We study the ground-state magnetism of the half-filled Hubbard model on the anisotropic triangular lattice, where two out of three bonds have hopping $t$ and the third one has $t^\prime$ in a unit triangle. Working in a spin-rotating frame and using the density matrix renormalization group method as an impurity solver, we provide a proper description of incommensurate magnetizations at zero temperature in the framework of the dynamical mean-field theory (DMFT). It is shown that the incommensurate spiral magnetic order for $t^\prime/t\gtrsim 0.7$ survives the dynamical fluctuations of itinerant electrons in the Hubbard interaction range from the strong-coupling (localized-spin) limit down to the insulator-to-metal transition. We also find that the magnetic moment reduction from the localized-spin limit is pronounced in the vicinity of the transition between the commensurate Néel and incommensurate spiral phases at $t^\prime/t\sim 0.7$. When the anisotropy parameter $t^\prime/t$ increases from the Néel-to-spiral transition, the magnitude of the magnetic moment immediately reaches a maximum and then rapidly decreases in the range of larger $t^\prime/t$ including the isotropic triangular lattice point $t^\prime/t=1$. This work gives a solid foundation for further extension of the study including nonlocal correlation effects neglected at the standard DMFT level.
The incommensurate spin fluctuation of the doped triangular antiferromagnet is studied within the t-J model. It is shown that the commensurate peak near the half-filling is split into six incommensurate peaks in the underdoped and optimally doped regimes. The incommensurability increases with the hole concentration at lower dopings, and saturates at higher dopings. Although the incommensurability is almost energy independent, the weight of these incommensurate peaks decreases with energy and temperature.
The double exchange model describing interactions of itinerant electrons with localized spins is usually used to explain ferromagnetism in metals. We show that for a variety of crystal lattices of different dimensionalities and for a wide range of model parameters the ferromagnetic state is unstable against a non-collinear spiral magnetic order. We revisit the phase diagram of the double exchange model on a triangular lattice and show in a large part of the diagram the incommensurate spiral state has a lower energy than the previously discussed commensurate states. These results indicate that …
Field-tuned incommensurate fan phase in an Ising-like triangular antiferromagnet
University of Oxford（牛津大学）；Institute for Solid State Physics, University of Tokyo（东京大学固体物理研究所）；Rutherford Appleton Laboratory（鲁瑟福阿普尔顿实验室）；University of Tennessee（田纳西大学）
Incommensurate order with translationally invariant projected entangled-pair states: Spiral states and quantum spin liquid on the anisotropic triangular lattice
Motivated by the magnetic properties of the spin-chain compounds LiCuSbO$_4$$\equiv$LiSbCuO$_4$ and Rb$_2$Cu$_2$Mo$_3$O$_{12}$, we study the ground state of the Heisenberg chain with dimerized nearest-neighbor ferromagnetic (FM)($J_1, J_1^\prime<0$) and next-nearest-neighbor antiferromagnetic ($J_2>0$) couplings. Using the density-matrix renormalization group technique and spin-wave theory we find a first-order transition between a fully-polarized FM and an incommensurate spiral state at $2α=β/(1+β)$, where $α$ is the frustration ratio $J_2/|J_1|$ and $β$ the degree of dimerization $J_1^\prime…
The observation of spinon excitations in the $S=\frac{1}{2}$ triangular antiferromagnet Ca$_3$ReO$_5$Cl$_2$ reveals a quasi-one-dimensional (1D) nature of magnetic correlations, in spite of the nominally 2D magnetic structure. This phenomenon is known as frustration-induced dimensional reduction. Here, we present high-field electron spin resonance spectroscopy and magnetization studies of Ca$_3$ReO$_5$Cl$_2$, allowing us not only to refine spin-Hamiltonian parameters, but also to investigate peculiarities of its low-energy spin dynamics. We argue that the presence of the uniform Dzyaloshinskii…
We study the anisotropic spin-half antiferromagnetic triangular Heisenberg lattice in two dimensions, seen as a set of chains with couplings J (J') along (in between) chains, respectively. Our focus is on the incommensurate correlation that emerges in this system in a wide parameter range due to the intrinsic frustration of the spins. We study this system with traditional DMRG using cylindrical boundary conditions to least constrain possible incommensurate order. Despite that the limit of essentially decoupled chains J'/J < 0.5 is not very accessible numerically, it appears that the spin-spin …
