Abstract:
The spin-Peierls transition in the ground state of a quasi-one-dimensional spin-1/2 Heisenberg model coupled to adiabatic bond phonons is studied using a quantum Monte Carlo (QMC) method. The transition from a gapless Neel state to a spin-gapped Peierls state is explored in the parameter space spanned by the spatial anisotropy and the strength of spin-lattice coupling. It is found that for any finite inter-chain coupling, the transition to a dimerized Peierls ground state occurs only when the spin-lattice coupling exceeds a finite, non-zero critical value. This is in contrast to the pure 1D model, where adiabatic phonons lead to a dimerized ground state for any non-zero spin-phonon coupling. The phase diagram in the above parameter space is mapped out. No evidence is found for a region of co-existing long range magnetic order and dimerization. The vanishing of the Neel order occurs simultaneously with the setting in of the dimerization.

Abstract:
The phase diagram of the Bose-Hubbard model in the presence of off-diagonal disorder is determined using Quantum Monte Carlo simulations. A sequence of quantum glass phases intervene at the interface between the Mott insulating and the Superfluid phases of the clean system. In addition to the standard Bose glass phase, the coexistence of gapless and gapped regions close to the Mott insulating phase leads to a novel Mott glass regime which is incompressible yet gapless. Numerical evidence for the properties of these phases is given in terms of global (compressibility, superfluid stiffness) and local (compressibility, momentum distribution) observables.

Abstract:
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.

Abstract:
We study an anisotropic Heisenberg antiferromagnet with ferromagnetic transverse spin exchange using exact quantum Monte Carlo methods. Such a model is relevant to a class of rare earth tetraboride materials that display a range of magnetization plateaus under applied magnetic field. The layered arrangement of magnetic ions in these materials is topologically equivalent to the Shastry-Sutherland lattice. In this frustrated geometry, we study the interplay of next-nearest neighbor interactions in stabilizing a plateau at half the saturation magnetization (or 1/2 plateau). We also show hysteresis-like behavior at the onset of the 1/3 plateau.

Abstract:
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.

Abstract:
We review the basic properties of the Haldane phase in spin-1 Heisenberg antiferromagnetic chains, including its persistence in quasi-one-dimensional geometries. Using large-scale numerical simulations, we map out the phase diagram for a realistic model applicable to experimental Haldane compounds. We also investigate the effect of different chain coupling geometries and confirm a general mean field universality of the critical coupling times the coordination number of the lattice. Inspired by the recent development of characterization of symmetry protected topological states, of which the Haldane phase of spin-1 Heisenberg antiferromagnetic chain is a preeminent example, we provide direct evidence that the quasi-one-dimensional Haldane phase is indeed a non-trivial symmetry protected topological state.

Abstract:
We consider a quasi-one-dimensional system of spin-1 Heisenberg antiferromagnetic chains in 2D and 3D hypercubic lattices with interchain coupling $J$ and uniaxial single-ion anisotropy $D$. Using large scale numerical simulations, we map out the $J-D$ phase diagram and investigate the low lying excitations of the Haldane phase in the $J\ll1$ limit. We also provide direct evidence that the Haldane phase remains a non-trivial symmetry protected topological state for small but finite $J$.

Abstract:
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$_4$.

Abstract:
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.

Abstract:
We consider an S=1 Heisenberg chain with strong exchange (Delta) and single--ion uniaxial anisotropy (D) in a magnetic field (B) along the symmetry axis. The low energy spectrum is described by an effective S=1/2 XXZ model that acts on two different low energy sectors for a given window of fields. The vacuum of each sector exhibits Ising-like antiferromagnetic ordering that coexists with the finite spin stiffness obtained from the exact solution of the effective XXZ model. In this way, we demonstrate the existence of a spin supersolid phase. We also compute the full Delta-B quantum phase diagram by means of a quantum Monte Carlo simulation.