Related papers: Exactly solvable inhomogeneous XY spin chain
We consider integrable models of the Haldane-Shastry type with open boundary conditions. We define monodromy matrices, obeying the reflection equation, which generate the symmetries of these models. Using a map to the Calogero-Sutherland…
An inhomogeneous T-Q equation has recently been proposed by Cao, Yang, Shi and Wang for the open spin-1/2 XXX chain with general (nondiagonal) boundary terms. We argue that a simplified version of this equation describes all the eigenvalues…
The anisotropic XY-model in a transverse field (s=1/2) on the one-dimensional alternating superlattice (closed chain) is considered. The solution of the model is obtained by introducing a generalized Jordan-Wigner transformation which maps…
We show that an inhomogeneous coagulation/decoagulation model can be mapped to a quadratic fermionic model via a Jordan-Wigner transformation. The spectrum for this inhomogeneous model is computed exactly and the spectral gap is described…
We study the sine-square deformed quantum XY chain with open boundary conditions, in which the interaction strength at the position $x$ in the chain of length $L$ is proportional to the function $f_x = \sin^2 [\pi/L (x-1/2)]$. The model can…
In this paper, we write exactly solvable generalizations of 1-dimensional quantum XY and Ising-like models by using $2^d$-dimensional Gamma ($\Gamma$) matrices as the degrees of freedom on each site. We show that these models result in…
We have considered a numerical scheme for the calculation of the equilibrium properties of spin-1/2 XY chains. Within its frames it is necessary to solve in the last resort only the 2N\times 2N eigenvalue and eigenvector problem but not the…
We study non-interacting fermionic systems dissipatively driven at their boundaries, focusing in particular on the case of a non-number-conserving Hamiltonian, which for example describes an $XY$ spin chain. We show that despite the lack of…
We construct a class of exactly solvable generalized Kitaev spin-$1/2$ models in arbitrary dimensions, which is beyond the category of quantum compass models. The Jordan-Wigner transformation is employed to prove the exact solvability. An…
Exactly solvable models are essential in physics. For many-body spin-1/2 systems, an important class of such models consists of those that can be mapped to free fermions hopping on a graph. We provide a complete characterization of models…
A unified theory of orthogonal polynomials of a discrete variable is presented through the eigenvalue problem of hermitian matrices of finite or infinite dimensions. It can be considered as a matrix version of exactly solvable Schr\"odinger…
A new family of free fermionic quantum spin chains with multispin interactions was recently introduced. Here we show that it is possible to build standard quantum Ising chains -- but with inhomogeneous couplings -- which have the same…
We use the quantum separation of variable (SOV) method to construct the eigenstates of the open XXZ chain with the most general boundary terms. The eigenstates in the inhomogeneous case are constructed in terms of solutions of a system of…
Commuting transfer matrices for linear chains of interacting non-Abelian anyons from the two-dimensional irreducible representation of the dihedral group $D_3$ (or, equivalently, the integer sector of the $su(2)_4$ spin-$1$ chain) are…
We present a general method of folding an integrable spin chain, defined on a line, to obtain an integrable open spin chain, defined on a half-line. We illustrate our method through two fundamental models with sl(2) Lie algebra symmetry:…
We consider the non-Hermitian XY spin chain with open boundary conditions when the anisotropy parameter is extended to complex values. By analyzing the quasi-Hamiltonian matrix, we demonstrate that the free-fermion structure of the…
A method of integral equations is developed to study inhomogeneous fluids with planar spins in an external field. As a result, the calculations for these systems appear to be no more difficult than those for ordinary homogeneous liquids.…
Proposed is a generalization of Jordan-Wigner transform that allows to exactly fermionize a large family of quantum spin Hamiltonians in dimensions higher than one. The key new steps are to enlarge the Hilbert space of the original model by…
The paper presents exact calculations of thermodynamic quantities for the spin-1/2 isotropic XY chain with random lorentzian intersite interaction and transverse field that depends linearly on the surrounding intersite interactions.
We provide a theoretical set up for studying the dynamics in quantum spin chain models with inhomogeneous two-body interaction. We frame in our formalism models that can be mapped into a fermion system with a quadratic Hamiltonian. Local…