We investigate the thermodynamic properties of the frustrated bilayer quantum Heisenberg antiferromagnet at low temperatures in the vicinity of the saturation magnetic field. The low-energy degrees of freedom of the spin model are mapped onto a hard-square gas on a square lattice. We use exact diagonalization data for finite spin systems to check the validity of such a description. Using a classical Monte Carlo method we give a quantitative description of the thermodynamics of the spin model at low temperatures around the saturation field. The main peculiarity of the considered two-dimensional Heisenberg antiferromagnet is related to a phase transition of the hard-square model on the square lattice, which belongs to the two-dimensional Ising model universality class. It manifests itself in a logarithmic (low-)temperature singularity of the specific heat of the spin system observed for magnetic fields just below the saturation field.

Based on exact diagonalization data for finite quantum Heisenberg antiferromagnets on two frustrated lattices (two-leg ladder and bilayer) and analytical arguments we map low-energy degrees of freedom of the spin models in a magnetic field on classical lattice-gas models. Further we use transfer-matrix calculations and classical Monte Carlo simulations to give a quantitative description of low-temperature thermodynamics of the quantum spin models. The classical lattice-gas model yields an excellent description of the quantum spin models up to quite large temperatures. The main peculiarity of the considered frustrated bilayer is a phase transition which occurs at low temperatures for a wide range of magnetic fields below the saturation magnetic field and belongs to the two-dimensional Ising model universality class. 1 2 J (a) J 1 2 J J (b) FIG. 1: (Color online) Lattices considered in this paper: (a) the frustrated two-leg ladder and (b) the frustrated bilayer. The vertical bonds have the strength J2 > 0 whereas all other bonds have the strength J1 > 0.

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We consider the spin-1/2 antiferromagnetic Heisenberg model on three frustrated lattices (the diamond chain, the dimer-plaquette chain, and the two-dimensional square-kagome lattice) with almost dispersionless lowest magnon band. Eliminating high-energy degrees of freedom at high magnetic fields, we construct low-energy effective Hamiltonians, which are much simpler than the initial ones. These effective Hamiltonians allow a more extended analytical and numerical analysis. In addition to the standard strong-coupling perturbation theory, we also use a localized-magnon-based approach leading to a substantial improvement of the strong-coupling approximation. We perform extensive exact diagonalization calculations to check the quality of different effective Hamiltonians by comparison with the initial models. Based on the effective-model description, we examine the low-temperature properties of the considered frustrated quantum Heisenberg antiferromagnets in the high-field regime. We also apply our approach to explore thermodynamic properties for a generalized diamond spin chain model suitable to describe azurite at high magnetic fields. Interesting features of these highly frustrated spin models consist in a steep increase of the entropy at very small temperatures and a characteristic extra low-temperature peak in the specific heat. The most prominent effect is the existence of a magnetic-field-driven Berezinskii-Kosterlitz-Thouless phase transition occurring in the two-dimensional model. DERZHKO, RICHTER, KRUPNITSKA, AND KROKHMALSKII PHYSICAL REVIEW B 88, 094426 (2013) (a) m m m J m J J J J m ,3 m J m m J J J J J m be shown that these localized-magnon states have the lowest energy in their corresponding S z subspace, if the strength of the antiferromagnetic bonds of the trapping cells J 2 exceeds a lower bound. 2,36 J J J J J m ,m FIG. 2. (Color online) The square-kagome lattice described by Hamiltonian (2.1). The trapping cells (squares) for localized magnons are indicated by bold solid red lines (J 2 bonds). 094426-2 FRUSTRATED QUANTUM HEISENBERG . . . PHYSICAL REVIEW B 88, 094426 (2013)

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We consider the spin- anisotropic XY chain in a transverse (z) field with the Dzyaloshinskii-Moriya interaction directed along z-axis in spin space to examine the effect of the Dzyaloshinskii-Moriya interaction on the zz, xx and yy dynamic structure factors. Using the Jordan-Wigner fermionization approach we analytically calculate the dynamic transverse spin structure factor. It is governed by a two-fermion excitation continuum. We analyze the effect of the Dzyaloshinskii-Moriya interaction on the two-fermion excitation continuum. Other dynamic structure factors which are governed by many-fermion excitations are calculated numerically. We discuss how the Dzyaloshinskii-Moriya interaction manifests itself in the dynamic properties of the quantum spin chain at various fields and temperatures.

We consider the exactly solvable spin-1/2 XX chain with the three-spin interactions of the XZX + Y ZY and XZY − Y ZX types in an external (transverse) magnetic field. We calculate the entropy and examine the magnetocaloric effect for the quantum spin system. We discuss a relation between the cooling/heating efficiency and the ground-state phase diagram of the quantum spin model. We also compare ability to cool/heat in the vicinity of the quantum critical and triple points. Moreover, we examine the magnetocaloric effect for the spin-1/2 XX chain with three-spin interactions in a random (Lorentzian) transverse magnetic field.