Valence-bond crystal phase of a frustrated spin-1/2 square-lattice antiferromagnet

Linear Combinations of Cluster Mean-Field States Applied to Spin Systems

We present an innovative cluster-based method employing linear combinations of diverse cluster mean-field states and apply it to describe the ground state of strongly correlated spin systems. In cluster mean-field theory, the ground state wave function is expressed as a factorized tensor product of optimized cluster states. While our prior work concentrated on a single cMF tiling, this study removes that constraint by combining different tilings of cMF states. Selection criteria, including translational symmetry and spatial proximity, guide this process. We present benchmark calculations for the one- and two-dimensional J1 - J2 and XXZ Heisenberg models. Our findings highlight two key aspects. First, the method offers a semiquantitative description of the 0.4 ≲ J2/J1 ≲ 0.6 regime of the J1 - J2 model─a particularly challenging regime for existing methods. Second, our results demonstrate the capability of our method to provide qualitative descriptions for all the models and regimes considered, establishing it as a valuable reference. However, the inclusion of additional (weak) correlations is necessary for quantitative agreement, and we explore methods to incorporate these extra correlations.

Symmetry-projected cluster mean-field theory applied to spin systems

We introduce Sz spin-projection based on cluster mean-field theory and apply it to the ground state of strongly correlated spin systems. In cluster mean-fields, the ground state wavefunction is written as a factorized tensor product of optimized cluster states. In previous work, we have focused on unrestricted cluster mean-field, where each cluster is Sz symmetry adapted. We here remove this restriction by introducing a generalized cluster mean-field (GcMF) theory, where each cluster is allowed to access all Sz sectors, breaking Sz symmetry. In addition, a projection scheme is used to restore global Sz, which gives rise to the Sz spin-projected generalized cluster mean-field (SzGcMF). Both of these extensions contribute to accounting for inter-cluster correlations. We benchmark these methods on the 1D, quasi-2D, and 2D J1 - J2 and XXZ Heisenberg models. Our results indicate that the new methods (GcMF and SzGcMF) provide a qualitative and semi-quantitative description of the Heisenberg lattices in the regimes considered, suggesting them as useful references for further inter-cluster correlations, which are discussed in this work.

Investigation of the temperature phase diagram of the 2D semi-classical ferrimagneticJ1-J2model

The temperature phase diagram (ToverJ₂) of the 2D semiclassicalJ1-J2Heisenberg model is discussed. The investigation was carried out using the self-consistent Bloch equation and a quantum statistical description of the magnetization. In addition to the three states of the zero-temperature phase diagram, theJ2-Tphase diagram shows two new phases, the paramagnetic phase and the semi-paramagneticS1-Néel state. The five occurring ground states, as well as the transitions between these states, are discussed. In particular, attention is paid to the interplay between temperature and frustration.

Coupled Cluster and Perturbation Theories Based on a Cluster Mean-Field Reference Applied to Strongly Correlated Spin Systems

We introduce perturbation and coupled-cluster theories based on a cluster mean-field reference for describing the ground state of strongly correlated spin systems. In cluster mean-field, the ground state wave function is written as a simple tensor product of optimized cluster states. The cluster language and the mean-field nature of the ansatz allow for a straightforward improvement which uses perturbation theory and coupled-cluster to account for intercluster correlations. We present benchmark calculations on the 1D chain and 2D square J₁-J₂ Heisenberg model, using cluster mean-field, perturbation theory, and coupled-cluster. We also present an extrapolation scheme that allows us to compute thermodynamic limit energies accurately. Our results indicate that, with sufficiently large clusters, the correlated methods (cPT2, cPT4, and cCCSD) can provide a relatively accurate description of the Heisenberg model in the regimes considered, which suggests that the methods presented can be used for other strongly correlated systems. Some ways to improve upon the methods presented in this work are discussed.

Investigation of the magnetic phase diagram of the 2D ferrimagnetic J 1-J 2 model

The zero-temperature phase diagram and spin dynamics of the 2D ferrimagnetic J 1-J 2 model with (S 1, S 2) = (1/2, 1) are investigated using the time-dependent cluster mean-field theory (t-CMFT). The t-CMFT enables the investigation of the quantum-mechanical as well as semi-classical phase diagram and spin dynamics by control of the entanglement. For the characterization of the ferrimagnetic system, the magnetization, the energy per atom, the cluster quantum states and the von Neumann entropy have been determined.

