlators using the ground state wavefunction of the modified Hamiltonian. Remarkably, this wavefunction is exactly given by a kind of Gutzwiller projection of an XY ferromagnet. Finally, we show that the deconfined spin liquid state persists over a finite range as the additional four-spin interaction is reduced, and study the effect of this reduction on the dynamics of spinons and visons.Comment: best in color but readable in B+

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

Destroying a topological quantum bit by condensing Ising vortices

The imminent realization of topologically-protected qubits in fabricated systems will provide not only an elementary implementation of fault-tolerant quantum computing architecture, but also an experimental vehicle for the general study of topological order. The simplest topological qubit harbors what is known as a Z$_2$ liquid phase, which encodes information via a degeneracy depending on the system's topology. Elementary excitations of the phase are fractionally charged objects called {\it spinons}, or Ising flux vortices called {\it visons}. At zero temperature a Z$_2$ liquid is stable under deformations of the Hamiltonian until spinon or vison condensation induces a quantum phase transition destroying the topological order. In this paper, we use quantum Monte Carlo to study a vison-induced transition from a Z$_2$ liquid to a valence-bond solid in a quantum dimer model on the kagome lattice. Our results indicate that this critical point is controlled by a new universality class beyond the standard Landau paradigm.Comment: 5 pages, 4 figures. Published versio

Fractionalization, topological order, and cuprate superconductivity

This paper is concerned with the idea that the electron is fractionalized in the cuprate high-$T_c$ 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