Related papers: Anyons in One Dimension
The dynamics of a quantum mechanical particle in a time-independent potential are found to contain many interesting phenomena. These are direct consequences of the (typical) existence of more than one time scale governing the problem. This…
Periodic boundary conditions are a common theoretical and computational tool used to emulate effectively infinite domains. However, two-dimensional periodic domains are topologically distinct from the infinite plane, eliciting the question:…
Exotic quantum states and fractionalized magnetic excitations, such as spinons in one-dimensional chains, are generally viewed as belonging to the domain of 3d transition metal systems with spins 1/2. Our neutron scattering experiments on…
We study conformal field theories describing two massless one-dimensional fields interacting at a single spatial point. The interactions we include are periodic functions of the bosonized fields separately plus a ``magnetic'' interaction…
We consider two-dimensional systems of point particles located on rectangular lattices and interacting via pairwise potentials. The goal of this paper is to investigate the phase transitions (and their nature) at fixed density for the…
We study the statistics of domain wall excitations in quantum spin chains. We focus on systems with finite symmetry groups represented by matrix product unitaries (MPUs), i.e. finite depth quantum circuits. Such symmetries can be anomalous,…
This work presents the derivation of the large time and distance asymptotic behavior of the field-field correlation functions of impenetrable one-dimensional anyons at finite temperature. In the appropriate limits of the statistics…
One of the profound consequences of the fractional quantum Hall (FQH) effect is the notion of fractionally charged anyons. In spite of extensive experimental study, puzzles remain, however. For example, both shot-noise and Aharonov-Bohm…
We formulate quantum mechanics in spacetimes with real-order fractional geometry and more general factorizable measures. In spacetimes where coordinates and momenta span the whole real line, Heisenberg's principle is proven and the…
In this paper we investigate the von Neumann entropy in the ground state of one-dimensional anyonic systems with the repulsive interaction. Based on the Bethe-ansatz method, the entanglement properties for the arbitrary statistical…
We comment on the significance of the results in the paper by Nakamura et al (2020). The experimental result measures the phase for a repeated elementary exchange of two identical quasiparticles, and shows that the quasiparticles are…
We study the interaction of two dyons in the region of their cores where they are non-linear and non-Abelian. We assume the superposition of two dyons as a solution of the equation of motion. The terms due to the non-linearity of the…
A basic statistical mechanics analysis of many-body systems with non-reciprocal pair interactions is presented. Different non-reciprocity classes in two- and three-dimensional binary systems (relevant to real experimental situations) are…
We study photon-meson transition formfactors of light mesons in the kinematics, where one photon is real and other is virtual. Dispersive approach to axial anomaly leads to the anomaly sum rule. The absence of corrections to it allows us to…
One-particle properties of non-interacting Fermions in a one-dimensional harmonic trap and at zero temperature are studied. Exact expressions and asymptotic results for large Fermion number N are given for the particle density distribution…
Paradigme shift in gauge topology, from instantons to their constituents -- instanton-dyons -- has recently lead to very significant advances. Like instantons, they have fermionic zero modes, and their collectivization at sufficiently high…
Recent measurements on 2d materials tuning between fractional quantum anomalous Hall phases and a plethora of correlated electronic states call for a detailed understanding of the dynamics of anyons. Here we develop a general theory of the…
We survey known results about phase transitions in various models of statistical physics when the underlying space is a nonamenable graph. Most attention is devoted to transitive graphs and trees.
It is shown that effects of particle identity entail reduction in the number of orbital degrees-of-freedom in non-relativistic 2-particle systems from 6 to 5. This effect of redundancy in description of orbital motion is found to be in…
The anyonic quantum walk is a dynamical model describing a single anyon propagating along a chain of stationary anyons and interacting via mutual braiding statistics. We review the recent results on the effects of braiding statistics in…