Related papers: Topological order of mixed states in quantum many-…
We show that the concept of topological order, introduced to describe ordered quantum systems which cannot be classified by broken symmetries, also applies to classical systems. Starting from a specific example, we show how to use pure…
We review recent developments in the study of out-of-equilibrium topological states of matter in isolated systems. The phenomenon of many-body localization, exhibited by some isolated systems usually in the presence of quenched disorder,…
Topological ordered states are exotic quantum states of matter that defy the usual description in terms of symmetry breaking and local order parameters. The type or order they feature is of non-local, topological nature, and it allows such…
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 entanglement entropy is a topological invariant which can detect topological order of quantum many-body ground state. We assume an existence of such order parameter at finite temperature which is invariant under smooth…
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…
Closed quantum systems with quenched randomness exhibit many-body localized regimes wherein they do not equilibrate even though prepared with macroscopic amounts of energy above their ground states. We show that such localized systems can…
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…
We investigate how imposing kinetic restrictions on quantum particles that would otherwise hop freely on a two-dimensional lattice can lead to topologically ordered states. The kinetically constrained models introduced here are derived as a…
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…
Topologically ordered systems exhibit large-scale correlation in their ground states, which may be characterized by quantities such as topological entanglement entropy. We propose that the concept of irreducible many-body correlation, the…
A general inequality between entanglement entropy and a number of topologically ordered states is derived, even without using the properties of the parent Hamiltonian or the formalism of topological quantum field theory. Given a quantum…
It is an ongoing quest to realize topologically ordered quantum states on different platforms including condensed matter systems, quantum simulators and digital quantum processors. Unlike conventional states characterized by their local…
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…
Calculation of topological order parameters, such as the topological entropy and topological mutual information, are used to determine whether states possess topological order. Their calculation is expected to give reliable results when the…
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 role of mixed states in topological quantum matter is less known than that of pure quantum states. Generalisations of topological phases appearing in pure states had received only quite recently attention in the literature. In…
Disorder and localization have dramatic influence on the topological properties of a quantum system. While strong disorder can close the band gap thus depriving topological materials of topological features, disorder may also induce…
Topology is key in describing unconventional quantum phases of matter and devising robust quantum technology. Exactly how topology mixes with quantum mechanics remains largely unclear, as testified by the lack of a unifying microscopic…
The thermal or equilibrium ensemble is one of the most ubiquitous states of matter. For models comprised of many locally interacting quantum particles, it describes a wide range of physical situations, relevant to condensed matter physics,…