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.

Bi3Mn4O12(NO3) (BMNO) is a honeycomb bilayers anti-ferromagnet, not showing any ordering down to very low temperatures despite having a relatively large Curie-Weiss temperature. Using ab initio density functional theory, we extract an effective spin Hamiltonian for this compound. The proposed spin Hamiltonian consists of anti-ferrimagnetic Heisenberg terms with coupling constants ranging up to third intra-layer and fourth inter-layer neighbors. Performing Monte Carlo simulation, we obtain the temperature dependence of magnetic susceptibility and so the Curie-Weiss temperature and find the coupling constants which best matches with the experimental value. We discover that depending on the strength of the interlayer exchange couplings, two collinear spin configurations compete with each other in this system. Both states have in plane Néel character, however, at small interlayer coupling spin directions in the two layers are antiparallel (N1 state) and discontinuously transform to parallel (N2 state) by enlarging the interlayer couplings at a first order transition point. Classical Monte Carlo simulation and density matrix renormalization group calculations confirm that exchange couplings obtained for BMNO are in such a way that put this material at the phase boundary of a first order phase transition, where the trading between these two collinear spin states prevents it from setting in a magnetically ordered state. Bi 3 Mn 4 O 12 (NO 3 ) (BMNO) is an experimental realization of frustrated honeycomb magnetic materials, synthesized by Smirnova et al. [1]. In this compound, the magnetic lattice can be effectively described by a weakly coupled honeycomb bilayers of Mn +4 ions (Fig. 1). The temperature dependence of magnetic susceptibility of BMNO does not indicate any ordering down to T = 0.4K, in spite of the Curie-Weiss temperature θ CW ≈ −257K [1, 2]. The absence of long-range ordering in BMNO is also confirmed by specific heat measurements [1, 2], neutron scattering [3] and high-field electron spin relaxation (ESR) experiments [4]. So far, the theoretical attempts to explain the magnetic properties of BMNO have been focusing on the frustration effect of second intra-layer coupling J 2 or the tendency toward dimerization by considering a large anti-ferromagnetic inter-layer nearest neighbor coupling J 1c [5][6][7][8][9][10][11][12]. In an attempt to calculate the exchange interactions by ab initio method, it is found that the dominant exchange interactions are nearest in-plane coupling (J 1 ) and also an effective inter-plane coupling (J c ) which exceeds J 1 [5]. However, in that work the experimental positions of the atoms in the structure are taken without geometry optimization and only 5 magnetic configurations are considered for the calculation of exchange interactions.In this paper, we obtain a Heisenberg spin Hamiltonian for BMNO, using an ab initio LDA+U calculation. In our calculations, we consider a detailed analysis of nonidentical Mn atoms which were assumed to be identical in the previous calculation [...

We quantitatively obtain the quantum ground-state phases of a Fermi system with on-site and dipole-dipole interactions in one-dimensional lattice chains within the density matrix renormalization group. We show, at a given spin polarization, the existence of six phases in the phase diagram and find that the phases are highly dependent on the spin degree of freedom. These phases can be constructed using available experimental techniques.Comment: 10 pages, 8 figure

Using modified spin wave (MSW) method, we study the J1 − J2 Heisenberg model with first and second neighbor antiferromagnetic exchange interactions. For symmetric S = 1/2 model, with the same couplings for all the equivalent neighbors, we find three phase in terms of frustration parameter α = J2/J1: (1) a commensurate collinear ordering with staggered magnetization (Néel.I state) for 0 ≤ᾱ 0.207 , (2) a magnetically gapped disordered state for 0.207 ᾱ 0.369, preserving all the symmetries of the Hamiltonian and lattice, hence by definition is a quantum spin liquid (QSL) state and (3) a commensurate collinear ordering in which two out of three nearest neighbor magnetizations are antiparallel and the remaining pair are parallel (Néel.II state), for 0.396 ᾱ ≤ 1. We also explore the phase diagram of distorted J1 −J2 model with S = 1/2. Distortion is introduced as an inequality of one nearest neighbor coupling with the other two. This yields a richer phase diagram by the appearance of a new gapped QSL, a gapless QSL and also a valence bond crystal (VBC) phase in addition to the previously three phases found for undistorted model.

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The phase diagram of Kane-Mele-Heisenberg (KMH) model in classical limit 47 , contains disordered regions in the coupling space, as the result of to competition among different terms in the Hamiltonian, leading to frustration in finding a unique ground state. In this work we explore the nature of these phase in the quantum limit, for a S = 1/2. Employing exact diagonalization (ED) in Sz and nearest neighbor valence bond (NNVB) bases, bond and plaquette valence bond mean field theories, We show that the disordered regions are divided into ordered quantum states in the form of plaquette valence bond crystal (PVBC) and staggered dimerized (SD) phases.

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The ground-state phase diagram of a two-leg fermionic dipolar ladder with inter-site interactions is studied using density matrix renormalization group (DMRG) techniques. We use a state-of-the-art implementation of the DMRG algorithm and finite size scaling to simulate large system sizes with high accuracy. We also consider two different model systems and explore stable phases in half and quarter filling factors. We find that in the half filling, the charge and spin gaps emerge in a finite value of the dipole-dipole and on-site interactions. In the quarter filling case, s-wave superconducting state, charge density wave, homogenous insulating and phase separation phases occur depend on the interaction values. Moreover, in the dipole-dipole interaction, the D-Mott phase emerges when the hopping terms along the chain and rung are the same, whereas, this phase has been only proposed for the anisotropic Hubbard model. In the half filling case, on the other hand, there is either charge-density wave or charged Mott order phase depends on the orientation of the dipole moments of the particles with respect to the ladder geometry.