Unsupervised Machine Learning of Quantum Phase Transitions Using Diffusion Maps

Experimental quantum simulators have become large and complex enough that discovering new physics from the huge amount of measurement data can be quite challenging, especially when little theoretical understanding of the simulated model is available. Unsupervised machine learning methods are particularly promising in overcoming this challenge. For the specific task of learning quantum phase transitions, unsupervised machine learning methods have primarily been developed for phase transitions characterized by simple order parameters, typically linear in the measured observables. However, such methods often fail for more complicated phase transitions, such as those involving incommensurate phases, valence-bond solids, topological order, and many-body localization. We show that the diffusion map method, which performs nonlinear dimensionality reduction and spectral clustering of the measurement data, has significant potential for learning such complex phase transitions unsupervised. This method may work for measurements of local observables in a single basis and is thus readily applicable to many experimental quantum simulators as a versatile tool for learning various quantum phases and phase transitions.

Exotic topological point and line nodes in the plaquette excitations of a frustrated Heisenberg antiferromagnet on the honeycomb lattice

A number of topological nodes including Dirac, quadratic and three-band touching points as well as a pair of degenerate Dirac line nodes are found to emerge in the triplet plaquette excitations of the frustrated spin-1/2J1-J2antiferromagnetic Heisenberg honeycomb model when the ground state of the system lies in a spin-disordered plaquette-valence-bond-solid phase. A six-spin plaquette operator theory of this honeycomb model has been developed for this purpose by using the eigenstates of an isolated Heisenberg hexagonal plaquette. Spin-1/2 operators are thus expressed in the Fock space spanned by the plaquette operators those are obtained in terms of exact analytic form of eigenstates for a single frustrated Heisenberg hexagon. Ultimately, an effective interacting boson model of this system is obtained on the basis of low energy singlets and triplets plaquette operators by employing a mean-field approximation. The values of ground state energy and spin gap of this system have been estimated and the validity of this formalism has been tested upon comparison with the known results. Emergence of topological point and line nodes on the basis of spin-disordered ground state noted in this investigation is very rare on any frustrated system as well as the presence of triplet flat band. Evolution of those topological nodes is studied throughout the full frustrated regime. Finally, emergence of topological phases has been reported upon adding a time-reversal-symmetry breaking term to the Hamiltonian. Coexistence of spin gap with either topological nodes or phases turns this honeycomb model an interesting one.

Spin-liquid-like state in a spin-1/2 square-lattice antiferromagnet perovskite induced by d10-d0 cation mixing

A quantum spin liquid state has long been predicted to arise in spin-1/2 Heisenberg square-lattice antiferromagnets at the boundary region between Néel (nearest-neighbor interaction dominates) and columnar (next-nearest-neighbor interaction dominates) antiferromagnetic order. However, there are no known compounds in this region. Here we use d¹⁰-d⁰ cation mixing to tune the magnetic interactions on the square lattice while simultaneously introducing disorder. We find spin-liquid-like behavior in the double perovskite Sr₂Cu(Te_0.5W_0.5)O₆, where the isostructural end phases Sr₂CuTeO₆ and Sr₂CuWO₆ are Néel and columnar type antiferromagnets, respectively. We show that magnetism in Sr₂Cu(Te_0.5W_0.5)O₆ is entirely dynamic down to 19 mK. Additionally, we observe at low temperatures for Sr₂Cu(Te_0.5W_0.5)O₆-similar to several spin liquid candidates-a plateau in muon spin relaxation rate and a strong T-linear dependence in specific heat. Our observations for Sr₂Cu(Te_0.5W_0.5)O₆ highlight the role of disorder in addition to magnetic frustration in spin liquid physics.

