Related papers: Order Fractionalization
As the dimensionality is reduced, the world becomes more and more interesting; novel and fascinating phenomena show up which call for understanding. Physics in one dimension is a fascinating topic for theory and experiment: for the former…
We explore quantum phase transitions using two probes of quantum chaos: out-of-time-order correlators (OTOCs) and the $r$-parameter obtained from the level spacing statistics. In particular, we address $p$-spin models associated with…
Motivated by recent progress in data assimilation, we develop an algorithm to dynamically learn the parameters of a chaotic system from partial observations. Under reasonable assumptions, we rigorously establish the convergence of this…
We introduce an entanglement witness that identifies off-diagonal long-range order (ODLRO) -- a distinctive form of entanglement -- in systems containing both fermionic and bosonic particles. By analyzing the particle-hole reduced density…
The single-particle spectral function for an incompressible fractional quantum Hall state in the presence of a scalar short-ranged attractive impurity potential is calculated via exact diagonalization within the spherical geometry. In…
The notion of fractional dynamics is related to equations of motion with one or a few terms with derivatives of a fractional order. This type of equation appears in the description of chaotic dynamics, wave propagation in fractal media, and…
The precise theoretical characterization of a fractionalized phase in spatial dimensions higher than one is through the concept of ``topological order''. We describe a physical effect that is a robust and direct consequence of this hidden…
Landau theory relates phase transitions to the minimization of the Landau functional (e.g., free energy functional), which is expressed as a power series of the order parameter. It has been shown that the critical behavior of certain…
We discuss symmetries intermediate between global and local and formalize the notion of dimensional reduction adduced from such symmetries. We apply this generalization to several systems including liquid crystalline phases of Quantum Hall…
The concept of symmetry breaking and the emergence of corresponding local order parameters constitute the pillars of modern day many body physics. The theory of quantum entanglement is currently leading to a paradigm shift in understanding…
From atomic crystals to bird flocks, most forms of order are captured by the concept of spontaneous symmetry breaking. This paradigm was challenged by the discovery of topological order, in materials where the number of accessible states is…
The physics of the fractional quantum Hall effect is the physics of interacting electrons confined to a macroscopically degenerate Landau level. In this Chapter we discuss the theory of the quantum Hall effect in systems where the electrons…
These lectures address the dynamics of phase ordering out of equilibrium in condensed matter and in quantum field theory in cosmological settings, emphasizing their similarities and differences. In condensed matter we describe the…
Half-filled Landau levels host an emergent Fermi-liquid which displays an instability towards pairing, culminating in a gapped even-denominator fractional quantum Hall ground state. While this pairing may be probed by tuning the…
Ordering of mobile defects in functional materials can give rise to fundamentally new phases possessing ferroic and multiferroic functionalities. Here we develop the Landau theory for strain induced ordering of defects (e.g. oxygen…
The fractional order system, which is described by the fractional order derivative and integral, has been studied in many engineering areas. Recently, the concept of fractional order has been generalized to the distributed order concept,…
In the framework of the Ginzburg-Landau harmonic potential approximation, we present a possible modeling of the time-dependence of the frequency of the order parameter mode suitable to account for the formation of correlated domains in…
Spontaneous symmetry breaking is deeply related to dimensionality of system. The Neel order going with spontaneous breaking of $U(1)$ symmetry is safely allowed at any temperature for three-dimensional systems but allowed only at zero…
Unidirectional transport and localized cyclotron motion are two opposite physical phenomena. Here, we study the interplay effects between them on nonreciprocal lattices subject to a magnetic field. We show that, in the long-wavelength…
Symmetry of the order parameter in some triplet superconductors corresponds to doubly-degenerate chiral states. We predict that in a sufficiently small sample this degeneracy can be lifted via macroscopic quantum tunneling. Moreover, if the…