相关论文: Integrable su(2)-invariant spin chains and the Hal…
Composing higher auxiliary-spin transfer matrices and their derivatives, we construct a family of quasilocal conserved operators of isotropic Heisenberg spin 1/2 chain and rigorously establish their linear independence from the well-known…
We investigate classes of quantum Heisenberg spin systems which have different coupling constants but the same energy spectrum and hence the same thermodynamical properties. To this end we define various types of isospectrality and…
We consider lambda and anisotropic deformations of the SU(2) principal chiral model and show how they can be quantized in the Hamiltonian formalism on a lattice as a suitable spin chain. The spin chain is related to the higher spin XXZ…
The Hoft structure of the central extension of the $U_q \left( \widehat{sl\left( n \right) }\right)$ algebra is considered. The intertwine matrix induces new integrable spin chain models. We show the relation of these models and the…
Using a formalism developed by Polychronakos, we explicitly construct a set of invariants of the motion for the Haldane-Shastry $SU(N)$ chain.
The Heisenberg spin ladder is studied in the semiclassical limit, via a mapping to the nonlinear $\sigma$ model. Different treatments are needed if the inter-chain coupling $K$ is small, intermediate or large. For intermediate coupling a…
A Haldane conjecture is revealed for spin-singlet charge modes in 2N-component fermionic cold atoms loaded into a one-dimensional optical lattice. By means of a low-energy approach and DMRG calculations, we show the emergence of gapless and…
In this paper we study a novel spin chain with nearest-neighbors interactions depending on the sites coordinates, which in some sense is intermediate between the Heisenberg chain and the spin chains of Haldane-Shastry type. We show that…
We establish a novel correspondence between 4D $\mathcal N=1$ supersymmetric gauge theories on $D^2\times T^2$ and open XYZ spin chains with generalized boundary conditions, extending beyond previous 3D Bethe/gauge duality frameworks. Our…
We study the phase diagram of coupled spin-1/2 chains with bilinear and (chiral) three-spin exchange interactions in a magnetic field. The model is soluble on a one-parametric line in the space of coupling constants connecting the limiting…
An integrable anisotropic Heisenberg spin chain with nearest-neighbour couplings, next-nearest-neighbour couplings and scalar chirality terms is constructed. After proving the integrability, we obtain the exact solution of the system. The…
We study a two-parameter family of quantum spin systems on the complete graph, which is the most general model invariant under the complex orthogonal group. In spin $S=\frac{1}{2}$ it is equivalent to the XXZ model, and in spin $S=1$ to the…
We study two Heisenberg spin-1/2 chains coupled by a frustrating ``zigzag'' interaction. We are particularly interested in the regime of weak interchain coupling, which is difficult to analyse by either numerical or analytical methods.…
The Hodge Conjecture is equivalent to a statement about conditions under which a complex vector bundle on a smooth complex projective variety admits a holomorphic structure. I advertise a class of abelian four-folds due to Mumford where…
A two-parameter family of quantum spin ladders with local bilinear and biquadratic interactions is shown to be solvable by a mapping onto fragments of integrable spin 1 chains. The phase diagram, consisting of four phases, and the ground…
By taking the freezing limit of a spin Calogero-Sutherland model containing `anyon like' representation of the permutation algebra, we derive the exact partition function of SU(m|n) supersymmetric Haldane-Shastry (HS) spin chain. This…
Lattice systems with certain Lie algebraic or quantum Lie algebraic symmetries are constructed. These symmetric models give rise to series of integrable systems. As examples the $A_n$-symmetric chain models and the SU(2)-invariant ladder…
The elliptic genera of two-dimensional N=2 superconformal field theories can be twisted by the action of the integral Heisenberg group if their U(1) charges are fractional. The basic properties of the resulting twisted elliptic genera and…
Given a finite subgroup G of SL(2,C) we define an additive 2-category H^G whose Grothendieck group is isomorphic to an integral form of the Heisenberg algebra. We construct an action of H^G on derived categories of coherent sheaves on…
This is the first in a series of papers devoted to the study of spin chains capturing the spectral problem of 4d $\mathcal{N}=2$ SCFTs in the planar limit. At one loop and in the quantum plane limit, we discover a quasi-Hopf symmetry…