Related papers: Crystalizing the Spinon Basis
The spectrum of the integrable spin-S Heisenberg chains is completely characterized in terms of spin-1/2 spinons. In the continuum limit they form a quasi-particle basis to the higher level SU(2) Wess-Zumino-Witten (WZW) models. Enumerating…
We consider the physical combinatorics of critical lattice models and their associated conformal field theories arising in the continuum scaling limit. As examples, we consider A-type unitary minimal models and the level-1 sl(2)…
In the model every quark or lepton is identified with a quartet of four "more elementary" particles. One particle in a quartet is a massive spin-0 boson and other three particles are massless spin-1/2 fermions.
We construct a quasi-particle basis of the integrable highest weight module of highest weight $3\Lambda_0$ for the twisted affine Lie algebra of type $A_2^{(2)}$ in the principal realization. More specifically, by introducing the concept of…
We study higher spin (pure and mixed spin) representations of the Yangian of $\mathfrak{sl}_2$. We provide a geometric realization in terms of the critical cohomology of representations of the quiver with potential of Bykov and Zinn-Justin…
Using a strategy that may be applied in theory or in experiments, we identify the regime in which a model binary soft matter mixture forms quasicrystals. The system is described using classical density functional theory combined with…
The level-$1$ integrable highest weight modules of $U_q(\widehat{sl}_2)$ admit a level-$0$ action of the same algebra. This action is defined using the affine Hecke algebra and the basis of the level-$1$ module generated by components of…
For each $n\geqslant3$, we construct an uncountable family of models of the crystal of the basic $U_q(\hat{\mathfrak{sl}}_n)$-module. These models are all based on partitions, and include the usual $n$-regular and $n$-restricted models, as…
We classify the simple infinite dimensional integrable modules with finite dimensional weight spaces over the quantized enveloping algebra of an untwisted affine algebra. We prove that these are either highest (lowest) weight integrable…
We construct a crystal base of the negative half of a quantum orthosymplectic superalgebra. It can be viewed as a limit of the crystal bases of $q$-deformed irreducible oscillator representations. We also give a combinatorial description of…
We give a brief survey of recent developments in the highest weight representation theory and the crystal basis theory of the quantum queer superalgebra $U_q(\mathfrak{q}(n))$.
Multiple-$Q$ states as represented by a magnetic skyrmion crystal and hedgehog crystal have been extensively studied in recent years owing to their unconventional physical properties. The materials hosting multiple-$Q$ states have been so…
Exotic quantum spin liquid (QSL) is formed with such hypothetic particles as fermionic spinons carrying spin 1/2 and no charge. Here we calculate its thermodynamic and relaxation properties. Our calculations unveil the fundamental…
We consider certain infinite dimensional modules of level 1 for the double Yangian $\text{DY}(\mathfrak{gl}_2)$ which are based on the Iohara-Kohno realization. We show that they possess topological bases of Feigin-Stoyanovsky-type, i.e.…
Previously defined spin-dependent quark densities that are matrix elements of specific density operators in proton states of definite spin-polarization generally have an infinite variety of non-spherical shapes. The present application is…
The coordinate Bethe ansatz solutions of the XXZ model for a one-dimensional spin-1/2 chain are analyzed with focus on the statistical properties of the constituent quasiparticles. Emphasis is given to the special cases known as XX, XXX,…
The ground-state electron density of a one-dimensional spin-orbit coupled quantum dot with a Zeeman term and strong electron interaction is studied at the fractional helical liquid points. We show that at fractional filling factors…
The spin structure of the system of quasifree fermions having total angular momentum $J=1/2$ is studied in a consistently covariant approach. Within this model the relations between the spin functions are obtained. Their particular cases…
Quantum spin rings represent fundamental model systems that exhibit distinctive quantum phenomena-such as quantum critical behavior and quasiparticle excitations-arising from their periodic boundary conditions and enhanced quantum…
We show some symmetry relations among the correlation functions of the integrable higher-spin XXX and XXZ spin chains, where we explicitly evaluate the multiple integrals representing the one-point functions in the spin-1 case. We review…