We consider 2D Heisenberg antiferromagnets on a triangular lattice with spatially anisotropic interactions in a high magnetic field close to the saturation. We show that this system possess rich phase diagram in field/anisotropy plane due to competition between classical and quantum orders: an incommensurate non-coplanar spiral state, which is favored classically, and a commensurate co-planar state, which is stabilized by quantum fluctuations. We show that the transformation between these two states is highly non-trivial and involves two intermediate phases -- the phase with co-planar incommen…
We consider the magnetic phase diagram of the two-dimensional Hubbard model on a square lattice. We take into account both spiral and collinear incommensurate magnetic states. The possibility of phase separation of spiral magnetic phases is taken into consideration as well. Our study shows that all the listed phases appear to be the ground state at certain parameters of the model. Relation of the obtained results to real materials, e.g. Cu-based high-temperature superconductors, is discussed.
In the present work we aim to characterize the lattice configurations and the magnetic behavior in the incommensurate phase of spin-Peierls systems. This phase emerges when the magnetic exchange interaction is coupled to the distortions of an underlying triangular lattice and has its experimental realization in the quasi-one dimensional compound family TiOX (X = Cl, Br). With a simple model of spin-1/2 chains inserted in a planar triangular geometry which couples them elastically, we are able to obtain the uniform-incommensurate and incommensurate-dimerized phase transitions seen in these comp…
We report an observation of a commensurate-incommensurate phase transition in a Dzyaloshinskii-Moriya spiral magnet Ba_2CuGe_2O_7. The transition is induced by applying a magnetic field in the plane of spin rotation. In this experiment we have direct control over the strength of the commensurate potential, while the preferred incommensurate period of the spin system remains unchanged. Experimental results for the period of the soliton lattice and bulk magnetization as a function of external magnetic field are in quantitative agreement with theory.
We study the $S = 1$ triangular lattice Ising antiferromagnet by Monte Carlo simulations. Frustrations between a major antiferromagnetic third-neighbor interaction $J_3$ and a minor ferromagnetic nearest-neighbor interaction $J_1$ cause incommensurate short-range orders at intermediate temperatures. At low temperatures (below $T/J_3 \lesssim 0.2$ for $J_1/J_3 = -1/3$), the system exhibits fourfold periodic ordered state. In the short-range order phase, the system shows a glassy two-step relaxation. We demonstrate that the features of the short-range order are attributed to the cooperation betw…
Exact and rigorous solutions of the ground-state problem for the classical Heisenberg model with nearest-neighbor interactions on two- and three-dimensional lattices composed of zigzag (triangular) ladders are obtained in a very simple way, with the use of a cluster method. It is shown how the geometrical frustration due to the presence of triangles as structural units leads to the emergence of incommensurate spiral orderings and their collinear limits. Interestingly, these orderings are determined by a single angle (along with the signs of the interactions between neighboring spins); therefor…
We investigate the interplay between commensurate lock-in and incommensurate supersolid phases of the hardcore bosons at half-filling with anisotropic nearest-neighbor hopping and repulsive interactions on triangular lattice. We use numerical quantum and variational Monte Carlo as well as analytical Schwinger boson mean-field analysis to establish the ground states and phase diagram. It is shown that, for finite size systems, there exist a series of jumps between different supersolid phases as the anisotropy parameter is changed. The density ordering wavevectors are locked to commensurate valu…
We study the spin-half Heisenberg models on an anisotropic two-dimensional lattice which interpolates between the square-lattice at one end, a set of decoupled spin-chains on the other end, and the triangular-lattice Heisenberg model in between. By series expansions around two different dimer ground states and around various commensurate and incommensurate magnetically ordered states, we establish the phase diagram for this model of a frustrated antiferromagnet. We find a particularly rich phase diagram due to the interplay of magnetic frustration, quantum fluctuations and varying dimensionali…
In a strongly frustrated square-lattice antiferromagnet with diagonal coupling J', for J/(2J') < 1, an incommensurate spiral state with propagation vector Q = (π+/- δ, π+/- δ) near (π,π) competes closely with the Neel collinear antiferromagnetic ground state. For classical Heisenberg spins the energy of the spiral state can be lowered as it adapts to the distortion of the crystal lattice. As a result, a weak superstructural modulation such as exist in doped cuprates might stabilize an incommensurate spiral phase for some range of the parameter J/(2J') close to 1.
