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Register a new userThree dimensional generalization of the $J_1$-$J_2$ Heisenberg model on a square lattice and role of the interlayer coupling $J_c$
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A possibility to describe magnetism in the iron pnictide parent compounds in terms of the two-dimensional frustrated Heisenberg $J_1$-$J_2$ model has been actively discussed recently. However, recent neutron scattering data has shown that the pnictides have a relatively large spin wave dispersion in the direction perpendicular to the planes. This indicates that the third dimension is very important. Motivated by this observation we study the $J_1$-$J_2$-$J_c$ model that is the three dimensional generalization of the $J_1$-$J_2$ Heisenberg model for $S = 1/2$ and S = 1. Using self-consistent spin wave theory we present a detailed description of the staggered magnetization and magnetic excitations in the collinear state. We find that the introduction of the interlayer coupling $J_c$ suppresses the quantum fluctuations and strengthens the long range ordering. In the $J_1$-$J_2$-$J_c$ model, we find two qualitatively distinct scenarios for how the collinear phase becomes unstable upon increasing $J_1$. Either the magnetization or one of the spin wave velocities vanishes. For $S = 1/2$ renormalization due to quantum fluctuations is significantly stronger than for S=1, in particular close to the quantum phase transition. Our findings for the $J_1$-$J_2$-$J_c$ model are of general theoretical interest, however, the results show that it is unlikely that the model is relevant to undoped pnictides.
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We study the quantum phase diagram and excitation spectrum of the frustrated $J_1$-$J_2$ spin-1/2 Heisenberg Hamiltonian. A hierarchical mean-field approach, at the heart of which lies the idea of identifying {it relevant} degrees of freedom, is developed. Thus, by performing educated, manifestly symmetry preserving mean-field approximations, we unveil fundamental properties of the system. We then compare various coverings of the square lattice with plaquettes, dimers and other degrees of freedom, and show that only the {it symmetric plaquette} covering, which reproduces the original Bravais lattice, leads to the known phase diagram. The intermediate quantum paramagnetic phase is shown to be a (singlet) {it plaquette crystal}, connected with the neighboring Neel phase by a continuous phase transition. We also introduce fluctuations around the hierarchical mean-field solutions, and demonstrate that in the paramagnetic phase the ground and first excited states are separated by a finite gap, which closes in the Neel and columnar phases. Our results suggest that the quantum phase transition between Neel and paramagnetic phases can be properly described within the Ginzburg-Landau-Wilson paradigm.
We investigate the magnetic properties of LiYbO$_2$, containing a three-dimensionally frustrated, diamond-like lattice via neutron scattering, magnetization, and heat capacity measurements. The stretched diamond network of Yb$^{3+}$ ions in LiYbO$_2$ enters a long-range incommensurate, helical state with an ordering wave vector ${bf{k}} = (0.384, pm 0.384, 0)$ that locks-in to a commensurate ${bf{k}} = (1/3, pm 1/3, 0)$ phase under the application of a magnetic field. The spiral magnetic ground state of LiYbO$_2$ can be understood in the framework of a Heisenberg $J_1-J_2$ Hamiltonian on a stretched diamond lattice, where the propagation vector of the spiral is uniquely determined by the ratio of $J_2/|J_1|$. The pure Heisenberg model, however, fails to account for the relative phasing between the Yb moments on the two sites of the bipartite lattice, and this detail as well as the presence of an intermediate, partially disordered, magnetic state below 1 K suggests interactions beyond the classical Heisenberg description of this material.
Strongly correlated systems with geometric frustrations can host the emergent phases of matter with unconventional properties. Here, we study the spin $S = 1$ Heisenberg model on the honeycomb lattice with the antiferromagnetic first- ($J_1$) and second-neighbor ($J_2$) interactions ($0.0 leq J_2/J_1 leq 0.5$) by means of density matrix renormalization group (DMRG). In the parameter regime $J_2/J_1 lesssim 0.27$, the system sustains a N{e}el antiferromagnetic phase. At the large $J_2$ side $J_2/J_1 gtrsim 0.32$, a stripe antiferromagnetic phase is found. Between the two magnetic ordered phases $0.27 lesssim J_2/J_1 lesssim 0.32$, we find a textit{non-magnetic} intermediate region with a plaquette valence-bond order. Although our calculations are limited within $6$ unit-cell width on cylinder, we present evidence that this plaquette state could be a strong candidate for this non-magnetic region in the thermodynamic limit. We also briefly discuss the nature of the quantum phase transitions in the system. We gain further insight of the non-magnetic phases in the spin-$1$ system by comparing its phase diagram with the spin-$1/2$ system.
We assess the ground-state phase diagram of the $J_1$-$J_2$ Heisenberg model on the kagome lattice by employing Gutzwiller-projected fermionic wave functions. Within this framework, different states can be represented, defined by distinct unprojected fermionic Hamiltonians that comprise of hopping and pairing terms, as well as a coupling to local Zeeman fields to generate magnetic order. For $J_2=0$, the so-called U(1) Dirac state, in which only hopping is present (such as to generate a $pi$-flux in the hexagons), has been shown to accurately describe the exact ground state [Y. Iqbal, F. Becca, S. Sorella, and D. Poilblanc, Phys. Rev. B 87, 060405 (2013); Y.-C. He, M. P. Zaletel, M. Oshikawa, and F. Pollmann, Phys. Rev. X 7, 031020 (2017)]. Here, we show that its accuracy improves in presence of a small $antiferromagnetic$ super-exchange $J_2$, leading to a finite region where the gapless spin liquid is stable; then, for $J_2/J_1=0.11(1)$, a first-order transition to a magnetic phase with pitch vector ${bf q}=(0,0)$ is detected, by allowing magnetic order within the fermionic Hamiltonian. Instead, for small $ferromagnetic$ values of $|J_2|/J_1$, the situation is more contradictory. While the U(1) Dirac state remains stable against several perturbations in the fermionic part (i.e., dimerization patterns or chiral terms), its accuracy clearly deteriorates on small systems, most notably on $36$ sites where exact diagonalization is possible. Then, upon increasing the ratio $|J_2|/J_1$, a magnetically ordered state with $sqrt{3} times sqrt{3}$ periodicity eventually overcomes the U(1) Dirac spin liquid. Within the ferromagnetic regime, the magnetic transition is definitively first order, at $J_2/J_1=-0.065(5)$.
We investigate the Hubbard model on a two-dimensional square lattice by the perturbation expansion to the fourth order in the on-site Coulomb repulsion U. Numerically calculating all diagrams up to the fourth order in self-energy, we examine the convergence of perturbation series in the lattice system. We indicate that the coefficient of each order term rapidly decreases as in the impurity Anderson model for T > 0.1t in the half-filled case, but it holds in the doped case even at lower temperatures. Thus, we can expect that the convergence of perturbation expansion in U is very good in a wide parameter region also in the lattice system, except for T < 0.1t in the half-filled case. We next calculate the density of states in the fourth-order perturbation. In the half-filled case, the shape in a moderate correlation regime is quite different from the three peak structure in the second-order perturbation. Remarkable upper and lower Hubbard bands locate at w = +(-)U/2, and a pseudogap appears at the Fermi level w=0. This is considered as the precursor of the Mott-Hubbard antiferromagnetic structure. In the doped case, quasiparticles with very heavy mass are formed at the Fermi level. Thus, we conclude that the fourth-order perturbation theory overall well explain the asymptotic behaviors in a strong correlation regime.
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