Dimensional crossover in spin-1 Heisenberg antiferromagnets: a quantum Monte Carlo study

We present results of large scale simulations of the spin-1 Heisenberg antiferromagnet on a tetragonal lattice. The stochastic series expansion quantum Monte Carlo method is used to calculate equilibrium thermodynamic variables in the presence of an external magnetic field. In particular, the low temperature magnetization curve is investigated in the quasi-one-dimensional (Q1D), quasi-two-dimensional (Q2D), and three-dimensional (3D) limits. Starting from the 3D limit, the Q1D (Q2D) limit is achieved by reducing the in-plane (out-of-plane) spin coupling strength towards zero. In the Q1D limit, a Haldane gap appears in the magnetization curve at low magnetic field. Additionally, near the saturation field the slope of the magnetization curve increases substantially, approaching the infinite-slope behavior of a one-dimensional spin-1 chain. A similar (though less pronounced) effect is seen in the Q2D limit. We also study the effect of uniaxial single-ion anisotropy on the magnetization curve for Q1D and Q2D systems. Our results will be important in understanding the field-induced behavior of a class of low-dimensional Ni-based quantum magnets.Comment: 4 pages, 4 figures. Submitted to proceedings of 26th International Conference on Low Temperature Physic

Dimensional Crossover in Quasi-one-dimensional Spin-1 Heisenberg Antiferromagnets

We study the quenching of the Haldane gap in quasi-one-dimensional systems of weakly coupled spin-1 antiferromagnetic Heisenberg chains. The critical interchain coupling Jc required to stabilize long range magnetic order can be accurately determined from large scale quantum Monte Carlo calculations. Several different geometries of coupled chains are studied, illustrating the dependence of Jc on the coordination of chains. For bipartite geometries, ferromagnetically coupled chains yield similar magnitudes for Jc.Comment: 5 pages, SCES 201

Columnar antiferromagnetic order and spin supersolid phase on the extended Shastry-Sutherland lattice

We use large scale quantum Monte Carlo simulations to study an extended version of the canonical Shastry-Sutherland model -- including additional interactions and exchange anisotropy -- over a wide range of interaction parameters and an applied magnetic field. The model is appropriate for describing the low energy properties of some members of the rare earth tetraborides. Working in the limit of large Ising-like exchange anisotropy, we demonstrate the stabilization of columnar antiferromagnetic order in the ground state at zero field and an extended magnetization plateau at 1/2 the saturation magnetization in the presence of an applied longitudinal magnetic field -- qualitatively similar to experimentally observed low-temperature phases in ErB$_4$. Our results show that for an optimal range of exchange parameters, a spin supersolid ground state is realized over a finite range of applied field between the columnar antiferromagnetic phase and the magnetization plateau. The full momentum dependence of the longitudinal and transverse components of the static structure factor is calculated in the spin supersolid phase to demonstrate the simultaneous existence of diagonal and off-diagonal long-range order. Our results will provide crucial guidance in designing further experiments to search for the interesting spin supersolid phase in ErB$_4$.Comment: 5 pages, 4 figure

Strange correlations in spin-1 Heisenberg antiferromagnets

We study the behavior of the recently proposed "strange correlator" [Phys. Rev. Lett. {\bf 112}, 247202 (2014)] in spin-1 Heisenberg antiferromagnetic chains with uniaxial single-ion anisotropy. Using projective quantum Monte Carlo, we are able to directly access the strange correlator in a variety of phases, as well as to examine its critical behavior at the quantum phase transition between trivial and non-trivial symmetry protected topological phases. After finding the expected long-range behavior in these two symmetry conserving phases, we go on to verify the topological nature of two-leg and three-leg spin-1 Heisenberg antiferromagnetic ladders. This demonstrates the power of the strange correlator in distinguishing between trivial and non-trivial symmetry protected topological phases.Comment: 7 pages, 6 figure

Magnetic phases in the S=1 Shastry-Sutherland model with uniaxial anisotropy

We explore the field induced magnetic phases of an $S=1$ $XXZ$ model with single-ion anisotropy and large Ising-like anisotropy on a Shastry Sutherland lattice over a wide range of Hamiltonian parameters and applied magnetic field. The multitude of ground state phases are characterized in detail in terms of their thermodynamic properties and the underlying classical (Ising limit) spin arrangements for the plateau phases are identified by calculating the static structure factors. The enlarged local Hilbert space of the $S=1$ spins results in several new ground state phases that are not realized for $S=1/2$ spins. These include the quantum paramagnetic state that is ubiquitous to $S=1$ spins with single ion anisotropy, two different spin supersolid phases (with distinct longitudinal ordering) and a magnetization plateau that arises as a direct descendant of the 1/3 plateau due to quantum fluctuations that are not possible for $S=1/2$ spins. We predict the same mechanism will lead to plateaus at smaller fractions of 1/3 for higher spins. The full momentum dependence of the longitudinal and transverse components of the static structure factor is calculated in the spin supersolid phase to demonstrate the simultaneous existence of diagonal and off-diagonal long-range order as well as the different longitudinal orderings.Comment: 7 pages, 7 figure

Magnons in a two dimensional transverse field XXZ model

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.Comment: 12 pages, 9 figure