The presence of incommensurate spiral spin-density waves (SDW) has been proposed to explain the $p$ (hole doping) to $1+p$ jump measured in the Hall number $n_H$ at a doping $p^*$. Here we explore {\it collinear} incommensurate SDW as another possible explanation of this phenomenon, distinct from the incommensurate {\it spiral} SDW proposal. We examine the effect of different SDW strengths and wavevectors and we find that the $n_H\sim p$ behavior is hardly reproduced at low doping. The calculated $n_H$ and Fermi surfaces give characteristic features that should be observed, thus the lack of th…
We present a Quantum Monte Carlo study of the Ising model in a transverse field on a square lattice with nearest-neighbor antiferromagnetic exchange interaction J and one diagonal second-neighbor interaction $J'$, interpolating between square-lattice ($J'=0$) and triangular-lattice ($J'=J$) limits. At a transverse-field of $B_x=J$, the disorder-line first introduced by Stephenson, where the correlations go from Neel to incommensurate, meets the zero temperature axis at $J'\approx 0.7 J$. Strong evidence is provided that the incommensurate phase at larger $J'$, at finite temperatures, is a floa…
Experimental observations of lightly doped La_{2-x}Sr_xCuO_4, x < 0.02, revealed remarkable magnetic properties such as the incommensurate noncollinear ordering (additional to the Neel ordering) and a tremendous doping dependence of the uniform longitudinal susceptibility. We show that the spiral solution of the t-t'-t''-J model obtained by taking into account the Coulomb trapping of holes by Sr ions describes these puzzling data perfectly well. Our solution firstly explains why the incommensurate structure is directed along the orthorhombic b-axis, and secondly allows a numerical calculation …
We report an observation of a commensurate-incommensurate phase transition in the Dzyaloshinskii-Moriya spiral antiferromagnet Ba_2 Cu Ge_2 O_7. The transition is induced by an external magnetic field applied along the c-axis of the tetragonal structure, i. e., in the plane of spin rotation. Bulk magnetic measurements and neutron diffraction experiments show that the transition occurs in a critical field Hc=2.1T. Experimental results for the period of the magnetic structure and magnetization as functions of magnetic field are in quantitative agreement with our exact analytical solution for Dzy…
Neutron scattering is used to investigate spin correlations in ultra pure single crystals of the S=1 triangular lattice NiGa2S4. Despite a Curie-Weiss temperature of Theta_CW=-80(2) K, static (tau > 1 ns) short range (xi_ab=26(3) Å) incommensurate order prevails for T>1.5 K. The incommensurate modulation Q_0=(0.155(3),0.155(3),0), Theta_CW, and the spin wave velocity (c=4400 m/s) can be accounted for by antiferromagnetic third-nearest neighbor interactions J_3=2.8(6) meV and ferromagnetic nearest neighbor coupling J_1=-0.35(9) J_3. Inter-plane correlations are limited to nearest neighbors and …
We study a triangular frustrated antiferromagnetic Heisenberg model with nearest-neighbor interaction $J_{1}$ and third-nearest-neighbor interactions $J_{3}$ by means of Schwinger-boson mean-field theory. It is shown that an incommensurate phase exists in a finite region in the parameter space for an antiferromagnetic $J_{3}$ while $J_{1}$ can be either positive or negtaive. A detailed solution is presented to disclose the main features of this incommensurate phase. A gapless dispersion of quasiparticles leads to the intrinsic $T^{2}$-law of specific heat. The local magnetization is significan…
We investigate the extended hard-core Bose-Hubbard model on the triangular lattice as a function of spatial anisotropy with respect to both tunneling and nearest-neighbor interaction strength. At half-filling the system can be tuned from decoupled one-dimensional chains to a two-dimensional solid phase with alternating density order by adjusting the anisotropic coupling. At intermediate anisotropy, however, frustration effects dominate and an incommensurate supersolid phase emerges, which is characterized by incommensurate density order as well as an anisotropic superfluid density. We demonstr…
