Related papers: Topological order in 1D Cluster state protected by…
We show that the standard 1+1d $\mathbb{Z}_2\times \mathbb{Z}_2$ cluster model has a non-invertible global symmetry, described by the fusion category Rep(D$_8$). Therefore, the cluster state is not only a $\mathbb{Z}_2\times \mathbb{Z}_2$…
Despite growing interest in beyond-group symmetries in quantum condensed matter systems, there are relatively few microscopic lattice models explicitly realizing these symmetries, and many phenomena have yet to be studied at the microscopic…
Recent experimental progress in controlling open quantum systems enables the pursuit of mixed-state nonequilibrium quantum phases. We investigate whether open quantum systems hosting mixed-state symmetry-protected topological states as…
We investigate the influence of local decoherence on a symmetry-protected topological (SPT) phase of the two-dimensional (2D) cluster state. Mapping the 2D cluster state under decoherence to a classical spin model, we show a topological…
We characterize phases of the compass ladder model by using degenerate perturbation theory, symmetry fractionalization, and numerical techniques. Through degenerate perturbation theory we obtain an effective Hamiltonian for each phase of…
A cluster state is a strongly entangled state, which is a source of measurement-based quantum computation. It is generated by applying controlled-Z (CZ) gates to the state $\left\vert ++\cdots +\right\rangle $. It is protected by the…
Topological order offers possibilities for processing quantum information which can be immune to imperfections. However, the question of its stability out of equilibrium is relevant for experiments, where coupling to an environment is…
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…
We introduce a notion of homogeneous topological order, which is obeyed by most, if not all, known examples of topological order including fracton phases on quantum spins (qudits). The notion is a condition on the ground state subspace,…
We present a toy model with a Hamiltonian $H^{(2)}_T$ on a folded one-dimensional spin chain. The non-trivial ground states of $H^{(2)}_T$ are separated by a gap from the excited states. By analyzing the symmetries in the model, we find…
We investigate the fate of coherence in the dynamical evolution of a symmetry protected quantum system. Under the formalism of system-plus-bath for open quantum system, the anti-unitary symmetry exhibits significant difference from the…
We investigate the physics of one-dimensional symmetry protected topological (SPT) phases protected by symmetries whose symmetry generators exhibit spatial modulation. We focus in particular on phases protected by symmetries with linear…
Topological qubits based on $SU(N)$-symmetric valence-bond solid models are constructed. A logical topological qubit is the ground subspace with two-fold degeneracy, which is due to the spontaneous breaking of a global parity symmetry. A…
We construct 2+1-dimensional lattice models of symmetry-protected topological (SPT) phases with non-invertible symmetries and investigate their properties using tensor networks. These models, which we refer to as generalized cluster models,…
One-dimensional valence bond solid (VBS) states represent the simplest symmetry protected topological phases. We show that their ground state entanglement spectrum contains both topological and non-topological structures. For the $SO(3)$…
The program of classifying symmetry protected topological (SPT) phases in 1D has been recently completed and has opened the doors to study closely the properties of systems belonging to these phases. It was recently found that being able to…
A symmetry-protected topologically ordered phase is a short-range entangled state, for which some imposed symmetry prohibits the adiabatic deformation into a trivial state which lacks entanglement. In this paper we argue that magnetization…
We generalize the hidden symmetry-breaking picture of symmetry-protected topological (SPT) order developed by Kennedy and Tasaki in the context of the Haldane phase. Our generalization applies to a wide class of SPT phases in…
It has recently been established that cluster-like states -- states that are in the same symmetry-protected topological phase as the cluster state -- provide a family of resource states that can be utilized for Measurement-Based Quantum…
The two-dimensional cluster state, a universal resource for measurement-based quantum computation, is also the gapped ground state of a short-ranged Hamiltonian. Here, we examine the effect of perturbations to this Hamiltonian. We prove…