Two-dimensional Quantum Antiferromagnets Research Articles

Extraordinary Magnetic Response of an Anisotropic 2D Antiferromagnet via Site Dilution.

A prominent characteristic of 2D magnetic systems is the enhanced spin fluctuations, which reduce the ordering temperature. We report that a magnetic field of only 1000th of the Heisenberg superexchange interaction can induce a crossover, which for practical purposes is the effective ordering transition, at temperatures about 6 times the Néel transition in a site-diluted two-dimensional anisotropic quantum antiferromagnet. Such a strong magnetic response is enabled because the system directly enters the antiferromagnetically ordered state from the isotropic disordered state, skipping the intermediate anisotropic stage. The underlying mechanism is achieved on a pseudospin-half square lattice realized in the [(SrIrO3)1/(SrTiO3)2] superlattice thin film that is designed to linearly couple the staggered magnetization to external magnetic fields by virtue of the rotational symmetry-preserving Dzyaloshinskii-Moriya interaction. Our model analysis shows that the skipping of the anisotropic regime despite finite anisotropy is due to the enhanced isotropic fluctuations under moderate dilution.

Stability of the Néel quantum critical point in the presence of Dirac fermions

We investigate the stability of the N\'eel quantum critical point of two-dimensional quantum antiferromagnets, described by a nonlinear $\ensuremath{\sigma}$ model, in the presence of a Kondo coupling to ${N}_{f}$ flavors of two-component Dirac fermion fields. The long-wavelength order parameter fluctuations are subject to Landau damping by electronic particle-hole fluctuations. Using the momentum-shell renormalization group (RG), we demonstrate that the Landau damping is weakly irrelevant at the N\'eel quantum critical point, despite the fact that the corresponding self-energy correction dominates over the quadratic gradient terms in the IR limit. In the ordered phase, the Landau damping increases under the RG, indicative of damped spin-wave excitations. Although the Kondo coupling is weakly relevant, sufficiently strong Landau damping renders the N\'eel quantum critical point quasistable for ${N}_{f}\ensuremath{\ge}4$ and thermodynamically stable for ${N}_{f}<4$. In the latter case, we identify a multicritical point which describes the transition between the N\'eel critical and Kondo runaway regimes. The symmetry breaking at this fixed point results in the opening of a gap in the Dirac fermion spectrum. Approaching the multicritical point from the disordered phase, the fermionic quasiparticle residue vanishes, giving rise to non-Fermi-liquid behavior.

Field evolution of magnetic phases and spin dynamics in the honeycomb lattice magnet Na2Co2TeO6 : Na23 NMR study

We report on the results of 23Na NMR in the honeycomb lattice magnet Na2Co2TeO6 which has been nominated as a Kitaev material. Measurements of magnetic shift and width of the NMR line as functions of temperature and magnetic field show that a spin-disordered phase does not appear up to a field of 9 T. In the antiferromagnetic phase just below the Neel temperature TN, we find a temperature region extending down to ~TN/2 where the nuclear spin-lattice relaxation rate 1/T1 remains enhanced and is further increased by a magnetic field. This region crosses over to a low temperature region characterized by the rapidly decreasing 1/T1 which is less field-sensitive. These observations suggest incoherent spin excitations with a large spectral weight at low energies in the intermediate temperature region transforming to more conventional spin-wave excitations at low temperatures. The drastic change of the low-energy spin dynamics is likely caused by strong damping of spin waves activated only in the intermediate temperature region, which may be realized for triple-q magnetic order possessing partially-disordered moments as scattering centers of spin waves. In the paramagnetic phase near TN, dramatic field suppression of 1/T1 is observed. From analysis of the temperature dependence of 1/T1 based on the renormalized-classical description of a two-dimensional quantum antiferromagnet, we find the field-dependent spin stiffness constant that scales with TN as a function of magnetic field. This implies field suppression of the energy scale characterizing both two-dimensional spin correlations and three-dimensional long-range order, which may be associated with an increasing effect of frustration in magnetic fields.

