In this paper, we study the XX model with particular non-diagonal boundaries. Using a fermionization technique for an extended version of this chain we are able to present a new operator which commutes with the extended and also the original Hamiltonian. It is a highly non-trivial conserved quantity in the spin-chain formalism which gives rise to an interesting combinatorial partition function....

We study solvable spin chains where either fields or couplings vary linearly in space and create a sandwich-like structure of the ground state. We find that the entanglement entropy between two halves of a chain varies logarithmically with the interface width. After quenching to a homogeneous critical system, the entropy grows logarithmically in time in the XX model, but quadratically in the tr...

Since the discovery of the inorganic spin-Peierls compound CuGeO3 the interest in the properties of spin-Peierls systems considerably increased [1]. The models that can be examined exactly play an important role in clarifying the generic features of such systems. An example of such a model is the spin1 2 XX chain that was studied in several papers [2, 3, 4] (note, however, that in the nonadiaba...

The XX spin-chain with non-Hermitian diagonal boundary conditions is shown to be quasi-Hermitian for special values of the boundary parameters. This is proved by explicit construction of a new inner product employing a ”quasi-fermion” algebra in momentum space where creation and annihilation operators are not related via Hermitian conjugation. For a special example, when the boundary fields lie...

We discuss a simple procedure for obtaining new integrable spin chains from old by replacing each single state of the original model by some collection of states. This works whenever the Lax matrix of the chain has a certain form. The simplest example is the su(n) XX model. We apply the techniques of the nested algebraic Bethe ansatz to solve such systems, in the bosonic and supersymmetric cases.

Some exact solutions of the (2+1)-dimensional integrable classical continuous isotropic Heisenberg spin chain (the M-XX equation) are obtained by using Hirota's method. These solutions are characterized by an integer topological charge.

We calculate the quantum phase diagram of the XXZ chain with nearestneighbor (NN) J1 and next-NN exchange J2 with anisotropies ∆1 and ∆2 respectively. In particular we consider the case ∆1 = −∆2 to interpolate between the XX chain (∆i = 0) and the isotropic model with ferromagnetic J2. For ∆1 < −1, a ferromagnetic and two antiferromagnetic phases exist. For |∆i| < 1, the boundary between the di...

We consider the nonequilibrium time evolution of the transverse magnetization in the critical Ising and XX quantum chains. For some inhomogeneously magnetized initial states we derive analytically the transverse magnetization profiles and show that they evolve into scaling forms in the long-time limit. In particular it is seen that the Ising chain exhibits some similarities with the conserved d...

The Jordan-Wigner transformation is known as a powerful tool in condensed matter theory, especially in the theory of low-dimensional quantum spin systems. The aim of this chapter is to review the application of the Jordan-Wigner fermionization technique for calculating dynamic quantities of low-dimensional quantum spin models. After a brief introduction of the Jordan-Wigner transformation for o...

We continue the study of the Inverse Participation Ratios (IPRs) of the XXZ Heisenberg spin chain initiated by Misguich, Pasquier and Luck (2016) by focusing on the case of the XX Heisenberg Spin Chain. For the ground state, Misguich et al. note that calculating the IPR is equivalent to Dyson’s constant term ex-conjecture. We express the IPRs of excited states as an apparently new “discrete” Ha...