Related papers: Kitaev model in regular hyperbolic tilings
We present an exactly solvable spin-orbital model based on the Gamma-matrix generalization of a Kitaev-type Hamiltonian. In the presence of small magnetic fields, the model exhibits a critical phase with a spectrum characterized by…
We study tilings of the plane composed of two repeating tiles of different assigned areas relative to an arbitrary periodic lattice. We classify isoperimetric configurations (i.e., configurations with minimal length of the interfaces) both…
We investigate the nature of the topological phase transition of the antiferromagnetic Kitaev model on the honeycomb lattice in the presence of a magnetic field along the [111] direction. The field opens a topological gap in the Majorana…
We describe how the entanglement renormalisation approach to topological lattice systems leads to a general procedure for treating the whole spectrum of these models, in which the Hamiltonian is gradually simplified along a parallel…
A new supersymmetric model for electrons with generalized hopping terms and Hubbard interaction on a one-dimensional lattice is solved by means of the Bethe Ansatz. We investigate the phase diagram of this model by studying the ground state…
We present a detailed study of the phase diagram of the Kitaev-Hubbard chain, that is the Kitaev chain in the presence of a nearest-neighbour density-density interaction, using both analytical techniques as well as DMRG. In the case of a…
We use a recently developed interpretable and unsupervised machine-learning method, the tensorial kernel support vector machine (TK-SVM), to investigate the low-temperature classical phase diagram of a generalized Heisenberg-Kitaev-$\Gamma$…
We present rigorous results for several variants of the Hubbard model in the strong-coupling regime. We establish a mathematically controlled perturbation expansion which shows how previously proposed effective interactions are, in fact,…
We introduce and solve a two-band model of spinless fermions with $p_x$-wave pairing on a square lattice. The model reduces to the well-known extended Harper-Hofstadter model with half-flux quanta per plaquette and weakly coupled Kitaev…
We define 2-dimensional topological substitutions. A tiling of the Euclidean plane, or of the hyperbolic plane, is substitutive if the underlying 2-complex can be obtained by iteration of a 2-dimensional topological substitution. We prove…
We consider the extended Hubbard model with attractive on-site interaction U and nearest-neighbor repulsions V. We construct an effective Hamiltonian H_{eff} for hopping t<<V and arbitrary U<0. Retaining the most important terms, H_{eff}…
In present work the effective singlet-triplet model for CuO2-layer on the grounds of multiband p-d model of strongly correlated electrons is obtained. The resulting Hamiltonian has a form of generalized singlet-triplet t-t'-J model for…
We introduce a broad class of simple models for quantum Hall states based on the expansion of their parent Hamiltonians near the one-dimensional limit of "thin cylinders", i.e. when one dimension $L_y$ of the Hall surface becomes comparable…
The celebrated Kitaev honeycomb model provides an analytically tractable example with an exact quantum spin liquid ground state. While in real materials, other types of interactions besides the Kitaev coupling ($K$) are present, such as the…
Topological spin liquids in two spatial dimensions are stable phases in the presence of a small magnetic field, but may give way to field-induced phenomena at intermediate field strengths. Sandwiched between the low-field spin liquid…
Kitaev magnets have emerged as pivotal systems for investigating frustrated magnetism, providing a unique platform to explore quantum phases governed by the interplay between bond-dependent anisotropy and external magnetic fields. However,…
The Kitaev surface-code model is the most studied example of a topologically ordered phase and typically involves four-spin interactions on a two-dimensional surface. A universal signature of this phase is topological entanglement entropy…
We derive a simple bijection between geometric plane perfect matchings on $2n$ points in convex position and triangulations on $n+2$ points in convex position. We then extend this bijection to monochromatic plane perfect matchings on…
We propose a new example of discrete holography that provides a new step towards establishing the AdS/CFT duality for discrete spaces. A class of boundary Hamiltonians is obtained in a natural way from regular tilings of the hyperbolic…
Turaev Viro invariants are amongst the most powerful tools to distinguish 3-manifolds: They are implemented in mathematical software, and allow practical computations. The invariants can be computed purely combinatorially by enumerating…