Related papers: Twisted Kitaev quantum double model as local topol…
This thesis addresses whether it is possible to build a robust memory device for quantum information. A three-dimensional gapped lattice spin model is found which demonstrates for the first time that a reliable quantum memory at finite…
Using superconducting quantum circuits, we propose an approach to construct a Kitaev lattice, i.e., an anisotropic spin model on a honeycomb lattice with three types of nearest-neighbor interactions. We study two particular cases to…
We investigate the extension of pure-state symmetry protected topological phases to mixed-state regime with a strong U(1) and a weak $\mathbb{Z}_2$ symmetries in one-dimensional spin systems by the concept of quantum channels. We propose a…
We propose a new formulation which realizes exact twisted supersymmetry for all the supercharges on a lattice by twisted superspace formalism. We show explicit examples of N=2 twisted supersymmetry invariant BF and Wess-Zumino models in two…
We present a generalization of the Luttinger-Tisza-Lyons-Kaplan (LTLK) theory of classical ground states of Bravais lattices with Heisenberg coupling to non-Bravais lattices. It consists of adding certain Lagrange parameters to the diagonal…
The classical nearest neighbor Kitaev-Heisenberg model on the triangular lattice is known to host $\mathbb{Z}_2$ spin-vortices forming a crystalline superstructure in the ground state. The $\mathbb{Z}_2$ vortices in this system can be…
We extend the Kitaev model defined for the Pauli-matrices to the Clifford algebra of $\Gamma$-matrices, taking the $4 \times 4$ representation as an example. On a decorated square lattice, the ground state spontaneously breaks time-reversal…
We provide a detailed study of the general structure of two-dimensional topological stabilizer quantum error correcting codes, including subsystem codes. Under the sole assumption of translational invariance, we show that all such codes can…
We prove the conjectured classification of topological phases in two spatial dimensions with gappable boundary, in a simplified setting. Two gapped ground states of lattice Hamiltonians are in the same quantum phase of matter, or…
We consider 1d Hamiltonian systems whose ground states display symmetry protected topological order. We show that ground states within the topological phase cannot be connected with each other through LOCC between a bipartition of the…
In recent years, there have been many studies on local stabilizer codes. Under the assumption of translation and scale invariance Yoshida classified such codes. His result implies that translation invariant 2D color codes are equivalent to…
We present quantum dimer models in two dimensions which realize metallic ground states with Z2 topological order. Our models are generalizations of a dimer model introduced in [PNAS 112,9552-9557 (2015)] to provide an effective description…
Topological quantum codes are intrinsically fault-tolerant to local noise, and underlie the theory of topological phases of matter. We explore geometry to enhance the performance of topological quantum codes by rotating the four dimensional…
We revisit the Kitaev model for fault tolerant quantum computing on a square lattice with underlying quantum double $D(G)$ symmetry, where $G$ is a finite group. We provide projection operators for its quasiparticles content as irreducible…
This work explores the use of a tree tensor network ansatz to simulate the ground state of a local Hamiltonian on a two-dimensional lattice. By exploiting the entropic area law, the tree tensor network ansatz seems to produce quasi-exact…
We analyze the class of Generalized Double Semion (GDS) models in arbitrary dimensions from the point of view of lattice Hamiltonians. We show that on a $d$-dimensional spatial manifold $M$ the dual of the GDS is equivalent, up to constant…
The ground state of the Kitaev quantum spin liquid on a honeycomb lattice is an intriguing many-body state characterized by its topological order and massive entanglement. One of the significant issues is to prepare and manipulate the…
The Kitaev honeycomb model is a paradigm of exactly-solvable models, showing non-trivial physical properties such as topological quantum order, abelian and non-abelian anyons, and chirality. Its solution is one of the most beautiful…
We establish an intriguing connection between quantum phase transitions and bifurcations in the ground-state fidelity per lattice site, and construct the universal order parameter for quantum Ising model in a transverse magnetic field on an…
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…