Classical Spin Liquid on the Maximally Frustrated Honeycomb Lattice

We show that the honeycomb Heisenberg antiferromagnet with J_{1}/2=J_{2}=J_{3}, where J_{1}, J_{2}, and J_{3} are first-, second-, and third-neighbor couplings, respectively, forms a classical spin liquid with pinch-point singularities in the structure factor at the Brillouin zone corners. Upon dilution with nonmagnetic ions, fractionalized degrees of freedom carrying 1/3 of the free moment emerge. Their effective description in the limit of low temperature is that of spins randomly located on a triangular lattice, with a frustrated sublattice-sensitive interaction of long-ranged logarithmic form. The XY version of this magnet exhibits nematic thermal order by disorder. This comes with a clear experimental diagnostic in neutron scattering, which turns out to apply also to the case of the celebrated planar order by disorder of the kagome Heisenberg antiferromagnet.

Plaquette ordered phase and quantum phase diagram in the spin-1/2 J(1)-J(2) square Heisenberg model

We study the spin-1/2 Heisenberg model on the square lattice with first- and second-neighbor antiferromagnetic interactions J(1) and J(2), which possesses a nonmagnetic region that has been debated for many years and might realize the interesting Z(2) spin liquid. We use the density matrix renormalization group approach with explicit implementation of SU(2) spin rotation symmetry and study the model accurately on open cylinders with different boundary conditions. With increasing J(2), we find a Néel phase and a plaquette valence-bond (PVB) phase with a finite spin gap. From the finite-size scaling of the magnetic order parameter, we estimate that the Néel order vanishes at J(2)/J(1)≃0.44. For 0.5<J(2)/J(1)<0.61, we find dimer correlations and PVB textures whose decay lengths grow strongly with increasing system width, consistent with a long-range PVB order in the two-dimensional limit. The dimer-dimer correlations reveal the s-wave character of the PVB order. For 0.44<J(2)/J(1)<0.5, spin order, dimer order, and spin gap are small on finite-size systems, which is consistent with a near-critical behavior. The critical exponents obtained from the finite-size spin and dimer correlations could be compatible with the deconfined criticality in this small region. We compare and contrast our results with earlier numerical studies.

Cluster mean-field theory study of J1-J2 Heisenberg model on a square lattice

We study the spin-1/2 J1-J2 Heisenberg model on a square lattice using the cluster mean-field theory. We find a rapid convergence of phase boundaries with increasing cluster size. By extrapolating the cluster size L to infinity, we obtain accurate phase boundaries J(c1)(2) ≈ 0.42 (between the Néel antiferromagnetic phase and non-magnetic phase), and J(c2)(2) ≈ 0.59 (between non-magnetic phase and the collinear antiferromagnetic phase). Our results support the second-order phase transition at J(c1)(2) and the first-order one at J(c2)(2). For the spin-anisotropic J1-J2 model, we present its finite temperature phase diagram and demonstrate that the non-magnetic state is unstable towards the first-order phase transition under intermediate spin anisotropy.

Plaquette valence bond ordering in a J1-J2 Heisenberg antiferromagnet on a honeycomb lattice

We study an S = 1/2 Heisenberg model on the honeycomb lattice with first and second neighbor antiferromagnetic exchange (J(1)-J(2) model), employing exact diagonalization in both the S(z) = 0 basis and nearest neighbor singlet valence bond (NNVB) basis. We find that for 0.2 < J(2)/J(1) < 0.3, the NNVB basis gives a proper description of the ground state in comparison with the exact results. By analyzing the dimer-dimer as well as the plaquette-plaquette correlations and also defining appropriate structure factors, we investigate possible symmetry breaking states as the candidates for the ground state in the frustrated region. We provide a body of evidence in favor of plaquette valence bond ordering for 0.2 < J(2)/J(1) < 0.3. By further increasing the ratio J(2)/J(1), this state undergoes a transition to the staggered dimerized state.

Evidence for deconfined quantum criticality in a two-dimensional Heisenberg model with four-spin interactions

Using ground-state projector quantum Monte Carlo simulations in the valence-bond basis, it is demonstrated that nonfrustrating four-spin interactions can destroy the Néel order of the two-dimensional S=1/2 Heisenberg antiferromagnet and drive it into a valence-bond solid (VBS) phase. Results for spin and dimer correlations are consistent with a single continuous transition, and all data exhibit finite-size scaling with a single set of exponents, z=1, nu=0.78+/-0.03, and eta=0.26+/-0.03. The unusually large eta and an emergent U(1) symmetry, detected using VBS order parameter histograms, provide strong evidence for a deconfined quantum critical point.

