Related papers: Abelian Topological Order on Lattice Enriched with…
Two-dimensional chiral magnets are known to host a variety of skyrmions, characterized by an integer topological charge. However, these systems typically favor uniform lattices as a thermodynamically stable phase composed of either…
We present a systematic framework to classify symmetry-enriched topological quantum spin liquids in two spatial dimensions. This framework can deal with all topological quantum spin liquids, which may be either Abelian or non-Abelian,…
We show that it is possible to formulate Abelian Chern-Simons theory on a lattice as a topological field theory. We discuss the relationship between gauge invariance of the Chern-Simons lattice action and the topological interpretation of…
The $su(2)$ coherent-state path-integral technique is employed to study lattice electrons strongly coupled to a quantum spin background. In the large-spin limit it is replaced with its classical counterpart that breaks the time-reversal…
Topologically protected spin states hold great promise for applications in next generation of memory circuits and spintronic devices. These intriguing textures typically emerge in bulk materials or heterostructures with broken inversion…
Topological matter is a popular topic in both condensed matter and cold atom research. In the past decades, a variety of models have been identified with fascinating topological features. Some, but not all, of the models can be found in…
Tensor network decompositions offer an efficient description of certain many-body states of a lattice system and are the basis of a wealth of numerical simulation algorithms. In a recent paper [arXiv:0907.2994v1] we discussed how to…
Kitaev's toric code is an exactly solvable model with $\mathbb{Z}_2$-topological order, which has potential applications in quantum computation and error correction. However, a direct experimental realization remains an open challenge.…
We present microscopic Hamiltonians that gap the Dirac fermions on the surface of topological crystalline insulators (TCIs) protected by reflection symmetry and create symmetry-preserving states with Abelian topological orders. For TCIs…
Three dimensional topological superconductors (TScs) protected by time reversal (T) symmetry are characterized by gapless Majorana cones on their surface. Free fermion phases with this symmetry (class DIII) are indexed by an integer n, of…
Here we investigate the internal sublattice symmetry, and thus the enriched topological classification of bosonic Bogoliubov excitations of thermodynamically stable free-boson systems with non-vanishing particle-number-nonconserving terms.…
We discuss the possible topological order/topological quantum field theory of different quantum Hall systems. Given the value of the Hall conductivity, we constrain the global symmetry of the low-energy theory and its anomaly. Specifically,…
Topological materials exhibit protected edge modes that have been proposed for applications in for example spintronics and quantum computation. While a number of such systems exist, it would be desirable to be able to test theoretical…
We explore various aspects of 2-form topological gauge theories in (3+1)d. These theories can be constructed as sigma models with target space the second classifying space $B^2G$ of the symmetry group $G$, and they are classified by…
We show that bosonic atoms loaded into orbital angular momentum $l=1$ states of a lattice in a diamond-chain geometry provides a flexible and simple platform for exploring a range of topological effects. This system exhibits robust edge…
We investigate domain walls between topologically ordered phases in two spatial dimensions and present a simple but general framework from which their degrees of freedom can be understood. The approach we present exploits the results on…
Fractal lattices, featuring the self-similarity symmetry, are often geometric descents of parent crystals, possessing all their discrete symmetries (such as rotations and reflections) except the translational ones. Here, we formulate three…
A crucial step in the history of General Relativity was Einstein's adoption of the principle of general covariance which demands a coordinate independent formulation for our spacetime theories. General covariance helps us to disentangle a…
A new technique is proposed to classify a topological field in abelian lattice gauge theories. We perform the classification by regarding the topological field as a local composite field of the gauge field tensor instead of the vector…
An interacting lattice model describing the subspace spanned by a set of strongly-correlated bands is rigorously coupled to density functional theory to enable ab initio calculations of geometric and topological material properties. The…