Using quantum Monte Carlo simulations and field-theory arguments, we study the fully frustrated (Villain) transverse-field Ising model on the square lattice. We consider a "primary" spin order parameter and a "secondary" dimer order parameter, which both lead to the same phase diagram but detect $Z_8$ and $Z_4$ symmetry, respectively. The spin order scales with conventional exponents, both in the finite temperature critical phase and at the $T = 0$ quantum critical point. The scaling of the dimer order requires more detailed investigations of the applicable low-energy theories; the height model at $T > 0$ and the $O(2)$ model in 2+1 dimensions at $T = 0$. Relating the order parameters to operators in these effective models, we predict the secondary critical exponents and confirm them numerically. The relationships between the primary and secondary order parameters have not been previously discussed in this context and provide insight more broadly for Ising models whose low-energy physics involves dimer degrees of freedom.
We use a Monte Carlo simulation to study the diluted antiferromagnetic Ising model on the frustrated lattices including the pyrochlore lattice to show the dilution effects. Using the Wang-Landau algorithm, which directly calculates the energy density of states, we accurately calculate the entropy of the system. We discuss the nonmonotonic dilution concentration dependence of residual entropy for the antiferromagnetic Ising model on the pyrochlore lattice, and compare it to the generalized Pauling approximation proposed by Ke et al. [Phys. Rev. Lett. 99, 137203 (2007)]. We also investigate othe…
Transverse field Ising model is a common model in quantum magnetism and is often illustrated as an example for quantum phase transition. Its physical origin in quantum magnets, however, is actually not quite well-understood. The quantum mechanical properties of this model on frustrated systems are not well-understood either. We here clarify the physical origin, both extrinsic one and intrinsic one, for the transverse field of the quantum Ising model, and then explain the quantum effects in the Kagome system. We discuss the quantum plaquette order and the quantum phase transition out of this or…
Working within the Stochastic Series Expansion (SSE) framework, we construct efficient quantum cluster algorithms for transverse field Ising antiferromagnets on the pyrochlore lattice and the planar pyrochlore lattice, for the fully frustrated square lattice Ising model in a transverse field (dual to the 2+1 dimensional odd Ising gauge theory), and for a transverse field Ising model with multi-spin interactions on the square lattice, which is dual to a 2+1 dimensional even Ising gauge theory (and reduces to the two dimensional quantum loop model in a certain limit). Our cluster algorithms use …
We investigate the nature of a $Z_2$-invariant XY ring-exchange interaction with a frustrated Ising coupling on the triangular lattice. In the limit of pure XY ring-exchange interaction, we show that the classical ground state is degenerate resulting from the $Z_2$-invariance of the Hamiltonian. Quantum fluctuations lift these classical degenerate ground states and produce an unusual state whose excitation spectrum exhibits a gapped maximum quadratic dispersion near ${\bf k}=0$ and vanishes at the midpoints of each side of the Brillouin zone. This result is in contrast to a gapless quadratic d…
We show that the highly frustrated transverse-field Ising model on the three-dimensional pyrochlore lattice realizes a first-order phase transition without symmetry breaking between the low-field Coulomb quantum spin liquid and the high-field polarized phase. The quantum phase transition is located quantitively by comparing low- and high-field series expansions. Furthermore, the intriguing properties of the elementary excitations in the polarized phase are investigated. We argue that this model can be achieved experimentally by applying mechanical strain to a classical spin ice material compri…
We consider itinerant spinless fermions as moving defects in a dilute two-dimensional frustrated Ising system where they occupy site vacancies. Fermions interact via local spin fluctuations and we analyze coupled self-consistent mean-field equations of the Green functions after expressing the spin and fermion operators in terms of Grassmann variables. The specific heat and effective mass are analyzed with the solutions satisfying the symmetry imposed by the coupling layout. At low temperature, we find that these solutions induce stripes along the lines of couplings with the same sign, and that…
Low-temperature magnetization curves and thermodynamics of a frustrated spin-1/2 Heisenberg triangular bilayer with the antiferromagnetic intradimer interaction and either ferromagnetic or antiferromagnetic interdimer interaction are investigated in a highly frustrated parameter region, where localized many-magnon eigenstates provide the most dominant contribution to magnetothermodynamics. Low-energy states of the highly frustrated spin-1/2 Heisenberg triangular bilayer can be accordingly found from a mapping correspondence with an effective triangular-lattice spin-1/2 Ising model in a field. …