Classical vertex model dualities in a family of two-dimensional frustrated quantum antiferromagnets

We study a general class of easy-axis spin models on a lattice of corner sharing even-sided polygons with all-to-all interactions within a plaquette. The low energy description corresponds to a quantum dimer model on a dual lattice of even coordination number with a multi dimer constraint. At an appropriately constructed frustration-free Rokhsar-Kivelson (RK) point, the ground state wavefunction can be exactly mapped onto a classical vertex model on the dual lattice. When the dual lattice is bipartite, the vertex models are bonded and are self dual under Wegner's duality, with the self dual point corresponding to the RK point of the original multi-dimer model. We argue that the self dual point is a critical point based on known exact solutions to some of the vertex models. When the dual lattice is non-bipartite, the vertex model is arrowed, and we use numerical methods to argue that there is no phase transition as a function of the vertex weights. Motivated by these wavefunction dualities, we construct two other distinct families of frustration-free Hamiltonians whose ground states can be mapped onto these vertex models. Many of these RK Hamiltonians provably host $\mathbb{Z}_2$ topologically ordered phases.

Cluster quantum Monte Carlo study of two-dimensional weakly coupled frustrated trimer antiferromagnets

We report results from spin trimer-based cluster quantum Monte Carlo simulations for the thermodynamic properties of two-dimensional frustrated quantum antiferromagnets that are composed of weakly-coupled three-spin (trimer) clusters. In particular, we consider the spin-1/2 kagome lattice with a strong breathing distortion, and the triangle-square lattice model proposed previously for the cuprate La${}_4$Cu${}_3$MoO${}_{12}$. For both cases, we demonstrate that an appropriately chosen trimer-based computational basis allows us to significantly reduce the quantum Monte Carlo sign problem down to the low-temperature regime. Besides exploring the thermodynamic behavior for the triangle-square lattice model we also assess a mean field theory-based prediction for the onset of chiral order. For the breathing distorted kagome lattice model, we observe a robust two-peak structure in the specific heat, both in the quantum spin liquid and the lattice-nematic regimes.

Another exact ground state of a two-dimensional quantum antiferromagnet

We present the exact dimer ground state of a quantum antiferromagnet on the maple-leaf lattice. A coupling anisotropy for one of the three inequivalent nearest-neighbor bonds is sufficient to stabilize the dimer state. Together with the Shastry-Sutherland Hamiltonian, we show that this is the only other model with an exact dimer ground state for all two-dimensional lattices with uniform tilings.

Chern-Simons superconductors and their instabilities

Two-dimensional quantum antiferromagnets host rich physics, including long-range ordering, high-$T_c$ superconductivity, quantum spin liquid behavior, topological ordering, a variety of other exotic phases, and quantum criticalities. Frustrating perturbations in antiferromagnets may give rise to strong quantum fluctuations, challenging the theoretical understanding of the many-body ground state. Here we develop a method to describe the quantum antiferromagnets using fermionic degrees of freedom. The method is based on a formally exact mapping between spin exchange models and theories describing fermionic matter with the emergent $U(1)$ Chern-Simons gauge field. For the planar N\'{e}el state, this mapping self-consistently generates the Chern-Simons superconductor mean-field ground state of introduced spinless fermions. We systematically compare the Chern-Simons superconductor state with the planar N\'{e}el state at the level of collective modes as well as order parameters. We reveal qualitative and quantitative correspondences between these two states. We demonstrate that such a construction using the fractionalized excitations and Chern-Simons gauge field can not only describe the N\'{e}el order but can also be applied to study quantum spin liquids. Furthermore, we show that the confinement-deconfinement transitions from the N\'{e}el order to quantum spin liquids are signaled and characterized by the instabilities of Chern-Simons superconductors, driven by strong frustration. The results suggest observing and classifying the descendants of antiferromagnets, including other ordered states and unconventional superconductors, as well as emergent quantum spin liquids.

The Two-Dimensional Infinite Heisenberg Classical Square Lattice: Zero-Field Partition Function and Correlation Length