We investigate the half-filled Hubbard model on an isotropic triangular lattice with the variational cluster approximation. By decreasing the on-site repulsion $U$ (or equivalently increasing pressure) we go from a phase with long range, three-sublattice, spiral magnetic order, to a non-magnetic Mott insulating phase -- a spin liquid -- and then, for $U\lesssim6.7t$, to a metallic phase. Clusters of sizes 3, 6 and 15 with open boundary conditions are used in these calculations, and an extrapolation to infinite size is argued to lead to a disordered phase at $U=8t$, but to a spiral order at $U\…
Strain-Tuned Incommensurate Kekulé Spiral Order in Twisted Bilayer Graphene: a Quantum Many-Body Study
The University of Hong Kong（香港大学）；University of Texas at Dallas（德克萨斯大学达拉斯分校）；Princeton University（普林斯顿大学）；Universität Würzburg（维尔茨堡大学）；Max Planck Institute for Solid State Reserach（马克斯·普朗克固体研究所）；Technische Universität München（慕尼黑工业大学）
We study the zero-temperature spin fluctuations of a two-dimensional itinerant-electron system with an incommensurate magnetic ground state described by a single-band Hubbard Hamiltonian. We introduce the (broken-symmetry) magnetic phase at the mean-field (Hartree-Fock) level through a \emph{spiral spin configuration} with characteristic wave vector $\gmathbf{Q}$ different in general from the antiferromagnetic wave vector $\gmathbf{Q_{AF}}$, and consider spin fluctuations over and above it within the electronic random-phase (RPA) approximation. We obtain a \emph{closed} system of equations for…
The anisotropic triangular model, which is believed to describe the materials Cs$_2$CuCl$_4$ and Cs$_2$CuBr$_4$, among others, is dominated by incommensurate spiral physics and is thus extremely resistant to numerical analysis on small system sizes. In this paper we use twisted boundary conditions and exact diagonalization techniques to study the phase diagram of this model. With these boundary conditions we are able to extract the inter- and intrachain ordering $q$-vectors for the $\frac{J'}{J} < 1$ region finding very close agreement with recent DMRG results on much larger systems. Our resul…
We succeeded in observing pressure-suppressed magnetic long range ordering (LRO) in the triangular lattice antiferromagnet CuFeO$_{2}$, using neutron diffraction experiments under an isotropic pressure. The magnetic LRO of the four-sublattice ground state under ambient pressure in CuFeO$_{2}$ almost disappears at the high pressure of 7.9 GPa, and is replaced by an incommensurate order with temperature-independent wave number of (0.192 0.192 1.5). The incommensurate wave number observed at 7.9 GPa corresponds to that observed just above the temperature at which lattice distortion and magnetic L…
We investigate the Hubbard model on the anisotropic triangular lattice with two hopping parameters $t$ and $t^\prime$ in different spatial directions, interpolating between decoupled chains ($t=0$) and the isotropic triangular lattice ($t=t^\prime$). Variational wave functions that include both Jastrow and backflow terms are used to compare spin-liquid and magnetic phases with different pitch vectors describing both collinear and coplanar (spiral) order. For relatively large values of the on-site interaction $U/t^\prime \gtrsim 10$ and substantial frustration, i.e., $0.3\lesssim t/t^\prime \le…
Incommensurate spiral order is a common occurrence in frustrated magnetic insulators. Typically, all magnetic moments rotate uniformly, through the same wavevector. However the honeycomb iridates family Li2IrO3 shows an incommensurate order where spirals on neighboring sublattices are counter-rotating, giving each moment a different local environment. Theoretically describing its spin dynamics has remained a challenge: the Kitaev interactions proposed to stabilize this state, which arise from strong spin-orbit effects, induce magnon umklapp scattering processes in spin-wave theory. Here we pro…
