Related papers: Holonomic quantum computation on graphene from Ati…
We present a formal geometric framework for the study of adiabatic quantum mechanics for arbitrary finite-dimensional non-degenerate Hamiltonians. This framework generalizes earlier holonomy interpretations of the geometric phase to…
The accumulation of non-trivial geometric phases in a material's response is often a tell-tale sign of a rich underlying internal structure. Studying quantum oscillations provides one of the ways to determine these geometrical phases, such…
We propose a general principle for the low-energy theory of narrow bands with concentrated Berry curvature and Fubini-Study metric in the form of a map to Anderson-"+" models composed of heavy fermions hybridizing and interacting with…
The recent experimental observations of designer Dirac Fermions and topological phases in molecular graphene are addressed theoretically. Using scattering theory we calculate the electronic structure of finite lattices of scattering centers…
The physics underlying the magnetization process of quantum antiferromagnets is revisited from the viewpoint of geometric phases. A continuum variant of the Lieb-Schultz-Mattis-type approach to the problem is put forth, where the…
Flat bands are of significant interest due to their potential for energy confinement and their ability to enable strongly correlated physics. Incorporating topology into flatband systems further enhances flatband mode robustness against…
We investigate the effect of spin-orbit coupling on the band structure of graphene-based two-dimensional Dirac fermion gases in the quantum Hall regime. Taking monolayer graphene as our first candidate, we show that a quantum phase…
We introduce a two-body quantum Hamiltonian model with spins-$\half$ located on the vertices of a 2D spatial lattice. The model exhibits an exact topological degeneracy in all coupling regimes. This is a remarkable non-perturbative effect.…
A geometric model for twisted $K$-homology is introduced. It is modeled after the Mathai-Melrose-Singer fractional analytic index theorem in the same way as the Baum-Douglas model of $K$-homology was modeled after the Atiyah-Singer index…
Gate-based quantum computers can in principle simulate the adiabatic dynamics of a large class of Hamiltonians. Here we consider the cyclic adiabatic evolution of a parameter in the Hamiltonian. We propose a quantum algorithm to estimate…
We illustrate the possibility of realizing band gaps in graphene-like systems that fall outside the existing classification of gapped Dirac Hamiltonians in terms of masses. As our primary example we consider a band gap arising due to…
The interplay of topological electronic band structures and strong interparticle interactions provides a promising path towards the constructive design of robust, long-range entangled many-body systems. As a prototype for such systems, we…
The theory of quantum computation can be constructed from the abstract study of anyonic systems. In mathematical terms, these are unitary topological modular functors. They underlie the Jones polynomial and arise in Witten-Chern-Simons…
We construct a unified operator framework for quantum holonomies generated from bosonic systems. For a system whose Hamiltonian is bilinear in the creation and annihilation operators, we find a holonomy group determined only by a set of…
We investigate the interaction between quantum anomalous Hall (QAH) phases hosted by two atomically thin hexagonal lattices and demonstrate the emergence of topological phases with large Chern numbers. Interlayer coupling between two…
A series of carbon allotropes with novel optoelectronic and rich topological properties is predicted by systematic first-principles calculations. These fascinating carbon allotropes can be derived by inserting acetylenic linkages…
We propose an efficient scheme for simulating the topological phases of matter based on silicon-vacancy (SiV) center arrays in phononic crystals. This phononic band gap structure allows for long-range spin-spin interactions with a tunable…
The quantum anomalous Hall (QAH) effect, first proposed in the Haldane model, is a paradigmatic example of the application of band topology in condensed matter physics. The recent experimental discoveries of high Chern number QAH effect in…
At half filling, the electronic structure of graphene can be modelled by a pair of free two-dimensional Dirac fermions. We explicitly demonstrate that in the presence of a geometrically induced gauge field, an everywhere-real Kekule…
When atomically thin two-dimensional (2D) materials are layered they often form incommensurate non-crystalline structures that exhibit long-period moir{\' e} patterns when examined by scanning probes. In this paper we present an approach…