The nonlinear σ-model has known a new interest for it allows to describe the properties of two-dimensional quantum antiferromagnets which, when properly doped, become superconductors up to a critical temperature notably high compared to other types of superconducting materials. This model has been conjectured to be equivalent at low temperatures to the two-dimensional Heisenberg model. In this article we rigorously examine 2d-square lattices composed of classical spins isotropically coupled between first-nearest neighbors (i.e., showing Heisenberg couplings). A general expression of the characteristic polynomial associated with the zero-field partition function is established for any lattice size. In the infinite-lattice limit a numerical study allows to select the dominant term: it is written as a l-series of eigenvalues, each one being characterized by a unique index l whose origin is explained. Surprisingly the zero-field partition function shows a very simple exact closed-form expression valid for any temperature. The thermal study of the basic l-term allows to point out crossovers between l- and (l+1)-terms. Coming from high temperatures where the l=0-term is dominant and going to zero Kelvin, l-eigen¬values showing increasing l-values are more and more selected. At absolute zero l becomes infinite and all the successive dominant l-eigenvalues become equivalent. As the z-spin correlation is null for positive temperatures but equal to unity (in absolute value) at absolute zero the critical temperature is absolute zero. Using an analytical method similar to the one employed for the zero-field partition function we also give an exact expression valid for any temperature for the spin-spin correlations as well as for the correlation length. In the zero-temperature limit we obtain a diagram of magnetic phases which is similar to the one derived through a renormalization approach. By taking the low-temperature limit of the correlation length we obtain the same expressions as the corresponding ones derived through a renor¬malization process, for each zone of the magnetic phase diagram, thus bringing for the first time a strong validation to the full exact solution of the model valid for any temperature.

Colossal quasiparticle radiation in the Lifshitz spin liquid phase of a two-dimensional quantum antiferromagnet

Strong quantum fluctuations in magnetic systems can create disordered quantum spin liquid phases of matter which are not predicted by classical physics. The complexity of the exotic phenomena on display in spin liquids has led to a great deal of theoretical and experimental interest. However, understanding the fundamental nature of the excitations in these systems remains challenging. In this work, we consider the Lifshitz quantum critical point in a two-dimensional frustrated $XY$ antiferromagnet. At this point, quantum fluctuations destroy long range order, leading to the formation of an algebraic Lifshitz spin liquid. We demonstrate that the bosonic magnon excitations are long-lived and well-defined in the Lifshitz spin liquid phase, though paradoxically, the dynamic structure factor has a broad non-Lorentzian frequency distribution with no single-particle weight. We resolve this apparent contradiction by showing that the Lifshitz spin liquid suffers from an infrared catastrophe: An external physical probe always excites an infinite number of arbitrarily low energy quasiparticles, which leads to significant radiative broadening of the spectrum.

Observing the Space- and Time-Dependent Growth of Correlations in Dynamically Tuned Synthetic Ising Models with Antiferromagnetic Interactions

We explore the dynamics of artificial one- and two-dimensional Ising-like quantum antiferromagnets with different lattice geometries by using a Rydberg quantum simulator of up to 36 spins in which we dynamically tune the parameters of the Hamiltonian. We observe a region in parameter space with antiferromagnetic (AF) ordering, albeit with only finite-range correlations. We study systematically the influence of the ramp speeds on the correlations and their growth in time. We observe a delay in their build-up associated to the finite speed of propagation of correlations in a system with short-range interactions. We obtain a good agreement between experimental data and numerical simulations taking into account experimental imperfections measured at the single particle level. Finally, we develop an analytical model, based on a short-time expansion of the evolution operator, which captures the observed spatial structure of the correlations, and their build-up in time.

Higgs amplitude mode in a two-dimensional quantum antiferromagnet near the quantum critical point

Spontaneous symmetry-breaking quantum phase transitions play an essential role in condensed matter physics. The collective excitations in the broken-symmetry phase near the quantum critical point can be characterized by fluctuations of phase and amplitude of the order parameter. The phase oscillations correspond to the massless Nambu$-$Goldstone modes whereas the massive amplitude mode, analogous to the Higgs boson in particle physics, is prone to decay into a pair of low-energy Nambu$-$Goldstone modes in low dimensions. Especially, observation of a Higgs amplitude mode in two dimensions is an outstanding experimental challenge. Here, using the inelastic neutron scattering and applying the bond-operator theory, we directly and unambiguously identify the Higgs amplitude mode in a two-dimensional S=1/2 quantum antiferromagnet C$_9$H$_{18}$N$_2$CuBr$_4$ near a quantum critical point in two dimensions. Owing to an anisotropic energy gap, it kinematically prevents such decay and the Higgs amplitude mode acquires an infinite lifetime.

