Related papers: Topological Orders from Reflection Positive Frustr…
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 report the findings of fractional topological states in one-dimensional periodically modulated quantum spin chains with up to third neighbor interactions. By exact numerical studies, we demonstrate the existence of topologically…
We introduce a real-parameter refinement of the classical integer hierarchies underlying Schmidt number, block-positivity, and $k$-positivity for maps between matrix algebras. Starting from a compact family of $\alpha$-admissible unit…
Topological order has proven a useful concept to describe quantum phase transitions which are not captured by the Ginzburg-Landau type of symmetry-breaking order. However, lacking a local order parameter, topological order is hard to…
The nontrivial topology of spin systems such as skyrmions in real space can promote complex electronic states. Here, we provide a general viewpoint at the emergence of topological electronic states in spin systems based on the methods of…
In non-maximally quantum chaotic systems, the exponential behavior of out-of-time-ordered correlators (OTOCs) results from summing over exchanges of an infinite tower of higher "spin" operators. We construct an effective field theory (EFT)…
In this letter, we report our systematic construction of the lattice Hamiltonian model of topological orders on open surfaces, with explicit boundary terms. We do this mainly for the Levin-Wen stringnet model. The full Hamiltonian in our…
We consider a quantum fully packed loop model on the square lattice with a frustration-free projector Hamiltonian and ring-exchange interactions acting on plaquettes. A boundary Hamiltonian is added to favour domain-wall boundary conditions…
Given a graded $E_1$-module over an $E_2$-algebra in spaces, we construct an augmented semi-simplicial space up to higher coherent homotopy over it, called its canonical resolution, whose graded connectivity yields homological stability for…
Semiclassical states in isotropic loop quantum cosmology are employed to show that the improved dynamics has the correct classical limit. The effective Hamiltonian for the quantum cosmological model with a massless scalar field is thus…
We study the structure of local algebras in relativistic conformal quantum field theory with phase boundaries. Phase boundaries are instances of a more general notion of boundaries that give rise to a variety of algebraic structures. These…
We apply algorithms based on Lieb-Robinson bounds to simulate time-dependent and thermal quantities in quantum systems. For time-dependent systems, we modify a previous mapping to quantum circuits to significantly reduce the computer…
We develop a new systematic approach to quantum field theory that is designed to lead to physical states that rapidly converge in an expansion in free-particle Fock-space sectors. To make this possible, we use light-front field theory to…
In the framework of the algebraic formulation, we discuss and analyse some new features of the local structure of a real scalar quantum field theory in a strongly causal spacetime. In particular we use the properties of the exponential map…
Topology provides an essential concept for achieving unchanged (or protected) quantum properties in the presence of perturbations. A challenge facing realistic applications is that the level of protection displayed in real systems is…
Using a result of H. Hanche-Olsen, we show that (subject to fairly natural constraints on what constitutes a system, and on what constitutes a composite system), orthodox finite-dimensional complex quantum mechanics with superselection…
Coupled relaxation oscillators, realized via chemical or other means, can exhibit a multiplicity of steady states, characterized by spatial patterns resulting from lateral inhibition. We show that perturbation-initiated transformations…
We present a numerical study of a quantum phase transition from a spin-polarized to a topologically ordered phase in a system of spin-1/2 particles on a torus. We demonstrate that this non-symmetry-breaking topological quantum phase…
Topological matter provides natural platforms for robust, non-local information storage, central to quantum error correction. Yet, while the relation between entanglement and topology is well established, little is known about the role of…
We establish the existence of a topological classification of many-particle quantum systems undergoing unitary time evolution. The classification naturally inherits phenomenology familiar from equilibrium -- it is robust against disorder…