Session L18: Focus Session: Low D/Frustrated Magnetism - 2D Lattices

Exotic quantum phases in a frustrated quantum spin model on a honeycomb lattice

A quantum spin liquid is a phase that defies the usual conventions, i.e. quantum fluctuations prevent long range order even at $T = 0$. The search for models that exhibit this type of behavior has intensified in recent years. In this work, we utilize the Lanczos algorithm to study hard-core bosons on a frustrated honeycomb lattice with nearest-neighbor ($t$) and next-nearest-neighbor hoppings ($t^\prime$). The two limits of this model, $t^\prime / t = 0$ and $t^\prime / t = \infty$, favor two different superfluid phases. In between, we find that an anomalous phase is stabilized by the strong frustration in this system and compare its properties with a quantum spin liquid and a fragmented Bose-Einstein condensate.   

Protecting the Kitaev honeycomb model from external fields

We propose an approach to generate many-body interactions from two-body interactions with stable cat states. Applied to the celebrated Kitaev honeycomb model, our approach opens a spectral gap in the gapless phase of the model without any external magnetic field. We confirm the non-Abelian topological properties of a generalized Kitaev model and demonstrate our approach's robustness to sources of error. Our work provides a complete framework for experimentally realizing and manipulating non-Abelian anyons, with direct application in topological quantum computation.   

Paramagnetic ground states and field-driven N\'eel order in S=3/2 Heisenberg antiferromagnets on a honeycomb lattice

We study the spin-3/2 Heisenberg antiferromagnet on a honeycomb lattice with exchange interactions which frustrate N\'eel order. Our motivation stems from the recent synthesis of $Bi_3 Mn_4 O_{12} (NO_3 )$, a spin-3/2 bilayer honeycomb lattice antiferromagnet which remains paramagnetic to the lowest temperature, but shows a field-induced N\'eel transition. We use a combination of spin wave theory, exact diagonalization, and bond operator theory to study the effects of quantum and thermal fluctuations, second-neighbor exchange, biquadratic exchange and bilayer coupling. Biquadratic terms give rise an AKLT valence bond solid ground state, and bilayer coupling leads to an interlayer dimer solid. Upon applying a magnetic field, both these states undergo a phase transition into a N\'eel long range ordered state. We comment on experimental consequences and disorder effects.   

Gapped $Z_2$ spin liquid and chiral antiferromagnetic phase in Hubbard model on the honeycomb lattice

In Schwinger-fermion representation we identify a $Z_2$ spin liquid called the sublattice-pairing state (SPS) as the gapped spin liquid phase discovered in recent Quantum Monte study of Hubbard model on a honeycomb lattice. We show that SPS is identical to the zero-flux $Z_2$ spin liquid state in Schwinger-boson representation by an explicit duality transformation. SPS is connected to an \emph{unusual} antiferromagnetic ordered phase, which we term as chiral-antiferromagnetic (CAF) phase, through an $O(4)$ critical point. CAF phase breaks $SU(2)$ spin rotation symmetry completely and has three Goldstone modes. Our results indicate that there is likely a hidden phase transition between CAF phase and the usual antiferromagnetic (Neel) phase at large $U/t$. We also propose numerical measurements to reveal the CAF phase and the hidden phase transition.   

Exotic phases in Mott insulating Iridates with strong spin-orbit coupling: Phase diagram of the Kitaev-Heisenberg model in a magnetic field

Motivated by the recent proposal of a Mott insulating state with strong spin-orbit coupling for the Iridate Na$_{2}$IrO$_{3}$[1], we discuss the collective ground states of the effective Iridium moments in the presence of Heisenberg-Kitaev exchange interactions and a time-reversal symmetry breaking magnetic field. For a field pointing in the (111) direction we find a rich phase diagram with both symmetry breaking magnetically ordered phases as well as an unconventional topological phase which is stable over a small range of coupling parameters. Our numerical simulations further indicate two exotic multicritical points at the boundaries between these ordered phases, which we will discuss.\\[4pt] [1] J. Chaloupka, G. Jackeli, and G. Khaliullin, Phys. Rev. Lett. 105, 027204 (2010).   

Schwinger boson spin liquid states on honeycomb lattice: projective symmetry group analysis and critical field theory

Motivated by the numerical evidence of a gapped spin liquid in the honeycomb Hubbard model [Meng et al. Nature 464, 847 (2010)], we analyse possible Z$_2$ spin liquids with gapped bosonic spinons coupled to Z$_2$ gauge field on honeycomb lattice within the Schwinger boson formalism. By the projective symmetry group method we find that there are only two relevant Z$_2$ spin liquids on honeycomb lattice with different (zero or $\pi$) gauge flux in the elemental hexagon. The zero-flux state seems to be a good candidate for the numerically observed spin liquid. It can acquire collinear AFM Neel order via a continuous O(4) transition. In the critical field theory of this transition the coupling of bosonic spinons to the Higgs field contains cubic powers of spatial derivatives, therefore does not break honeycomb lattice symmetry and allows for a continuous transition to a commensurate collinear Neel order. We will also discuss several observable features of this spin liquid.   

