Spin Chain

We present some open problems in the field of exactly solvable models. Two of the problems are related to the correlation functions of the XXX spin chain and the XXZ spin chain, one to the entropy of subsystems and one to the six vertex model with domain wall boundary conditions.

In many experimental situations, a physical system undergoes stochastic evolution which may be described via random maps between two compact spaces. In the current work, we study the applicability of large deviations theory to time-averaged quantities which describe such stochastic maps, in particular time-averaged currents and density functionals. We derive the large deviations principle for these quantities, as well as

We consider the most general three-state spin chain with U(1)^3 symmetry and nearest neighbour interaction. Our model contains as a special case the spin chain describing the holomorphic three scalar sector of the three parameter complex deformation of N=4 SYM, dual to type IIB string theory in the generalized Lunin-Maldacena backgrounds discovered by Frolov. We formulate the coordinate space Bethe ansatz, calculate the S-matrix and determine for which choices of parameters the S-matrix fulfills the Yang-Baxter equations. For these choices of parameters we furthermore write down the R-matrix. We find in total four classes of integrable models. In particular, each already known model of the above type is nothing but one in a family of such models.

We discuss the stringy properties of high-energy QCD using its hidden integrability in the Regge limit and on the light-cone. It is shown that multi-colour QCD in the Regge limit belongs to the same universality class as superconformal Script N = 2 SUSY YM with Nf = 2Nc at the strong coupling orbifold point. The analogy with integrable structure governing

Motivated by recent experiments on quasi-1D vanadium oxides, we study quantum phase transitions in a one-dimensional spin-orbital model describing a Haldane chain and a classical Ising chain locally coupled by the relativistic spin-orbit interaction. By employing a field-theoretical approach, we analyze the topology of the ground-state phase diagram and identify the nature of the phase transitions. In the strong coupling limit, a long-range N\'eel order of entangled spin and orbital angular momentum appears in the ground state. We find that, depending on the relative scales of the spin and orbital gaps, the linear chain follows two distinct routes to reach the N\'eel state. First, when the orbital exchange is the dominating energy scale, a two-stage ordering takes place in which the magnetic transition is followed by melting of the orbital Ising order; both transitions belong to the two-dimensional Ising universality class. In the opposite limit, the low-energy orbital modes undergo a continuous reordering transition which represents a line of Gaussian critical points. On this line the orbital degrees of freedom form a Tomonaga-Luttinger liquid. We argue that the emergence of the Gaussian criticality results from merging of the two Ising transitions in the strong hybridization region where the characteristic spin and orbital energy scales become comparable. Finally, we show that, due to the spin-orbit coupling, an external magnetic field acting on the spins can induce an orbital Ising transition.

Using random-phase approximation results, mean-field theory, and refined data for the polarization vectors we determine the coupling constants of the four Peierls-active phonon modes to the spin chains. We then derive the values of the coupling of the spin system to the linear ionic displacements, the bond lengths and the angles between bonds. Our values are consistent with microscopic theories and various experimental results. We discuss the applicability of static approaches to the spin-phonon coupling. The c-axis anomaly of the thermal expansion is explained. We give the values of the coupling constants in an effective one-dimensional Hamiltonian.

We report a neutron diffraction and muon spin relaxation μSR study of static and dynamical magnetic properties of BaCo2V2O8, a quasi-one-dimensional spin-chain system. A proposed model for the antiferromagnetic structure includes: a propagation vector k⃗AF=(0,0,1), independent of external magnetic fields for fields below a critical value Hc(T). The ordered moments of 2.18 μB per Co ion are aligned along the crystallographic c axis. Within the screw chains, along the c axis, the moments are arranged antiferromagnetically. In the basal planes the spins are arranged ferromagnetically (forming zigzag paths) along one of the axes and antiferromagnetically along the other. The temperature dependence of the sublattice magnetization is consistent with the expectations of the three-dimensional (3D) Ising model. A similar behavior is observed for the internal static fields at different muon stopping sites. Muon time spectra measured at weak longitudinal fields and temperatures much higher than TN can be well described using a single muon site with an exponential muon spin relaxation that gradually changes into an stretched exponential on approaching TN. The temperature-induced changes of the relaxation suggest that the Co fluctuations dramatically slow down and the system becomes less homogeneous as it approaches the antiferromagnetic state.

We report a neutron diffraction and muon spin relaxation muSR study of static and dynamical magnetic properties of BaCo2V2O8, a quasi-one-dimensional spin-chain system. A proposed model for the antiferromagnetic structure includes: a propagation vector k_AF = (0, 0, 1), independent of external magnetic fields for fields below a critical value H_c(T). The ordered moments, of 2.18 \mu_B per Co ion, are aligned along the crystallographic c-axis. Within the screw chains, along the c axis, the moments are arranged antiferromagnetically. In the basal planes the spins are arranged ferromagnetically (forming zig-zags paths) along one of the axis and antiferromagnetically along the other. The temperature dependence of the sub-lattice magnetization is consistent with the expectations of the 3D Ising model. A similar behavior is observed for the internal static fields at different muon stopping sites. Muon time spectra measured at weak longitudinal fields and temperatures much higher than T_N can be well described using a single muon site with an exponential muon spin relaxation that gradually changes into an stretched exponential on approaching T_N. The temperature-induced changes of the relaxation suggest that the Co fluctuations dramatically slow down and the system becomes less homogeneous as it approaches the antiferromagnetic state.