Thermodynamic Behavior of Spin-1 Heisenberg Chain: a Comparative Study

In this work, we present a comparative study of thermodynamic quantum equilibrium observables of spin-1 Heisenberg chain. As a theoretical approach, the modified spin-wave theory is chosen. From the numerical side, we consider finite-temperature Lanczos, kernel polynomial, and density matrix renormalization techniques. The results show general consistency of thermodynamic quantities, such as heat capacity and magnetic susceptibility, calculated within the approaches. For the modified spin-wave, the results show some inaccuracy especially at low temperature, failure in capturing the gapped features of spin-1 Heisenberg chain, while the numerical approaches illustrate a good achievement at $$T\rightarrow 0$$ T → 0 within the proper parameters chosen.

On scalar products and form factors by Separation of Variables: the antiperiodic XXZ model

We consider the XXZ spin-1/2 Heisenberg chain with antiperiodic boundary conditions. The inhomogeneous version of this model can be solved by Separation of Variables (SoV), and the eigenstates can be constructed in terms of Q-functions, solution of a Baxter TQ-equation, which have double periodicity compared to the periodic case. We compute in this framework the scalar products of a particular class of separate states which notably includes the eigenstates of the transfer matrix. We also compute the form factors of local spin operators, i.e. their matrix elements between two eigenstates of the transfer matrix. We show that these quantities admit determinant representations with rows and columns labelled by the roots of the Q-functions of the corresponding separate states, as in the periodic case, although the form of the determinant are here slightly different. We also propose alternative types of determinant representations written directly in terms of the transfer matrix eigenvalues.

Defect-induced ferromagnetism in a S = 1/2 quasi-one-dimensional Heisenberg antiferromagnetic chain compound

We present evidences that defects in the spin S = 1/2 Heisenberg antiferromagnetic chain (HAFC) compound can lead to ferromagnetism by studying the magnetic and thermal properties of the newly discovered quasi-one-dimensional (1D) metal–organic framework [CH3NH3][Cu(HCOO)3] (MACuF). Our findings suggest that the long-range ferromagnetic order at 3.7 K can be attributed to Cu2+ ions from the 2D networks constructed by the endpoints of the broken chains. In such a case, the intrinsic magnetism can emerge in this quasi-1D Heisenberg chain system at the background of the short-range antiferromagnetism. This unusual ferromagnetism found in HAFC not only enriches magnetic features in the low-dimensional systems, but helps to understand some of the exotic magnetic phenomena in other real quasi-1D magnetic materials.

T − W relation and free energy of the Heisenberg chain at a finite temperature

A new nonlinear integral equation (NLIE) describing the thermodynamics of the Heisenberg spin chain is derived based on the t − W relation of the quantum transfer matrices. The free energy of the system in a magnetic field is thus obtained by solving the NLIE. This method can be generalized to other lattice quantum integrable models. Taking the SU(3)-invariant quantum spin chain as an example, we construct the corre- sponding NLIEs and compute the free energy. The present results coincide exactly with those obtained via other methods previously.