Related papers: Algebraic representation of correlation functions …
A new approach to the correlation functions is presented for the XXZ model in the anti-ferroelectric regime. The method is based on the recent realization of the quantum affine symmetry using vertex operators. With the aid of a boson…
Exact integral representations of spin one-point functions (ground state expectation values) are reported for the spin-1 analog of the XXZ model in the region $-1<q<0$. The method enables one to calculate arbitrary $n$-point functions in…
Using multiple integral representations, we derive exact expressions for the correlation functions of the spin-1/2 Heisenberg chain at the free fermion point.
The XXZ open spin chain with general integrable boundary conditions is shown to possess a q-deformed analogue of the Onsager's algebra as fundamental non-abelian symmetry which ensures the integrability of the model. This symmetry implies…
We introduce and solvev a special family of integrable interacting vertex models that generalizes the well known six-vertex model. In addition to the usual nearest-neighbor interactions among the vertices, there exist extra hard-core…
In this paper, we consider the quantum XYZ open spin-1/2 chain with boundary fields. We focus on the particular case in which the six boundary parameters are related by a single constraint enabling us to describe part of the spectrum by…
Algebraic framework for construction of a commuting set of operators that can be interpreted as integrals of motion of the open spin chain with boundary conditions and nearest neighbour interaction is investigated.
We derive a master equation for the dynamical spin-spin correlation functions of the XXZ spin-1/2 Heisenberg finite chain in an external magnetic field. In the thermodynamic limit, we obtain their multiple integral representation.
In this paper we continue our derivation of the correlation functions of open quantum spin 1/2 chains with unparallel magnetic fields on the edges; this time for the more involved case of the XXZ spin 1/2 chains. We develop our study in the…
The correlation functions of the spin-1/2 XXZ chain in the ground state were expressed in the form of multiple integrals for -1<\Delta \leq 1 and 1<\Delta. In particular, adjacent four-point correlation functions were given as certain…
We present a construction of integrable quantum spin chains where local spin-spin interactions are weighted by ``position''-dependent potential containing abelian non-local spin dependance. This construction applies to the previously…
Combining a lattice path integral formulation for thermodynamics with the solution of the quantum inverse scattering problem for local spin operators, we derive a multiple integral representation for the time-dependent longitudinal…
We show how to exploit algebraic relations of operators (or matrices) which constitute the non-equilibrium matrix product steady state of a boundary driven quantum spin chain to find partial differential equations determining all the…
The state of quantum systems, their energetics, and their time evolution is modeled by abstract operators. How can one visualize such operators for coupled spin systems? A general approach is presented which consists of several shapes…
In this review, I describe a recent approach based on the representation theory of the $q-$Onsager algebra which is used to derive exact results for the XXZ open spin chain. The complete spectrum and eigenstates are obtained as rational…
We consider the question of what quantum spin chains naturally encode in their Hilbert space. It turns out that quantum spin chains are rather rich systems, naturally encoding solutions to various problems in combinatorics, group theory,…
We systematise and develop a graphical approach to the investigations of quantum integrable vertex statistical models and the corresponding quantum spin chains. The graphical forms of the unitarity and various crossing relations are…
We apply the recently developed thermal form factor expansion method to evaluate the real-time longitudinal spin-spin correlation functions of the spin-$\frac{1}{2}$ XXZ chain in the antiferromagnetically ordered regime at temperature…
We give a descriptive review of the Fermionic basis approach to the theory of correlation functions of the XXZ quantum spin chain. The emphasis is on explicit formulae for short-range correlation functions which will be presented in a way…
The non-Abelian symmetries of the half-infinite XXZ spin chain for all possible types of integrable boundary conditions are classified. For each type of boundary conditions, an analog of the Chevalley-type presentation is given for the…