Magnons in a two-dimensional transverse-field XXZ model

Abstract

The XXZ model on a square lattice in the presence of a transverse magnetic field is studied within the spin wave theory to investigate the resulting canted antiferromagnet. The small and large field regimes are probed separately both for easy-axis and easy-plane scenarios which reveal an unentangled factorized ground state at an intermediate value of the field. Goldstone modes are obtained for the field-free XY antiferromagnet as well as for the isotropic antiferromagnet with field up to its saturation value. Moreover, for an easy-plane anisotropy, we find that there exists a non-zero field, where magnon degeneracy appears as a result of restoration of an U(1) sublattice symmetry and that, across that field, there occurs a magnon band crossing. For completeness, we then obtain the system phase diagram for S = 1/2 via large scale quantum Monte Carlo simulations using the stochastic series expansion technique. Our numerical method is based on a quantization of spin along the direction of the applied magnetic field and does not suffer from a sign-problem, unlike comparable algorithms based on a spin quantization along the axis of anisotropy. With this formalism, we are also able to obtain powder averages of the transverse and longitudinal magnetizations, which may be useful for understanding experimental measurements on polycrystalline samples.

Photoinduced entanglement in a magnonic Floquet topological insulator

“…At very large frequency, the DMI term becomes negligible and the XXZ model of the Floquet Hamiltonian shows finite entanglement as soon as the anisotropy becomes easy planar. Product state of the easy axis FM turns into a entangled state with moments oriented in the spin-xy plane 41 . Finally for ∆ α → ∞, the ground state still has no product state form as no direction in xy plane is preferred for the spin-moments.…”

Two-dimensional quantum-spin-1/2 XXZ magnet in zero magnetic field: Global thermodynamics from renormalisation group theory

“…The isotropic Heisenberg (XXX) model has an SU (2) symmetry, which remains unbroken at finite temperatures for d 2, as suggested by the Mermin-Wagner theorem. 4 The model does not show a finite-temperature phase transition in d = 2, 4,5 unless a symmetry-breaking external magnetic field or an interaction anisotropy is present [6][7][8][9][10] . As shall be discussed in Section IV A 2, even a slight anisotropy can induce an ordered phase at finite-temperatures.…”

“…The low-lying excitations are gapless, and can be understood by linear spin-wave theory or by vortex theory. 9 In this quantum spin-liquid phase at low-temperatures, due to a large density of low-energy states, specific heat is expected to be linear in temperature 126,127 : Note the cusp at ∆ = 0 and the discontinuity at ∆ = 1. Sommerfeld coefficient is zero at |∆| = 1 and remains zero in Ising-like regimes (|∆| > 1, see Fig.…”

“…In addition to the disordered paramagnetic phase (PM) at high temperatures, we identify three ordered phases at low temperatures: ferromagnetic and antiferromagnetic ordering (FM and AFM) for the Ising-like regimes of ∆ > 1 and ∆ < −1, and a vortex-type ordering in the Kosterlitz-Thouless (KT) phase for the XY-like regime of |∆| < 1. We emphasize that in the KT phase (also called spinflipping phase in the presence of U (1)-symmetry-breaking external magnetic field 8 , or XY phase in zero-field 91 ), the ordering in s x (and s y ) components is a topological bound-vortex-antivortex ordering 74,75 with vanishing magnetization in all directions 9,92 , but non-zero helicity modulus 93 . On the contrary, the FM (AFM) ordering results in a non-vanishing magnetization (staggered magnetization) in s z spin components 94 , as well as non- vanishing spin-spin correlations 95 .…”

Magnon excitations in $Cs_2CuAl_4O_8$ - a bond alternating S=1/2 spin chain with next nearest neighbor coupling

“…1). The spin-coordinates at each lattice point in the helical state is then rotated by the canting angle, so that it mimics a ferromagnetic state along the ẑ axis in the rotated frame 11 . A successive Holstein-Primakoff transformation in these new frame gives the Hamiltonian in terms of the spin-wave operators where the constant zero-energy part of the diagonalized Hamiltonian becomes a function of the canting angle.…”