Finite-size scaling of the Shannon-Rényi entropy in two-dimensional systems with spontaneously broken continuous symmetry

We study the scaling of the (basis dependent) Shannon entropy for two-dimensional quantum antiferromagnets with N\'eel long-range order. We use a massless free-field description of the gapless spin wave modes and phase space arguments to treat the fact that the finite-size ground state is rotationally symmetric, while there are degenerate physical ground states which break the symmetry. Our results show that the Shannon entropy (and its R\'enyi generalizations) possesses some universal logarithmic term proportional to the number $N_\text{NG}$ of Nambu-Goldstone modes. In the case of a torus, we show that $S_{n>1} \simeq {\rm const.} N+ \frac{N_\text{NG}}{4}\frac{n}{n-1} \ln{N}$ and $S_1 \simeq {\rm const.} N - \frac{N_\text{NG}}{4} \ln{N}$, where $N$ is the total number of sites and $n$ the R\'enyi index. The result for $n>1$ is in reasonable agreement with the quantum Monte Carlo results of Luitz et al. [Phys. Rev. Lett. 112, 057203 (2014)], and qualitatively similar to those obtained previously for the entanglement entropy. The Shannon entropy of a line subsystem (embedded in the two-dimensional system) is also considered. Finally, we present some density-matrix renormalization group (DMRG) calculations for a spin$\frac{1}{2}$ XY model on the square lattice in a cylinder geometry. These numerical data confirm our findings for logarithmic terms in the $n=\infty$ R\'enyi entropy (also called $-\ln{p_{\rm max}}$). They also reveal some universal dependence on the cylinder aspect ratio, in good agreement with the fact that, in that case, $p_{\rm max}$ is related to a non-compact free-boson partition function in dimension 1+1.

Two holes in a two-dimensional quantum antiferromagnet: A variational study based on entangled-plaquette states

We show that the entangled-plaquette variational ansatz can be adapted to study the two-dimensional $t-J$ model in the presence of two mobile holes. Specifically, we focus on a square lattice comprising up to $N=256$ sites in the parameter range $0.4\leq J/ t\leq2.0$. Ground state energies are obtained via the optimization of a wave function in which the weight of a given configuration is expressed in terms of variational coefficients associated with square and linear entangled plaquettes. Our estimates are in excellent agreement with exact results available for the $N=16$ lattice. By extending our study to considerably larger systems we find, based on the analysis of the long distance tail of the probability of finding two holes at spatial separation $r$, and on our computed two-hole binding energies, the existence of a two-hole bound state for all the values of $J/t$ explored here. It is estimated that d-wave binding of the two holes does not occur for $J/t<J_c/t\simeq 0.19$.

Emergent quasi-one-dimensionality in a kagome magnet: A simple route to complexity

We study the ground state phase diagram of the quantum spin-$1/2$ Heisenberg model on the kagom\'{e} lattice with first- ($J_1 < 0$), second- ($J_2 < 0$), and third-neighbor interactions ($J_d > 0$) by means of analytical low-energy field theory and numerical density-matrix renormalization group (DMRG) studies. The results offer a consistent picture of the $J_d$-dominant regime in terms of three sets of spin chains weakly coupled by the ferromagnetic inter-chain interactions $J_{1,2}$. When either $J_1$ or $J_2$ is dominant, the model is found to support one of two cuboctohedral phases, cuboc1 and cuboc2. These cuboc states host non-coplanar long-ranged magnetic order and possess finite scalar spin chirality. However, in the compensated regime $J_1 \simeq J_2$, a valence bond crystal phase emerges between the two cuboc phases. We find excellent agreement between an analytical theory based on coupled spin chains and unbiased DMRG calculations, including at a very detailed level of comparison of the structure of the valence bond crystal state. To our knowledge, this is the first such comprehensive understanding of a highly frustrated two-dimensional (2d) quantum antiferromagnet. We find no evidence of either the one-dimensional (1d) gapless spin liquid or the chiral spin liquids, which were previously suggested by parton mean field theories.

Spectral properties for a family of two-dimensional quantum antiferromagnets

We study the spectral properties of a family of quantum antiferromagnets on two-dimensional (2D) lattices. This family of models is obtained by a deformation of the well-studied 2D quantum antiferromagnetic model of Affleck, Kennedy, Lieb and Tasaki (AKLT); they are described by two-body, frustration-free Hamiltonians on a three-colourable lattice of spins. Although the existence of a spectral gap in the 2D AKLT model remains an open question, we rigorously prove the existence of a gap for a subset of this family of quantum antiferromagnets. Along with providing new progress for the gap problem in AKLT-type antiferromagnets in 2D, this result has implications for the theory of quantum computation as it provides a family of two-body Hamiltonians for which the ground state is a resource for universal quantum computation and for which a spectral gap is proven to exist.

