Related papers: $U(1)$ symmetry-enriched toric code
We discuss the ground state of a two dimensional electron-lattice system described by a Su-Schrieffer-Heeger type Hamiltonian with a half-filled electronic band, for which it has been pointed out in the previous paper [J. Phys. Soc. Jpn. 69…
A quantum deformation of 3-dimensional lattice gauge theory is defined by applying the Reshetikhin-Turaev functor to a Heegaard diagram associated to a given cell complex. In the root-of-unity case, the construction is carried out with a…
We demonstrate that two toric code layers on the square lattice coupled by an Ising interaction display two distinct phases with intrinsic topological order. The second-order quantum phase transition between the weakly-coupled…
We provide a construction of examples of semistable degeneration via toric geometry. The applications include a higher dimensional generalization of classical degeneration of K3 surface into 4 rational components, an algebraic geometric…
This is an outline of work in progress concerning an algebro-geometric form of the Strominger-Yau-Zaslow conjecture. We introduce a limited type of degeneration of Calabi-Yau manifolds, which we call toric degenerations. For these, the…
We analyze the geometric aspects of unitary evolution of general states for a multilevel quantum system by exploiting the structure of coadjoint orbits in the unitary group Lie algebra. Using the same method in the case of SU(3) we study…
We present a solution of Kitaev's spin model on the honeycomb lattice and of related topologically ordered spin models. We employ a Jordan-Wigner type fermionization and find that the Hamiltonian takes a BCS type form, allowing the system…
We investigate the quantum phase diagram of the $K$-layer Ising toric code corresponding to $K$ layers of two-dimensional toric codes coupled by Ising interactions. While for small Ising interactions the system displays $\mathbb{Z}_2^K$…
We analyse the low temperature properties of a system of classical Heisenberg spins on a hexagonal lattice with Kitaev couplings. For a lattice of 2N sites with periodic boundary conditions, we show that the ground states form an (N+1)…
We study measurement-based quantum computation (MQC) using as quantum resource the planar code state on a two-dimensional square lattice (planar analogue of the toric code). It is shown that MQC with the planar code state can be efficiently…
A hallmark feature of topologically ordered states of matter is the dependence of ground state degeneracy (GSD) on the topology of the manifold determined by the global shape of the system. Although the topology of a physical system is…
The Z_2 topological order in Z_2 spin liquid and in exactly soluble Kitaev toric code model is the simplest topological order for 2+1D bosonic systems. More general 2+1D bosonic topologically ordered states can be constructed via exact…
A lattice gauge theory is described by a redundantly large vector space that is subject to local constraints, and can be regarded as the low energy limit of an extended lattice model with a local symmetry. We propose a numerical…
We construct a family of short-range resonating-valence-bond wave functions on a layered cubic lattice, allowing for a tunable anisotropy in the amplitudes assigned to nearest-neighbour valence bonds along one axis. Monte Carlo simulations…
We construct an exactly soluble spin-$\frac{1}2$ model on a honeycomb lattice, which is a generalization of Kitaev model. The topological phases of the system are analyzed by study of the ground state sector of this model, the vortex-free…
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…
We analyze the toric code model in the presence of quenched disorder, which is introduced via different types of random magnetic fields. In general, close to a quantum phase transition between a spin polarized phase and a topologically…
We present a general computational framework to investigate ground state properties of quantum spin models on infinite two-dimensional lattices using automatic differentiation-based gradient optimization of infinite projected entangled-pair…
The Kitaev-Heisenberg model on the honeycomb lattice has been studied for the purpose of finding exotic states such as quantum spin liquid and topological orders. On the kagome lattice, in spite of a spin-liquid ground state in the…
In topological phases of matter, the interplay between intrinsic topological order and global symmetry is an interesting task. In the study of topological orders with discrete global symmetry, an important systematic approach is the…