Related papers: Topological Order and Reflection Positivity
We establish a framework with reflection positivity as the first principle for establishing the boundary theory of topologically ordered quantum spin systems. For any reflection positive frustration-free Hamiltonian, We proved that the…
The unrivaled robustness of topologically ordered states of matter against perturbations has immediate applications in quantum computing and quantum metrology, yet their very existence poses a challenge to our understanding of phase…
Systems displaying quantum topological order feature robust characteristics that are very attractive to quantum computing schemes. Topological quantum field theories have proven to be powerful in capturing the quintessential attributes of…
Topological order has become a new paradigm to distinguish ground states of interacting many-body systems without conventional long-range order. Here we discuss possible extensions of this concept to density matrices describing statistical…
I define models of quantum loops and nets which have ground states with topological order. These make possible excited states comprised of deconfined anyons with non-abelian braiding. With the appropriate inner product, these quantum loop…
We discuss the possible topological order/topological quantum field theory of different quantum Hall systems. Given the value of the Hall conductivity, we constrain the global symmetry of the low-energy theory and its anomaly. Specifically,…
The concept of topological phases has been generalized to higher-order topological insulators and superconductors with novel boundary states on corners or hinges. Meanwhile, recent experimental advances in controlling dissipation (such as…
Topology captures the essence of what remains unchanged under a transformation. In this study, a topological invariant called super conformality was found to preserve a critical angle between the constitutive plane and its second order…
We analyze the computational aspects of detecting topological order in a quantum many-body system. We contrast the widely used topological entanglement entropy with a recently introduced operational definition for topological order based on…
Topological states of fermionic matter can be induced by means of a suitably engineered dissipative dynamics. Dissipation then does not occur as a perturbation, but rather as the main resource for many-body dynamics, providing a targeted…
Topological order is a new type order that beyond Landau's symmetry breaking theory. The topological entanglement entropy provides a universal quantum number to characterize the topological order in a system. The topological entanglement…
We introduce the concept of composite topological order in multicomponent systems. In such a state topological order appears only in higher-than-usual composites, with no topological order in elementary fields. We propose that such a state…
Topological order in strongly correlated systems, including quantum spin liquids, quantum Hall states in lattices and topological superconductivity is treated. Various metallic non-Fermi-liquid states are discussed, including fractionalized…
Can a large system be fully characterized using its subsystems via inductive reasoning? Is it possible to completely reduce the behavior of a complex system to the behavior of its simplest "atoms"? In the following paper we answer these…
We define a notion of {\it positive part} of a lattice $\Lambda$ and we endow the set of such positive parts with a topology. We then study some properties of this topology, by comparing it with the one of $V^*/\RM_{> 0}$, where $V^*$ is…
We investigate the role that vortex loops play in characterizing eigenstates of interacting Majoranas. We first give some general results, and then we focus on ladder Hamiltonian examples to test further ideas. Two methods yield exact…
We define a hierarchy of systems with topological completely positive entropy in the context of continuous countable amenable group actions on compact metric spaces. For each countable ordinal we construct a dynamical system on the…
The discovery of topological order has revolutionized the understanding of quantum matter in modern physics and provided the theoretical foundation for many quantum error correcting codes. Realizing topologically ordered states has proven…
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…
We define topological time crystals, a dynamical phase of periodically driven quantum many-body systems capturing the coexistence of intrinsic topological order with the spontaneous breaking of discrete time-translation symmetry. We show…