Related papers: Topological order, mixed states and open systems
Continuous transitions between states with the {\em same} symmetry but different topological orders are studied. Clean quantum Hall (QH) liquids with neutral quasiparticles are shown to have such transitions. For clean bilayer (nnm) states,…
The topology of entanglement in multipartite states with translational invariance is discussed in this article. Two global features are foundby which one can distinguish distinct states. These are the cyclic unit and the quantised geometric…
Crystalline symmetries give rise to topological invariants that can distinguish quantum phases of matter. Understanding these in strongly interacting systems is an ongoing research direction requiring non-perturbative methods. Recent…
A new definition and interpretation of geometric phase for mixed state cyclic unitary evolution in quantum mechanics are presented. The pure state case is formulated in a framework involving three selected Principal Fibre Bundles, and the…
In an open system, the geometric phase should be described by a distribution. We show that a geometric phase distribution for open system dynamics is in general ambiguous, but the imposition of reasonable physical constraints on the…
The non-classical features of quantum mechanics are reproduced using models constructed with a classical theory - general relativity. The inability to define complete initial data consistently and independently of future measurements,…
Topologically ordered phase has emerged as one of most exciting concepts that not only broadens our understanding of phases of matter, but also has been found to have potential application in fault-tolerant quantum computation. The direct…
A model is proposed that describes the evolution of a mixed state of a quantum system for which gain and loss of energy or amplitude are present. Properties of the model are worked out in detail. In particular, invariant subspaces of the…
Synchronization is a ubiquitous phenomenon in complex systems. The Kuramoto model serves as a paradigmatic framework for understanding how coupled oscillators achieve collective rhythm. Conventional approaches focus on pairwise…
While a pure quantum state may accumulate both the Berry phase and dynamic phase as it undergoes a cyclic path in the parameter space, the situation is more complicated when mixed quantum states are considered. From the Ulhmann bundle, a…
We present a comprehensive analysis of the emerging order and chaos and enduring symmetries, accompanying a generic (high-barrier) first-order quantum phase transition (QPT). The interacting boson model Hamiltonian employed, describes a QPT…
In recent years, there has been a surge of interest in higher-order topological phases (HOTPs) across various disciplines within the field of physics. These unique phases are characterized by their ability to harbor topological protected…
The quantum states which satisfy the equality in the generalised uncertainty relation are called intelligent states. We prove the existence of intelligent states for the Anandan-Aharonov uncertainty relation based on the geometry of the…
The interplay of topology and symmetry in a material's band structure may result in various patterns of topological states of different dimensionality on the boundary of a crystal. The protection of these "higher-order" boundary states…
We investigate the stability of the topological phase of the toric code model in the presence of a uniform magnetic field by means of variational and high-order series expansion approaches. We find that when this perturbation is strong…
The state of a quantum system, adiabatically driven in a cycle, may acquire a measurable phase depending only on the closed trajectory in parameter space. Such geometric phases are ubiquitous, and also underline the physics of robust…
We study topological transport in the steady state of a quantum particle hopping on a one-dimensional lattice in the presence of dissipation. The model exhibits a rich phase structure, with the average particle velocity in the steady state…
Topological phases of matter give rise to exotic physics that can be leveraged for next generation quantum computation and spintronic devices. Thus, the search for topological phases and the quantum states that they exhibit have become the…
Non-Hermiticity appears ubiquitously in various open classical and quantum systems and enriches classification of topological phases. However, the role of nonsymmorphic symmetry, crystalline symmetry accompanying fractional lattice…
The rise of quantum information science has opened up a new venue for applications of the geometric phase (GP), as well as triggered new insights into its physical, mathematical, and conceptual nature. Here, we review this development by…