Inelastic neutron scattering study on the spin-chain compound Sr$_3$NiIrO$_6$ reveals gapped quasi-1D magnetic excitations. The observed one-magnon band between 29.5 and 39 meV consists of magnon modes of the Ni$^{2+}$ ions. The fitting of the spin wave spectrum reveals strongly coupled Ising-like chains along the $c$-axis that are weakly coupled into a frustrated triangular lattice in the $ab$-plane. The magnetic excitations survive up to 200 K well above the magnetic ordering temperature of $T_N \sim 75$ K, also indicating a quasi-1D nature of the magnetic interactions in Sr$_3$NiIrO$_6$. Ou…
Many-body systems subject to a high-frequency drive can show intriguing thermalization behavior. Prior to heating to a featureless infinite-temperature state, these systems can spend an exponentially long time in prethermal phases characterized by various kinds of order. Here, we uncover the rich non-equilibrium phase diagram of a driven frustrated two-dimensional Ising magnet with competing short-range ferromagnetic and long-range dipolar interactions. We show that the ordered stripe and nematic phases, which appear in equilibrium as a function of temperature, underpin subsequent prethermal p…
Classical spin liquids from frustrated Ising models in hyperbolic space
Technische Universität Dresden（德累斯顿工业大学）；Julius-Maximilians-Universität Würzburg（维尔茨堡大学）；Max-Planck-Institut für Physik komplexer Systeme（马克斯·普朗克复杂系统物理研究所）
By using extensive tensor network calculations, we map out the phase diagram of the frustrated $J_1$-$J_2$ Ising model on the square lattice. In particular, we focus on the cases with controversy in the phase diagram, especially the stripe transition in the regime $g = |J_2/J_1|>\frac{1}{2}$, $(J_2>0,J_1<0)$. While recent studies claimed that the phase transition is of first order when $\frac{1}{2}<g<g^*$ (with the smallest $g^*$ being $0.67$), our simulations suggest that if there is such a first-order region, it is smaller than those found in earlier studies by other methods. Combining with …
We demonstrate the appearance of thermal order by disorder in Ising pyrochlores with staggered antiferromagnetic order frustrated by an applied magnetic field. We use a mean-field cluster variational method, a low-temperature expansion and Monte Carlo simulations to characterise the order-by-disorder transition. By direct evaluation of the density of states we quantitatively show how a symmetry-broken state is selected by thermal excitations. We discuss the relevance of our results to experiments in $2d$ and $3d$ samples, and evaluate how anomalous finite-size effects could be exploited to det…
Magnetic order in the frustrated Ising-like chain compound Sr$_3$NiIrO$_6$
我们研究了Sr_3NiIrO_6单晶的磁化强度与磁场和温度的关系。这些测量结果证明了存在一个易轴的各向异性和两个异常的磁化率。在多晶样品上实现的中子粉末衍射揭示了在75 K以下出现的磁反射，其磁传播矢量为k ~（0，0，1），这在以前的中子研究中是未检测到的[T.N. Nguyen和H. C zur Loye，J. Solid State Chem.，117，300（1995）]。磁性基态的性质，和存在的两个异常共同的这个家庭的材料，讨论的基础上得到的结果，中子衍射，磁化测量，和对称性参数。
Ising versus XY anisotropy in frustrated R$_{2}$Ti$_{2}$O$_7$ compounds as seen by polarized neutrons
用极化中子衍射方法研究了具有单轴（R=Ho，Tb）和平面（R=Er，Yb）各向异性的R $_{2}$ Ti $_{2}$ O $_7$烧绿石化合物的场致磁序。局域磁化率张量\{ $χ_\parallel,χ_\perp$ \}的确定提供了在顺磁相（2-270 K）的场诱导结构的通用描述，无论场值（1-7 T）和方向。比较热变化的$χ_\parallel$和$χ_\perp$与计算使用稀土晶体场表明，交换和偶极相互作用必须考虑。我们确定在每种情况下的分子场张量，并表明它可以是强各向异性的。
Ca3Co2O6 is a frustrated magnet consisting of a triangular arrangement of chains of Ising spins. It shows regular magnetization steps vs magnetic field every 1.2 T that are metastable with very slow dynamics. This has puzzled the community for many years and given rise to numerous potential theories. Here we approach the problem by seeking the elusive magnetic equilibrium state at T = 2 K. To this end, we explore two approaches: (1) bypassing the slow dynamics produced by changing fields by instead field-cooling directly to the target temperature, and (2) quantum annealing in transverse magnet…
Continuous symmetries are believed to emerge at many quantum critical points in frustrated magnets. In this work, we study two candidates of this paradigm: the transverse-field frustrated Ising model (TFFIM) on the triangle and the honeycomb lattices. The former is the prototypical example of this paradigm, and the latter has recently been proposed as another realization. Our large-scale Monte Carlo simulation confirms that the quantum phase transition (QPT) in the triangle lattice TFFIM indeed hosts an emergent O(2) symmetry, but that in the honeycomb lattice TFFIM is a first-order QPT and do…
We report the neutron scattering results on magnetic orderings and excitations in $\mathrm{Ba}_2\mathrm{CoTeO}_6$ composed of two almost isolated subsystems A and B, which are described as an $S\,{=}\,1/2$ triangular Heisenberg-like antiferromagnet and a frustrated honeycomb Ising-like antiferromagnet, respectively. Stripy ordering of subsystem B was confirmed below $T_{\rm N1}\,{=}\,12.0$ K, whereas sharp streaks were observed along $(1/3, 1/3, L)$ and $(2/3, 2/3, L)$ at 0.3 K (${\ll}\,T_{\rm N2}\,{=}\,3.0$ K). This indicates the two-dimensional nature of ordering in subsystem A. It was found…
