Related papers: Mapping topological order in coordinate space
We propose an alternative formulation of the $Z_2$ topological index for quantum spin Hall systems and band insulators when time reversal invariance is not broken. The index is expressed in terms of the Chern numbers of the bands of the…
We demonstrate the realization of topological band structures by exploiting the intrinsic spin-orbit coupling of dipolar interactions in combination with broken time-reversal symmetry. The system is based on polar molecules trapped in a…
We show that the concept of topological order, introduced to describe ordered quantum systems which cannot be classified by broken symmetries, also applies to classical systems. Starting from a specific example, we show how to use pure…
A scheme is proposed to construct integer and fractional topological quantum states of fermions in two spatial dimensions. We devise models for such states by coupling wires of non-chiral Luttinger liquids of electrons, that are arranged in…
The engineering of topological non-trivial states of matter, using cold atoms, has made great progress in the last decade. Driven by experimental successes, it has become of major interest in the cold atom community. In this work we…
Topological insulators are noninteracting, gapped fermionic systems which have gapless boundary excitations. They are characterized by topological invariants, which can be written in many different ways, including in terms of Green's…
We study the extended Bose-Hubbard model on the square lattice at half filling as a function of next-nearest neighbor hopping amplitude and interaction strength. To variationally map out the phase diagram of this model, we develop a…
We elucidate how Chern and topological insulators fulfill an area law for the entanglement entropy. By explicit construction of a family of lattice Hamiltonians, we are able to demonstrate that the area law contribution can be tuned to an…
We theoretically propose a new route to control magnetic and topological orders in a broad class of insulating magnets with a DC electric field. We show from the strong-coupling expansion that magnetic exchange interactions along the…
We proof the existence of two different topological classes of low-energy k.p Hamiltonians for Chern insulators. Using the paradigmatic example of single-valley two-band models, we show that k.p Hamiltonians that we dub local have a…
Topological order has been proposed to go beyond Landau symmetry breaking theory for more than twenty years. But it is still a challenging problem to generally detect it in a generic many-body state. In this paper, we will introduce a…
The topology of an object describes global properties that are insensitive to local perturbations. Classic examples include string knots and the genus (number of handles) of a surface: no manipulation of a closed string short of cutting it…
Protected by the chiral symmetry, three dimensional chiral topological insulators are characterized by an integer-valued topological invariant. How this invariant could emerge in physical observables is an important question. Here we show…
It has recently been shown that in every spatial dimension there exist precisely five distinct classes of topological insulators or superconductors. Within a given class, the different topological sectors can be distinguished, depending on…
We show that the topological index of a wavefunction, computed in the space of twisted boundary phases, is preserved under Hilbert space truncation, provided the truncated state remains normalizable. If truncation affects the boundary…
Topological quantum phases of matter have been a topic of intense interest in contemporary condensed matter physics. Extensive efforts are devoted to investigate various exotic properties of topological matters including topological…
We define a class of insulators with gapless surface states protected from localization due to the statistical properties of a disordered ensemble, namely due to the ensemble's invariance under a certain symmetry. We show that these…
The interplay between the two fundamental concepts of topological order and reflection positivity allows one to characterize the ground states of certain many-body Hamiltonians. We define topological order in an appropriate fashion and show…
The notion of topology in physical systems is associated with the existence of a nonlocal ordering that is insensitive to a large class of perturbations. This brings robustness to the behaviour of the system and can serve as a ground for…
Topological insulators subject to a time-symmetry-breaking perturbation are predicted to display a magneto-electric effect that causes the electric and magnetic induction fields to mix at the material's surface. This effect induces…