Fractionalized gapless quantum vortex liquids

The standard theoretical approach to gapless spin liquid phases of two-dimensional frustrated quantum antiferromagnets invokes the concept of fermionic slave particles into which the spin fractionalizes. As an alternate we explore new kinds of gapless spin liquid phases in frustrated quantum magnets with XY anisotropy where the vortex of the spin fractionalizes into gapless itinerant fermions. The resulting gapless fractionalized vortex liquid phases are studied within a slave particle framework that is dual to the usual one. We demonstrate the stability of some such phases and describe their properties. We give an explicit construction in an XY-spin-1 system on triangular lattice, and interpret it as a critical phase in the vicinity of spin-nematic states.

Identifying topological order in the Shastry-Sutherland model via entanglement entropy

It is known that for a topologically ordered state the area law for the entanglement entropy shows a negative universal additive constant contribution, $\ensuremath{-}\ensuremath{\gamma}$, called the topological entanglement entropy. We theoretically study the entanglement entropy of the two-dimensional Shastry-Sutherland quantum antiferromagnet using exact diagonalization on clusters of 16 and 24 spins. By utilizing the Kitaev-Preskill construction [A. Kitaev and J. Preskill, Phys. Rev. Lett. 96, 110404 (2006)] we extract a finite topological term, $\ensuremath{-}\ensuremath{\gamma}$, in the region of bond-strength parameter space corresponding to high geometrical frustration. Thus, we provide strong evidence for the existence of an exotic topologically ordered state and shed light on the nature of this model's strongly frustrated, and long controversial, intermediate phase.

Varied perturbation theory for the dispersion dip in the two-dimensional Heisenberg quantum antiferromagnet

We study the roton-like dip in the magnon dispersion at the boundary of the Brillouin zone in the isotropic S = 1/2 Heisenberg quantum antiferromagnet. This high-energy feature is sometimes seen as indication of a fractionalization of the magnons to spinons. In this article, we provide evidence that the description of the dip in terms of magnons can be improved significantly by applying more advanced evaluation schemes. In particular, we illustrate the usefulness of the application of the principle of minimal sensitivity in varied perturbation theory. Thereby, we provide an example for the application of this approach to an extended condensed matter problem governed by correlations which can trigger analogous investigations for many other systems.

Spin vortices, skyrmions and the Kosterlitz-Thouless transition in the two-dimensional antiferromagnet

We investigate spin-vortex excitations in the two-dimensional antiferromagnet on the basis of the nonlinear sigma model. The model of two-dimensional Heisenberg quantum antiferromagnet is mapped onto the (2+1)D nonlinear sigma model. The 2D nonlinear sigma model has an instanton (or skyrmion) solution which describes an excitation of spin-vortex type. Quantum fluctuations of instantons are reduced to the study of the Coulomb gas, and the gas of instantons of the 2D nonlinear sigma model is in the plasma phase. We generalize this picture of instanton gas to the (2+1)D nonlinear sigma model. We show, using some approximation, that there is a Kosterlitz-Thouless transition from the plasma phase to the molecular phase as the temperature is lowered.

Effects of ring exchange interaction on the Néel phase of two-dimensional, spatially anisotropic, frustrated Heisenberg quantum antiferromagnet

Higher order quantum effects on the magnetic phase diagram induced by four-spin ring exchange on plaquettes are investigated for a two-dimensional quantum antiferromagnet with S=1/2. Spatial anisotropy and frustration are allowed for. Using a perturbative spin-wave expansion up to second order in 1/S we obtain the spin-wave energy dispersion, sublattice magnetization, and the magnetic phase diagram. We find that for substantial four-spin ring exchange the quantum fluctuations are stronger than in the standard Heisenberg model. A moderate amount of four-spin ring exchange couplings stabilizes the ordered antiferromagnetic Neel state while a large amount renders it unstable. Comparison with inelastic neutron scattering data points toward a moderate ring exchange coupling of 27% to 29% of the nearest-neighbor exchange coupling.