Motivated by the recent discoveries of some compounds such as the $\mathrm{Bi}_{2}\mathrm{Fe}_{4}\mathrm{O}_{9}$ which crystallizes in an orthorhombic crystal structure with the $\mathrm{Fe}^{3+}$ ions, and iron-based oxyfluoride ${\rm Bi}_{4}{\rm Fe}_{5}{\rm O}_{13}{\rm F}$ compounds following the pattern of Cairo pentagonal structure, among some other compounds. We propose a model for one stripe of the Cairo pentagonal Ising-Heisenberg lattice, one of the edges of a pentagon is different, and this edge will be associated with a Heisenberg exchange interaction, while the Ising exchange intera…
We investigate the quantum dynamics of the transverse field Ising model on the triangular lattice through large-scale quantum Monte Carlo simulations and stochastic analytic continuation. At weak transverse field, we capture for the first time the excitations related to topological quantum strings, which exhibits continuum features described by XY chain along the strings and those in accord with "Luttinger string liquid" in the perpendicular direction. The continuum features can be well understood from the perspective of topological strings. Furthermore, we identify the contribution of strings…
We determine the zero and finite temperature phase diagram of the fully frustrated quantum Ising model on the bathroom tile (4-8) lattice. The phase diagram exhibits a wealth of 2+1d physics, including 1. classical Coulomb dimer liquids of both square and triangular lattice types; 2. quantum order-by-disorder induced phases breaking $\mathbb{Z}_4$, $\mathbb{Z}_6$, and $\mathbb{Z}_8$ symmetries; 3. finite temperature Kosterlitz-Thouless (KT) phases floating over the $\mathbb{Z}_6$ and $\mathbb{Z}_8$ orders; and, 4. staircases of (in)-commensurate symmetry breaking phases at intermediate couplin…
Model for frustrated spin-orbital chains: application to CaV2O4
受准一维化合物CaV_2O_4研究的启发，我们研究了自旋-轨道链的基态，该链具有类伊辛轨道哈密顿量和S=1自旋之间的阻挫相互作用.现场自旋-轨道相互作用和Jahn-Teller效应与现场间的超交换竞争，导致丰富的相图，其中反铁轨道相从轨道顺磁体分离的连续伊辛过渡。两个不同的自旋液体取决于潜在的轨道顺序被发现在小自旋轨道耦合的限制。在相反的极限下，锯齿形链表现为自旋为2的链，具有伊辛各向异性。CaV 2 O 4的影响进行了讨论。
Incommensurability plays a critical role in many strongly correlated systems. In some cases, the origin of such exotic order can be theoretically understood in the framework of 1d line-like topological excitations known as ``quantum strings''. Here we study an extended transverse field Ising model on a triangular lattice. Using the large scale quantum Monte Carlo simulations, we find that the spatial anisotropy can stabilize an incommensurate phase out of the commensurate clock order. Our results for the structure factor and the string density exhibit a linear relationship between incommensura…
Recent experiments on the Co-based $d^7$ honeycomb materials BaCo$_2$(AsO$_4$)$_2$ and BaCo$_2$(PO$_4$)$_2$ have drawn renewed interest to XXZ models with competing interactions beyond the nearest neighbor exchange. While the case of dominant antiferromagnetic exchange has been extensively studied, the actual materials exhibit a ferromagnetic nearest neighbor exchange. Here we show that such a sign change of the dominant nearest neighbor coupling has substantial consequences on the phase diagram. In particular, the nature of the quantum disordered phase of interest changes from a plaquette val…
Fracton Spin Liquid and Exotic Frustrated Phases in Ising-like Octochlore Magnets
University of California, Irvine（加州大学尔湾分校）；University of Waterloo（滑铁卢大学）；Waterloo Institute for Nanotechnology, University of Waterloo（滑铁卢大学滑铁卢纳米技术研究所）；Max Planck Institute for the Physics of Complex Systems（马克斯·普朗克复杂系统物理研究所）；Rice University（莱斯大学）
We investigate the ground state nature of the transverse field Ising model on the $J_1-J_2$ square lattice at the highly frustrated point $J_2/J_1=0.5$. At zero field, the model has an exponentially large degenerate classical ground state, which can be affected by quantum fluctuations for non-zero field toward a unique quantum ground state. We consider two types of quantum fluctuations, harmonic ones by using linear spin wave theory (LSWT) with single-spin flip excitations above a long range magnetically ordered background and anharmonic fluctuations, by employing a cluster-operator approach (…
The emergence of complex modulated structures in the magnetization pattern of thin films is a well-established experimental phenomenology caused by the frustrating effects of competing interactions. Using a coarse-grained version of the Ising ferromagnet with dipolar interactions, we develop a method that uses the information from the microscopic Hamiltonian to predict the specific topological phases present in the temperature-external magnetic field phase diagram. This is done by the combination of mean-field variational calculations and the renormalization group equations from the classical …
