Related papers: Hopfions in lattice dimer model
Topological materials (TMs) are well-known for their topological protected properties. Phononic system has the advantage of direct observation and engineering of topological phenomena on the macroscopic scale. For the inverse design of 3D…
Motivated by experimental progress in the growth of heavy transition metal oxides, we theoretically study a class of lattice models of interacting fermions with strong spin-orbit coupling. Focusing on interactions of intermediate strength,…
We extend the planar Pfaffian formalism for the evaluation of the Ising partition function to lattices of high topological genus g. The 3D Ising model on a cubic lattice, where g is proportional to the number of sites, is discussed in…
The Hofstadter problem is the lattice analog of the quantum Hall effect and is the paradigmatic example of topology induced by an applied magnetic field. Conventionally, the Hofstadter problem involves adding $\sim 10^4$ T magnetic fields…
Topological defects, called magnetic hedgehogs, realize emergent magnetic monopoles, which are not allowed in the ordinary electromagnetism described by Maxwell's equations. Such monopoles were experimentally discovered in magnets in two…
We study the stability of Hopfions embedded in the Ginzburg-Landau (GL) model of two oppositely charged components. It has been shown by Babaev et al. [Phys. Rev. B 65, 100512 (2002)] that this model contains the Faddeev-Skyrme (FS) model,…
We investigate the Hubbard Hamiltonian on ladders where the number of sites per rung alternates between two and three. These geometries are bipartite, with a non-equal number of sites on the two sublattices. Thus they share a key feature of…
Hopf insulator is a representative class of three-dimensional topological insulators beyond the standard topological classification methods based on K-theory. In this letter, we discover the metallic counterpart of the Hopf insulator in the…
We study topological properties of classical spherical center vortices with the low-lying eigenmodes of the Dirac operator in the fundamental and adjoint representations using both the overlap and asqtad staggered fermion formulations. In…
Recently, the concept of topological insulators has been generalized to topological semimetals, including three-dimensional (3D) Weyl semimetals, 3D Dirac semimetals, and 3D node-line semimetals. In particular, several compounds (e.g.,…
A universal topological marker has been proposed recently to map the topological invariants of Dirac models in any dimension and symmetry class to lattice sites. Using this topological marker, we examine the conditions under which the…
In the continuum O(3) sigma model in two spatial dimensions, there are topological solitons whose size can be stabilized by adding Skyrme and potential terms. This paper describes a lattice version, namely a natural way of modifying the 2d…
Using a {\it collective} Monte Carlo algorithm we study the low-temperature and long-distance properties of two systems of two-dimensional classical tops. Both systems have the same spin-wave dynamics (low-temperature behavior) as a large…
It is known that the topological Hopf term in two-dimensional (2D) spin systems can be derived by coupling to massless Dirac fermions. We establish a universal rule governing the generation of Hopf terms in 2D quantum spin systems coupled…
We present a theory of three dimensional fractionalized topological insulators in the form of U(1) spin liquids with gapped fermionic spinons in the bulk and topologically protected gapless spinon surface states. Starting from a spin-1/2…
We introduce a Hamiltonian for fermions on a lattice and prove a theorem regarding its topological properties. We identify the topological criterion as a $\mathbb{Z}_2-$ topological invariant $p(\textbf{k})$ (the Pfaffian polynomial). The…
Recent experiments show that periodic modulations of cold atoms in optical lattices may be used to engineer and explore interesting models. We show that double modulation, combining lattice shaking and modulated interactions allows for the…
Crystalline symmetries give rise to topological invariants that can distinguish quantum phases of matter. Understanding these in strongly interacting systems is an ongoing research direction requiring non-perturbative methods. Recent…
The combinatorial mutation of polygons, which transforms a given lattice polygon into another one, is an important operation to understand mirror partners for two-dimensional Fano manifolds, and the mutation-equivalent polygons give…
We discuss how to apply the dimer method to Ising models on group lattices having non trivial topological genus $g$. We find that the use of group extension and the existence of both external and internal group isomorphisms greatly reduces…