Related papers: Exactly solvable inhomogeneous XY spin chain
An exact Jordan-Wigner type of transformation is presented in 1D connecting spin-1/2 operators to spinful canonical Fermi operators. The transformation contains two free parameters allowing a broad interconnection possibility in between…
We provide the eigenfunctions for a quantum chain of $N$ conformal spins with nearest-neighbor interaction and open boundary conditions in the irreducible representation of $SO(1,5)$ of scaling dimension $\Delta = 2 - i \lambda$ and spin…
We define and study a long-range version of the XX model, arising as the free-fermion point of the XXZ-type Haldane--Shastry (HS) chain. It has a description via non-unitary fermions, based on the free-fermion Temperley--Lieb algebra, and…
The general solution to the reflection equation associated with the jordanian deformation of the SL(2) invariant Yang R-matrix is found. The same K-matrix is obtained by the special scaling limit of the XXZ-model with general boundary…
We review the papers on the Jordan-Wigner transformation in two dimensions to comment on a possibility of examining the statistical mechanics properties of two-dimensional spin-1/2 models. We discuss in some detail the two-dimensional…
For one-dimensional spin and pseudospin models that allow mapping to a Markov chain, the free energy of the system at a finite temperature can be expressed in terms of bond concentrations. Minimizing the free energy function makes it…
One random spin-1/2 XY chain that after Jordan-Wigner fermionization reduces to the extended Lloyd's model is considered. The random-averaged one-fermion Green functions have been calculated exactly that yields thermodynamics of the spin…
We develop an efficient algorithm for a spatially inhomogeneous matrix-valued quantum Boltzmann equation derived from the Hubbard model. The distribution functions are $2 \times 2$ matrix-valued to accommodate the spin degree of freedom,…
We obtain the symmetry algebra of multi-matrix models in the planar large N limit. We use this algebra to associate these matrix models with quantum spin chains. In particular, certain multi-matrix models are exactly solved by using known…
The transfer-matrix eigenvalues of the isotropic open Heisenberg quantum spin-1/2 chain with non-diagonal boundary magnetic fields are known to satisfy a TQ-equation with an inhomogeneous term. We derive here a discrete Wronskian-type…
Exact eigenvalue correlation functions are computed for large $N$ hermitian one-matrix models with eigenvalues distributed in two symmetric cuts. An asymptotic form for orthogonal polynomials for arbitrary polynomial potentials that support…
We study an exactly solvable one-dimensional spin-$\frac{1}{2}$ model which can support weak zero modes in its ground state manifold. The spin chain has staggered XXZ-type and ZZ-type spin interaction on neighboring bonds and is thus dubbed…
We propose a scheme for constructing classical spin Hamiltonians from Hunds coupled spin-fermion models in the limit J_H/t \to \infinity. The strong coupling between fermions and the core spins requires self-consistent calculation of the…
With the XXZ spin chains as examples, we prove two theorems: (1) the functional relations derived from the off-diagonal Bethe Ansatz scheme are the sufficient and necessary conditions to characterize the complete spectrum of the…
For arbitrary Ising-like models of any dimension and Hamiltonians with a finite support with all possible multispin interactions and boundary conditions with a shift, the exact value of the free energy in the thermodynamic limit is obtained…
We consider the reduced density matrix of a large block of consecutive spins in the ground states of the XY spin chain on an infinite lattice. We derive the spectrum of the density matrix using the expression of the Renyi entropy in terms…
The full spectrum of transfer matrices of the general eight-vertex model on a square lattice is obtained by numerical diagonalization. The eigenvalue spacing distribution and the spectral rigidity are analyzed. In non-integrable regimes we…
In [8], some exact splittings are proposed for inhomogeneous quadratic differential equations including, for example, transport equations, kinetic equations, and Schr{\"o}dinger type equations with a rotation term. In this work, these exact…
The isotropic XY model $(s=1/2)$ in a transverse field, with uniform long-range interactions among the transverse components of the spins, on the inhomogeneous periodic chain, is studied. The model, composed of $N$ segments with $n$…
The celebrated Jordan--Wigner transformation provides an efficient mapping between spin chains and fermionic systems in one dimension. Here we extend this spin-fermion mapping to arbitrary tree structures, which enables mapping between…