Nature of the spin liquid state of the Hubbard model on the honeycomb lattice

Recent numerical work (Nature 464, 847 (2010)) indicates the existence of a spin liquid phase (SL) that intervenes between the antiferromagnetic and semimetallic phases of the half filled Hubbard model on a honeycomb lattice. To better understand the nature of this exotic phase, we study the quantum $J_1-J_2$ spin model on the honeycomb lattice, which provides an effective description of the Mott insulating region of the Hubbard model. Employing the variational Monte Carlo approach, we analyze the phase diagram of the model, finding a phase transition between antiferromagnet and an unusual $Z_2$ SL state which we identify as the SL phase of the Hubbard model. At higher $J_2/J_1 > 0.3$ we find a transition to a dimerized state with spontaneously broken rotational symmetry.   

Finite-temperature phase transition to $m=1/2$ plateau phase in a S=1/2 XXZ model on Shastry-Sutherland Lattices

We study the finite-temperature transition to the $m=1/2$ magnetization plateau in a model of interacting $S=1/2$ spins with longer range interactions and strong exchange anisotropy on the geometrically frustrated Shastry-Sutherland lattice. This model was shown to capture the qualitative features of the field-induced magnetization plateaus in the rare-earth tetraboride, ${\rm TmB_4}$. Our results show that the transition to the plateau state occurs via two successive transitions with the two-dimensional Ising universality class, when the quantum exchange interactions are finite, whereas a single phase transition takes place in the purely Ising limit. To better understand these behaviors, we perform Monte Carlo simulations of the classical generalized four-state chiral clock model and compare the phase diagrams of the two models. The magnetic properties and critical behavior of the finite-temperature transition to the $m=1/2$ plateau state are also discussed.   

Study of spin-lattice coupling in the Shastry-Sutherland compound SrCu$_2$(BO$_3$)$_2$

SrCu$_2$(BO$_3$)$_2$ supports a network of orthogonally coupled spin-dimers whose ground state consists of localized spin-singlets which can be described by the exactly solvable Shastry-Sutherland Hamiltonian. On applying strong magnetic fields ($>$20T), however, the spin gap in SrCu$_2$(BO$_3$)$_2$ is closed and triplet excitations are generated. As a consequence of the strong geometric frustration, the triplet band is nearly dispersionless and a sequence of steps and plateaux in the magnetisation at integer fractions of the saturation magnetisation are observed, corresponding to static magnetic textures that are commensurate with the lattice. Here we present high resolution measurements in pulsed magnetic fields up to 65T of the magnetostriction and magnetocaloric effect which 1) shed light on the coupling between spin and lattice degrees of freedom and 2) are aimed to address discrepancies between existing data and theoretical predictions for the sequence of field-induced plateaus. Experiments were carried out at the Dresden High Magnetic Field Laboratory and the pulsed field facility of the National High Magnetic Field Laboratory.   

Phase Transitions in the $J_1-J_2$ Ising Model on the Square Lattice

The $J_1-J_2$ Ising model on the square lattice is one of the simplest classical models to study the effects of competing interactions and the resulting phase transitions. In spite of previous studies, there remains a controversy regarding the nature of the transition into the ``stripe`` phase in this model for $J_2/J_1>0.5$. In this study, we use the Binder cumulant of the order parameter to address this question. We use the Wang-Landau and Metropolis algorithms to simulate the model in the relevant parameter space. From our numerics, we determine that the transition is first-order for $0.5 [Preview Abstract]

Low Temperature $^{31}$P-NMR Study of the Frustrated Square-Lattice Compound BaCdVO(PO$_{4}$)$_{2}$

BaCdVO(PO$_{4})_{2}$ is known to be a S = $\raise.5ex\hbox{$\scriptstyle 1$}\kern-.1em/ \kern-.15em\lower.25ex\hbox{$\scriptstyle 2$} $ frustrated square-lattice (FSL) system with a ferromagnetic nearest neighbor exchange coupling J$_{1}\sim $ -3.36 K and an antiferromagnetic next nearest neighbor exchange coupling J$_{2}\sim $ 3.53 K. We have carried out $^{31}$P-NMR measurements at low temperatures down to 0.1 K to investigate magnetic properties of this compound from a microscopic point of view. $^{31}$P spin-lattice relaxation rates (1/T$_{1})$ measured at H = 0.8 T are almost independent of temperature above 2 K, show a peak at 1.05 K and become constant below 0.4 K. The temperature dependence of 1/T$_{1}$ indicates the existence of antiferromagnetic ordering at T$_{N}\sim $ 1.05 K which is also evidenced by the broadening of the NMR spectrum below that temperature. We will compare our NMR results with those of a similar FSL system, Pb$_{2}$VO(PO$_{4})_{2}$ and discuss the similarities and differences in the magnetic properties of these two systems.   