Tensor network study of the spin-1/2 square-lattice $J_1$-$J_2$-$J_3$ model: incommensurate spiral order, mixed valence-bond solids, and multicritical points
We study the effects of spin-orbit coupling (SOC) on the large-U Hubbard model on anisotropic triangular lattice at half-filling using the Schwinger-boson method. We find that the SOC will in general lead to a zero temperature condensation of the Schwinger bosons with a single condensation momentum. As a consequence, the spin-spin correlation vanishes along the z-axis but develops in the $x$-$y$ plane, with the ordering wave vector being dramatically dependent on the SOC. Moreover, the phase boundary of the magnetic ordered state extends to the region of large spatial anisotropy with increased…
We study the competition between magnetic and spin-liquid phases in the Hubbard model on the anisotropic triangular lattice, which is described by two hopping parameters t and t' in different spatial directions and is relevant for layered organic charge-transfer salts. By using a variational approach that includes spiral magnetic order, we provide solid evidence that a spin-liquid phase is stabilized in the strongly-correlated regime and close to the isotropic limit t'/t=1. Otherwise, a magnetically ordered spiral state is found, connecting the (collinear) Néel and the (coplanar) 120° phases. …
We report the first detailed investigation of K$_2$MnS$_2$ and K$_2$MnSe$_2$ from the K$_2$MnS$_2$ structure type and their magnetic solid solution K$_2$MnS$_{2-x}$Se$_x$ and find that compounds of this structure type consist of strongly-coupled pseudo-one-dimensional antiferromagnetic chains that collectively represent a frustrated two-dimensional triangular antiferromagnet. Bulk samples of K$_2$MnS$_{2-x}$Se$_x$ with $0 \leq x \leq 2$ are characterized using X-ray diffraction, neutron diffraction, magnetization and heat capacity measurements. An incommensurate cycloid magnetic structure with…
The ground state of an S=1/2 antiferromagnetic Heisenberg model on a spatially anisotropic triangular lattice, which is an effective model of Mott insulators on a triangular layer of organic charge transfer salts or Cs2CuCl4, is numerically studied. We apply a numerical variational method by using a tensor network with entanglement renormalization, which improves the capability of describing a quantum state. Magnetic ground states are identified for 0.7 <= J2/J1 <= 1 in the thermodynamic limit, where J1 and J2 denote the inner-chain and inter-chain coupling constants, respectively. Except for …
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…
We report thermodynamic properties, magnetic ground state, and microscopic magnetic model of the spin-1 frustrated antiferromaget Li$_{2}$NiW$_{2}$O$_{8}$ showing successive transitions at $T_{\rm N1}\simeq 18$ K and $T_{\rm N2}\simeq 12.5$ K in zero field. Nuclear magnetic resonance and neutron diffraction reveal collinear and commensurate magnetic order with the propagation vector $\mathbf k=(\frac12,0,\frac12)$ below $T_{\rm N2}$. The ordered moment of 1.8 $μ_B$ at 1.5 K is directed along $[0.89(9),-0.10(5),-0.49(6)]$ and matches the magnetic easy axis of spin-1 Ni$^{2+}$ ions, which is det…
Correlation between dielectric and magnetic properties was investigated on the triangular lattice antiferromagnets ACrO2 (A= Cu, Ag, Li, or Na) showing 120-degree spiral spin structure with easy-axis anisotropy. For the A= Cu and Ag compounds with delafossite structure, ferroelectric polarization emerges upon the spiral spin order, implying the strong coupling between the ferroelectricity and spiral spin structure. On the other hand, for the A = Li and Na compounds with ordered rock salt structure, no polarization but only clear anomalies in dielectric constant can be observed upon the spiral …
