Related papers: Generating topological order from a 2D cluster sta…
We analyse the topology of the state space of two systems: i) N Ising spins +/-1 with the antiferromagnetic interactions on a triangular lattice, with the condition of minimum of energy, ii) a roundabout of three access roads and three exit…
In this paper a duality between the d=2 Wen-plaquette model in a transverse field and the d=1 Ising model in a transverse field is used to learn the nature of the quantum phase transition (QPT) between a spin-polarized phase and a…
The notion of duality -- that a given physical system can have two different mathematical descriptions -- is a key idea in modern theoretical physics. Establishing a duality in lattice statistical mechanics models requires the construction…
In this paper and its sequel, we construct topologically invariant defects in two-dimensional classical lattice models and quantum spin chains. We show how defect lines commute with the transfer matrix/Hamiltonian when they obey the defect…
We show that the two dimensional Ising model is complete, in the sense that the partition function of any lattice model on any graph is equal to the partition function of the 2D Ising model with complex coupling. The latter model has all…
Although it is well known that all quantum states can be produced by single qubit measurements on the cluster states, it is not a simple task to explicitly find which measurement patterns on the cluster states can generate different quantum…
The goal of this paper is to exhibit a deep relation between the partition function of the Ising model on a planar trivalent graph and the generating series of the spin network evaluations on the same graph. We provide respectively a…
In this work, we present a construction of a cluster state lattice Hamiltonian that exhibits the symmetry of the Ising fusion algebra. This construction is formulated within the framework of weak Hopf symmetry topological field theory…
We study the two-dimensional Ising model on a network with a novel type of quenched topological (connectivity) disorder. We construct random lattices of constant coordination number and perform large scale Monte Carlo simulations in order…
Measurement-based quantum computation offers exponential computational speed-up via simple measurements on a large entangled cluster state. We propose and demonstrate a scalable scheme for the generation of photonic cluster states suitable…
We present a unifying framework to study physical systems which exhibit topological quantum order (TQO). The guiding principle behind our approach is that of symmetries and entanglement. We introduce the concept of low-dimensional…
There are indications from the large-N analysis that multi-channel Kondo lattices have topological order. We use the coupled-wire construction to study the channel paramagnetic regime of a two-channel Kondo lattice model of spin-1/2 SU(2)…
Here we show how the Minimally Entangled States (MES) of a 2d system with topological order can be identified using the geometric measure of entanglement. We show this by minimizing this measure for the doubled semion, doubled Fibonacci and…
Higher-order topological phase as a generalization of Berry phase attracts an enormous amount of research. The current theoretical models supporting higher-order topological phases, however, cannot give the connection between lower and…
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 investigate the computational power of the recently introduced class of isometric tensor network states (isoTNSs), which generalizes the isometric conditions of the canonical form of one-dimensional matrix-product states to tensor…
We present a method of extracting information about the topological order from the ground state of a strongly correlated two-dimensional system computed with the infinite projected entangled pair state (iPEPS). For topologically ordered…
Quantum entanglement is a particularly useful characterization of topological orders which lack conventional order parameters. In this work, we study the entanglement in topologically ordered states between two arbitrary spatial regions,…
Topological pumping and duality transformations are paradigmatic concepts in condensed matter and statistical mechanics. In this paper, we extend the concept of topological pumping of particles to topological pumping of quantum…
A systematic study of both classical and quantum geometric frustrated Ising models with a competing ordering mechanism is reported in this paper. The ordering comes in the classical case from a coupling of 2D layers and in the quantum model…