Related papers: Topological order, mixed states and open systems

Global symmetries greatly enrich the landscape of topological quantum phases, playing an essential role from topological insulators to fractional quantum Hall effect. Topological phases in mixed quantum states, originating from…

Topological orders are a class of exotic states of matter characterized by patterns of long-range entanglement. Certain topologically ordered systems are proposed as potential realization of fault-tolerant quantum computation. Topological…

We investigate quantum tomography in scenarios where prior information restricts the state space to a smooth manifold of lower dimensionality. By considering stability we provide a general framework that relates the topology of the manifold…

In connection with recent discussion of topological order and topological phase transitions in quantum systems, we reexamine circumstances that lead to the appearance of a topological glass in certain classical lattice spin models. Local…

We propose the following definition of topological quantum phases valid for mixed states: two states are in the same phase if there exists a time independent, fast and local Lindbladian evolution driving one state into the other. The…

We consider finite macroscopic systems, i.e., systems of large but finite degrees of freedom, which we believe are poorly understood as compared with small systems and infinite systems. We focus on pure states that do not have the `cluster…

Quest for a new form of matter inside compact stars compels us to examine the thermodynamical properties of the phase transitions. We closely consider the first-order phase transitions and the phase equilibrium on the basis of the Gibbs…

Disorder inevitably exists in realistic samples, manifesting itself in various exotic properties for the topological states. In this paper, we summarize and briefly review work completed over the last few years, including our own, regarding…

Distinct from the dynamical phase, in a cyclic evolution, a system's state may acquire an additional component, a.k.a. geometric phase. The latter is a manifestation of a closed path in state space. Geometric phases underlie various…

Many systems in nature and the synthetic world involve ordered arrangements of units on two-dimensional surfaces. We review here the fundamental role payed by both the topology of the underlying surface and its detailed curvature. Topology…

We study the geometric Uhlmann phase of entangled mixed states in a composite system made of two coupled spin-$\frac 1 2$ particles with a magnetic field acting on one of them. Within a depolarizing channel setup, an exact analytical…

It is pointed out that quantum states, in general, contain a new kind of orders that cannot be characterized by symmetry. A concept of quantum order is introduced to describe such orders. As two concrete examples, we discussed quantum…

Topological phases are characterised by a topological invariant that remains unchanged by deformations in the Hamiltonian. Materials exhibiting topological phases include topological insulators, superconductors exhibiting strong spin-orbit…

The geometric phases of cyclic evolutions for mixed states are discussed in the framework of unitary evolution. A canonical one-form is defined whose line integral gives the geometric phase which is gauge invariant. It reduces to the…

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…

In primary school, we were told that there are four states of matter: solid, liquid, gas, and plasma. In college, we learned that there are much more than four states of matter. For example, there are ferromagnetic states as revealed by the…

A recent proposal of Sjoqvist et.al. to extend Pancharatnam's criterion for phase difference between two different pure states to the case of mixed states in quantum mechanics is analyzed and the existence of phase singularities in the…

We discuss the appearance of fractional topological phases on cyclic evolutions of entangled qudits. The original result reported in Phys. Rev. Lett. \textbf{106}, 240503 (2011) is detailed and extended to qudits of different dimensions.…

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…

Understanding how higher-order interactions affect collective behavior is a central problem in nonlinear dynamics and complex systems. Most works have focused on a single higher-order coupling function, neglecting other viable choices. Here…