Magnetic phase diagram of spatially anisotropic, frustrated spin-1/2 Heisenberg antiferromagnet on square and stacked square lattices

Magnetic phase diagram of a spatially anisotropic, frustrated spin-1/2 Heisenberg antiferromagnet on a square and a stacked square lattice is investigated using second-order spin-wave expansion. It is shown that with increase in next nearest neighbor frustration the second-order corrections play a significant role in stabilizing the magnetization. We obtain two ordered magnetic phases (Ne\'{e}l and stripe) separated by a paramagnetic disordered phase. Within second-order spin-wave expansion we find that the width of the disordered phase diminishes with increase in the interlayer coupling (for the 3D case) or with decrease in spatial anisotropy but it does not disappear. Our obtained phase diagram differs significantly from the phase diagram obtained using linear spin-wave theory.   

Study of Orbital Degenerate System in Frustrated Checkerboard Lattice

Orbital degree of freedom is one of the recent attractive themes in transition-metal oxides. In contrast to the spin degree of freedom, the orbital interaction explicitly depends on the bond direction, and a certain kind of frustration exists. In the geometrical frustrated lattice, cooperating and competing effects between the orbital frustration and the geometrical frustration provide new features in the static and dynamical properties of orbital. The present purpose is to study the intrinsic orbital frustration effect in a geometrical frustrated lattice. We introduce the spin-less Hubbard-type model with the doubly degenerate $d_{yz}$ and $d_{zx}$ orbitals in the checkerboard lattice. The effective Hamiltonian for the strong correlation limit is derived. We have the $J_{z} S_{i}^{z} S_{j}^{z}$ type Ising interaction for the nearest-neighbor bonds and the $J_{x} S_{i}^{x} S_{j}^{x}$ type Ising one for the next nearest-neighbor bonds. Here \textbf{\textit{S}} is the orbital pseudo-spin operator. In the mean-field approximation, there is a macroscopic number of degeneracy at the frustration point $J_{x}$/$J_{z}$=2. In the classical Monte-Carlo simulation, we have a staggered orbital order and the reentrant phase-boundary. In the analyses by the spin-wave approximation and the exact diagonalization method, a large damping of the high-energy orbital dynamics due to the frustration is observed.   

Thermodynamics of the AF Heisenberg Model on the Checkerboard Lattice; a Numerical Linked-Cluster Expansion Study

Employing numerical linked-cluster expansions (NLCEs) along with exact diagonalizations of finite clusters with periodic boundary condition, we study the energy, specific heat, entropy, and various susceptibilities of the antiferromagnetic (AF) Heisenberg model on the checkerboard lattice. NLCEs, combined with extrapolation techniques, allow us to access temperatures much lower than those accessible to exact diagonalization and other series expansions. We find that the high-temperature peak in specific heat decreases as the frustration increases, consistent with the large amount of unquenched entropy in the region around maximum classical frustration, where the nearest-neighbor and next-nearest-neighbor exchange interactions ($J$ and $J'$, respectively) have the same strength, and with the formation of a second peak at lower temperatures. The staggered susceptibility shows a change of character when $J'$ increases beyond $0.75J$, implying the disappearance of the long-range AF order at zero temperature. For $J'=4J$, in the limit of weakly-coupled crossed chains, we find large susceptibilities for stripe and N\'{e}el order with ${\bf Q}=(\pi/2,\pi/2)$ at low temperatures with AF correlations along the chains. Other magnetic and bond orderings, such as a plaquette valence-bond solid and a crossed-dimer order suggested by previous studies, have also been investigated.   

Quantum Phases of the Cairo Pentagonal Lattice

We present an analytical and numerical study of the spin S=1/2 antiferromagnetic Heisenberg model on the Cairo pentagonal lattice. This is the dual of the Shastry-Sutherland lattice and has been discussed as a possible new candidate for having a spin liquid ground state [1]. More recently a S=5/2 version of this model has been realized in the Bi2Fe4O9 system [2]. Here we use a model with two different types of exchange couplings and investigate the nature of the ground state as a function of their ratio. This strategy allows us to understand the nature of a number of phases and derive effective models for their description with and without a magnetic field. Of particular interest is a surprising interplay between a collinear and a four-sublattice orthogonal phase due to an underlying order-by-disorder mechanism. Furthermore we address the issue of possible nonmagnetic ground states such as singlet and spin nematic phases. \\[4pt] [1] K. S. Raman, R. Moessner, and S. L. Sondhi, PRB 72, 064413 (2005)\\[0pt] [2] E. Ressouche, V. Simonet, B. Canals, M. Gospodinov, and V. Skumryev, PRL 103, 267204 (2009)