By using variational wave functions and quantum Monte Carlo techniques, we investigate the complete phase diagram of the Heisenberg model on the anisotropic triangular lattice, where two out of three bonds have super-exchange couplings $J$ and the third one has instead $J^\prime$. This model interpolates between the square lattice and the isotropic triangular one, for $J^\prime/J \le 1$, and between the isotropic triangular lattice and a set of decoupled chains, for $J/J^\prime \le 1$. We consider all the fully-symmetric spin liquids that can be constructed with the fermionic projective-symmet…
We consider the ground state magnetic phase diagram of the two-dimensional Hubbard model with nearest and next-nearest neighbor hopping in terms of electronic density and interaction. We treat commensurate ferro- and antiferromagnetic, as well as incommensurate (spiral) magnetic phases. The first-order magnetic transitions with changing chemical potential, resulting in a phase separation (PS) in terms of density, are found between ferromagnetic, antiferromagnetic and spiral magnetic phases. We argue that the account of PS has a dramatic influence on the phase diagram in the vicinity of half-fi…
It was recently observed that materials showing most striking multiferroic phenomena are frustrated spin-density-wave magnets. We present a simple phenomenological theory, which describes the orientation of the induced electric polarization for various incommensurate magnetic states, its dependence on temperature and magnetic field, and anomalies of dielectric susceptibility at magnetic transitions. We show that electric polarization can be induced at domain walls and that magnetic vortices carry electric charge.
We present calculations of the magnetic ground state of Cs_2CuCl_4 in an applied magnetic field, with the aim of understanding the commensurately ordered state that has been discovered in recent experiments. This layered material is a realization of a Heisenberg antiferromagnet on an anisotropic triangular lattice. Its behavior in a magnetic field depends on field orientation, because of weak Dzyaloshinskii-Moriya interactions.We study the system by mapping the spin-1/2 Heisenberg Hamiltonian onto a Bose gas with hard core repulsion. This Bose gas is dilute, and calculations are controlled, cl…
We develop a low-energy effective theory for spin-1/2 frustrated two-leg Heisenberg spin ladders. We obtain a new type of interchain coupling that breaks parity symmetry. In the presence of an XXZ-type anisotropy, this interaction gives rise to a novel ground state, characterized by incommensurate correlations. In the case of a single ladder, this state corresponds to a spin nematic phase. For a frustrated quasi-one-dimensional system of infinitely many weakly coupled chains, this state develops true three dimensional spiral order. We apply our theory to recent neutron scattering experiments o…
Putting a new spin on the incommensurate Kekulé spiral: from spin-valley locking and collective modes to fermiology and implications for superconductivity
The high magnetic field behaviour of the triangular lattice antiferromagnet CuFeO_2 is studied using single crystal neutron diffraction measurements in a field of up to 14.5 T and also by magnetisation measurements in a field of up to 12 T. At low temperature, two well-defined first order magnetic phase transitions are found in this range of applied magnetic field (H // c): at H_c1=7.6(3)/7.1(3) T and H_c2=13.2(1)/12.7(1) T when ramping the field up/down. In a field above H_c2 the magnetic Bragg peaks show unusual history dependence. In zero field T_N1=14.2(1) K separates a high temperature pa…
We investigate a two-dimensional single-band Hubbard model with a nearest-neighbor hopping. We treat a commensurate collinear order as well as incommensurate spiral magnetic phases at a finite temperature using a Hubbard-Stratonovich transformation with a two-field representation and solve this problem in a static approximation. We argue that temperature dramatically influence the collinear and spiral magnetic phases, phase separation in the vicinity of half-filling. The results imply a possible interpretation of unusual behavior of magnetic properties of single-layer cuprates.
