Related papers: Generating topological order from a 2D cluster sta…
Topology in quantum systems is typically considered in infinite crystals in one, two, or higher integer dimensions. Here, we show that one can continuously transform a system between a topological phase associated with one dimension and a…
We study a Hamiltonian system describing a three spin-1/2 cluster-like interaction competing with an Ising-like exchange. We show that the ground state in the cluster phase possesses symmetry protected topological order. A continuous…
Motivated by experimental progress in the growth of heavy transition metal oxides, we theoretically study a class of lattice models of interacting fermions with strong spin-orbit coupling. Focusing on interactions of intermediate strength,…
The mutual feedback between quantum condensed matter and cold atom physics has been quite fruitful throughout history and continues to inspire ongoing research. Motivated by the recent activities on the quantum simulation of topological…
Non-local orders, entanglement entropy, and quantum fidelity are investigated in an infinite-size bond-alternating Ising chain with the Dzyaloshinskii-Moriya interaction by employing the infinite matrix product state representation with the…
The cluster state quantum computation is a versatile approach to build a scalable quantum computer. In this thesis we theoretically demonstrate that a one dimensional array of double quantum dots with long spin relaxation time can evolve to…
It has recently been demonstrated that it is possible to open a gap in a magnetic Weyl semimetal, while preserving the chiral anomaly along with the charge conservation and translational symmetries, which all protect the gapless nodes in a…
Higher-order topological phases feature topologically protected boundary states in lower dimensions. Specifically, the zero-dimensional corner states are protected by the $d$th-order topology of a $d$-dimension system. In this work, we…
Quantum phase transitions between different topologically ordered phases exhibit rich structures and are generically challenging to study in microscopic lattice models. In this work, we propose a tensor-network solvable model that allows us…
The purpose of this paper is to investigate the ground-state properties of two-dimensional Heisenberg models on a square lattice with a given dimerization. Our aim is threefold: First, we want to investigate the dimensional transition from…
Measurement based quantum computation requires the generation of a cluster state (quantum resource) prior to starting a computation. Generation of this entangled state can be difficult with many schemes already proposed. We present an…
Coexistence of various ordered chaotic states in a Hamiltonian system is studied with the use of a symplectic coupled map lattice. Besides the clustered states for the attractive interaction, a novel chaotic ordered state is found for a…
We introduce the notion of polynomial-depth duality transformations, which relates two sets of operator algebras through a conjugation by a poly-depth quantum circuit, and make use of this to construct efficient Gibbs samplers for a variety…
Transitions between different topologically ordered phases have been studied by artificially creating boundaries between these gapped phases and thus studying their effects relating to condensation and tunneling of particles from one phase…
We demonstrate formation of hierarchical structures in two-dimensional systems with multiple length scales in the inter-particle interaction. These include states such as clusters of clusters, concentric rings, clusters inside a ring, and…
In many physical scenarios, close relations between the bulk properties of quantum systems and theories associated to their boundaries have been observed. In this work, we provide an exact duality mapping between the bulk of a quantum spin…
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…
This paper rests to a large extend on a paper I wrote some time ago on 'Duality in generalized Ising models and phase transitions without local order parameter'. It deals with Ising models with interactions containing products of more than…
Topological order in a 2d quantum matter can be determined by the topological contribution to the entanglement R\'enyi entropies. However, when close to a quantum phase transition, its calculation becomes cumbersome. Here we show how…
We study the phase diagram of a class of models in which a generalized cluster interaction can be quenched by Ising exchange interaction and external magnetic field. We characterize the various phases through winding numbers. They may be…