Nonlinear sigma model method for the J1-J2 Heisenberg model: disordered ground state with plaquette symmetry

A novel nonlinear sigma model method is proposed for the two-dimensional J1-J2 model, which is extended to include plaquette-type distortion. The nonlinear sigma model is properly derived without spoiling the original spin degrees of freedom. The method shows that a single disordered phase continuously extends from a frustrated uniform regime to an unfrustrated distorted regime. By the continuity and Oshikawa's commensurability condition, the disordered ground states for the uniform J1-J2 model are plaquette states with fourfold degeneracy.

Valence-bond spin-liquid state in two-dimensional frustrated spin-1/2 Heisenberg antiferromagnets

Fermionic valence-bond approach in terms of SU(4) representation is proposed to describe the J1-J2 frustrated Heisenberg antiferromagnetic (AF) model on a bipartite square lattice. A uniform mean field solution without breaking the translational and rotational symmetries describes a valence-bond spin-liquid state, interpolating the two different AF ordered states in the large J1 and large J2 limits, respectively. This novel spin-liquid state is gapless with the vanishing density of states at the Fermi nodal points. Moreover, a sharp resonance peak in the dynamic structure factor is predicted for momenta q=(0,0) and (pi,pi) in the strongly frustrated limit J(2)/J(1) approximately 1/2, which can be checked by neutron scattering experiments.

Peierls-like transition induced by frustration in a two-dimensional antiferromagnet

We show that the introduction of frustration into the spin- 1/2 two-dimensional (2D) antiferromagnetic Heisenberg model on a square lattice via a next-nearest-neighbor exchange interaction can lead to a Peierls-like transition, from a tetragonal to an orthorhombic phase, when the spins are coupled to adiabatic phonons. The two different orthorhombic ground states define an Ising order parameter, which is expected to lead to a finite temperature transition. Implications for Li(2)VOSiO(4), the first realization of that model, will be discussed.

Resonating valence bond wave functions for strongly frustrated spin systems

The resonating-valence-bond (RVB) theory for two-dimensional quantum antiferromagnets is shown to be the correct paradigm for large enough "quantum frustration." This scenario, proposed a long time ago but never confirmed by microscopic calculations, is strongly supported by a new type of variational wave function, which is extremely close to the exact ground state of the J(1)-J(2) Heisenberg model for 0.4 less than approximately J(2)/J(1) less than approximately 0.5. This wave function is proposed to represent the generic spin-half RVB ground state in spin liquids.

Independent freezing of charge and spin dynamics in La1.5Sr0.5CoO4

We present elastic and quasielastic neutron scattering measurements characterizing peculiar short-range charge-orbital and spin order in the layered perovskite material La1.5Sr0.5CoO4. We find that below T(c) approximately 750 K holes introduced by Sr doping lose mobility and enter a statically ordered charge glass phase with loosely correlated checkerboard arrangement of empty and occupied d(3z(2)-r(2)) orbitals ( Co3+ and Co2+). The dynamics of the resultant mixed spin system is governed by the anisotropic nature of the crystal-field Hamiltonian and the peculiar exchange pattern produced by the orbital order. It undergoes a spin freezing transition at a much lower temperature, T(s) less, similar30 K.

Field induced ordering in highly frustrated antiferromagnets

We predict that an external field can induce a spin ordering in highly frustrated classical Heisenberg magnets. We find analytically stabilization of collinear states by thermal fluctuations at a one-third of the saturation field for kagome and garnet lattices and at a half of the saturation field for pyrochlore and frustrated square lattices. This effect is studied numerically for the frustrated square-lattice antiferromagnet by Monte Carlo simulations for classical spins and by exact diagonalization for S = 1/2. The field induced collinear states have a spin gap and produce magnetization plateaus.

Spontaneous plaquette dimerization in the J1-J2 heisenberg model

We investigate the nonmagnetic phase of the spin-half frustrated Heisenberg antiferromagnet on the square lattice using exact diagonalization (up to 36 sites) and quantum Monte Carlo techniques (up to 144 sites). The spin gap and the susceptibilities for the most important crystal symmetry breaking operators are computed. A genuine and somehow unexpected "plaquette resonating valence bond," with spontaneously broken translation symmetry and no broken rotation symmetry, comes out from our numerical simulations as the most plausible ground state for J(2)/J(1) approximately 0.5.