Related papers: Topological order, mixed states and open systems
Study of symmetry, topology and geometric phase can reveal many new and interesting results on the topological states of matter. Here we present a completely new and interesting result of symmetry, topology and quantization of geometric…
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 phenomena are commonly studied in phases of matter which are separated from a trivial phase by an unavoidable quantum phase transition. This can be overly restrictive, leaving out scenarios of practical relevance -- similar to…
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…
In open quantum systems, we directly relate anomalies of higher-form symmetries to the long-range entanglement of any mixed state with such symmetries. First, we define equivalence classes of long-range entanglement in mixed states via…
Impurities, defects, and other types of imperfections are ubiquitous in realistic quantum many-body systems and essentially unavoidable in solid state materials. Often, such random disorder is viewed purely negatively as it is believed to…
The existence of topological order is frequently associated with strongly coupled quantum matter. Here, we demonstrate the existence of topological phases in classical systems of densely packed, hard, anisotropic polyhedrally shaped…
The classification of topological phases of matter is fundamental to understand and characterize the properties of quantum materials. In this paper we study phases of matter in one-dimensional open quantum systems. We define two mixed…
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…
We consider arbitrary mixed state in unitary evolution and provide a comprehensive description of corresponding geometric phase in which two different points of view prevailing currently can be unified. Introducing an ancillary system and…
We describe recent progress in our understanding of the interplay between interactions, symmetry, and topology in states of quantum matter. We focus on a minimal generalization of the celebrated topological band insulators to interacting…
Discrete quantum walks are dynamical protocols for controlling a single quantum particle. Despite of its simplicity, quantum walks display rich topological phenomena and provide one of the simplest systems to study and understand…
Topological order characterizes those phases of matter that defy a description in terms of symmetry and cannot be distinguished in terms local order parameters. This type of order plays a key role in the theory of the fractional quantum…
We study a quantum phase transition between a phase which is topologically ordered and one which is not. We focus on a spin model, an extension of the toric code, for which we obtain the exact ground state for all values of the coupling…
Decoherence is a major obstacle to the preparation of topological order in noisy intermediate-scale quantum devices. Here, we show that decoherence can also give rise to new types of topological order. Specifically, we construct concrete…
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…
Meaningful topological invariants for mixed quantum states are challenging to identify as there is no unique way to define them, and most choices do not directly relate to physical observables. Here, we propose a simple pragmatic approach…
Co-existence of different states is a profound concept, which possibly underlies the phase transition and the symmetry breaking. Because of a property inherent to quantum mechanics (cf. uncertainty), the co-existence is expected to appear…
Topological phases of matter offer a promising platform for quantum computation and quantum error correction. Nevertheless, unlike its counterpart in pure states, descriptions of topological order in mixed states remain relatively…
Motivated by studies of typical properties of quantum states in statistical mechanics, we introduce phase-random states, an ensemble of pure states with fixed amplitudes and uniformly distributed phases in a fixed basis. We first show that…