Paweł Jakubczyk

The basis of wavelets for a finite Heisenberg magnet

Abstract We propose here a method for an immediate diagonalisation of the XXX Heisenberg magnetic ring for the spin 1 2 with a finite number N of nodes. The key ingredient is the basis of wavelets, i.e. Fourier transforms on orbits of the translation group on the set of all magnetic configurations with a definite number r of spin deviations from ferromagnetic saturation. The method demonstrates the Yang–Baxter structure of the relevant classical configuration space, reduces by N the size of the secular equation, and explains the dynamics of the Heisenberg ring in terms of geometry of orbits. We show in particular, that a κ-tuply rarefied orbit, with κ a divisor of N, stimulates neighbour regular (N-element) orbits to twist in a way to become a κ-tuply cover of the adjacent rarefied orbit.

Renormalization theory for the Fulde-Ferrell-Larkin-Ovchinnikov states at T>0

Within the renormalization group framework we study the stability of superfluid density wave states, known as Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phases, with respect to thermal order-parameter fluctuations in two and three-dimensional (

Schwinger geometry, Bethe Ansatz, and a magnonic qudit

d\in \{2,3\}

Computer implementation of the Kerov–Kirillov–Reshetikhin algorithm ☆

) systems. We analyze the renormalization-group flow of the relevant ordering wave-vector

On the SU(2)×SU(2) symmetry in the Hubbard model

\vec{Q_0}

Combinatorial approach to the representation of the Schur-Weyl duality in one-dimensional spin systems

. The calculation indicates an instability of the FFLO-type states towards either a uniform superfluid or the normal state in

On Application of the Jucys–Murphy Operators in the Hubbard Model of Solids

d\in\{2,3\}

Rigged strings, Bethe Ansatz, and the geometry of the classical configuration space of the Heisenberg magnetic ring

and

Kostka matrices at the level of bases and the complete set of commuting Jucys-Murphy operators

T>0

Entanglement of one-magnon Schur-Weyl states

. In