Field-induced transitions from incommensurate to commensurate phases in helical antiferromagnets
National Research University Higher School of Economics（国立高等经济大学）；Petersburg Nuclear Physics Institute named by B.P. Konstantinov of National Research Center “Kurchatov Institute”（国立库尔恰托夫研究所彼得堡核物理研究所）
The spin-1 Heisenberg model on a triangular lattice with the ferromagnetic nearest, $J_1=-(1-p)J,$ $J>0$, and antiferromagnetic third-nearest-neighbor, $J_3=pJ$, exchange interactions is studied in the range of the parameter $0 \leqslant p \leqslant 1$. Mori's projection operator technique is used as a method, which retains the rotation symmetry of spin components and does not anticipate any magnetic ordering. For zero temperature several phase transitions are observed. At $p\approx 0.2$ the ground state is transformed from the ferromagnetic spin structure into a disordered state, which in its…
We show that the mesoscopic incommensurate $\mathbb{Z}_2$ vortex crystals proposed for layered triangular anisotropic magnets can be most saliently identified by two distinctive signatures in dynamical spin response experiments: The presence of pseudo-Goldstone `phonon' modes at low frequencies $ω$, associated with the collective vibrations of the vortex cores, and a characteristic multi-scattered intensity profile at higher $ω$, arising from a large number of Bragg reflections and magnon bandgaps. These are direct fingerprints of the large vortex sizes and magnetic unit cells and the solitoni…
We investigate a highly frustrated spin-1 model on the triangular lattice, with nearest- and next-nearest-neighbor antiferromagnetic $S\cdot S$ interactions and nearest-neighbor $(S\cdot S)^2$ interactions. Using the density matrix renormalization group (DMRG) technique, we find three magnetically ordered phases, namely 120$^\circ$ spiral order, stripe order, and tetrahedral order, as well as two spin nematic phases: ferroquadrupolar and antiferroquadrupolar. While our data could be consistent with a spin liquid phase between the 120$^\circ$ spiral and antiferroquadrupolar orders, the more lik…
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…
Within the framework of the $s$-$d(f)$ exchange model in the mean-field approximation for square, simple cubic, body-centered and face-centered cubic lattices, the formation of a ferromagnetic, spiral, and commensurate antiferromagnetic order is investigated. The possibility of the formation of inhomogeneous states (magnetic phase separation), which necessarily arises during first-order phase transitions in the electron filling parameter, is taken into account. The saturation of the antiferromagnetic and spiral states is studied depending on the parameters of the model. The results obtained in…
The phase diagram of the spin-1/2 Heisenberg antiferromagnet on an anisotropic triangular lattice of weakly coupled chains, a model relevant to Cs2CuCl4, is investigated using a renormalization group analysis, which includes marginal couplings important for connecting to numerical studies of this model. In particular, the relative stability of incommensurate spiral spin-density order and collinear antiferromagnetic order is studied. While incommensurate spiral order is found to exist over most of the phase diagram in the presence of a Dzyaloshinskii-Moriya (DM) interaction, at small interchain…
We analyze the competition of magnetism and superconductivity in the two-dimensional Hubbard model with a moderate interaction strength, including the possibility of incommensurate spiral magnetic order. Using an unbiased renormalization group approach, we compute magnetic and superconducting order parameters in the ground state. In addition to previously established regions of Neel order coexisting with d-wave superconductivity, the calculations reveal further coexistence regions where superconductivity is accompanied by incommensurate magnetic order.
