Quantum rotors on theAB2chain with competing interactions

Abstract

We present the ground state phase diagram of q = 1/2 quantum-rotor chains with competing interactions (frustration) calculated through cluster variational mean field approaches. We consider two interaction patterns, named F1 and F2 models, between the quantum-rotor momentum and position operators, which follow exchange patterns of known one-dimensional spin-1/2 systems with a ferrimagnetic state in their phase diagrams. The spin-1/2 F1 model is known as the diamond chain and is related to the azurite compound, while the spin-1/2 F2 model was recently shown to present a frustration-induced condensation of magnons. We provide a detailed comparison between the quantum-rotor phase diagrams, in single-and multi-site mean-field approaches, and known results for the spin-1/2 models, including exact diagonalization and density matrix renormalization group data for these systems, as well as phase diagrams of the associated classical models.

Lieb and hole-doped ferrimagnetism, spiral, resonating valence-bond states, and phase separation in large-U AB 2 Hubbard chains

“…the chain is formed by pairs of S = 1/2 monomers and S = 0 dimers, with a small local polarization of the diamond spins [44], in agreement with reliable electronic structure calculations using density functional theory (DFT) combined with density matrix renormalization group (DMRG) results [45]. These dimer-monomer states have been found previously in the context of modeling frustrated AB 2 chains [46][47][48], and confirmed through a modeling using quantum rotors [49]. In contrast to azurite, whose dimers appear perpendicular to the chain direction, in the spin-1/2 inequilateral diamond-chain compounds [50] A 3 Cu 3 AlO 2 (SO 4 ) 4 (A = K, Rb, Cs), the magnetic exchange interactions force the dimers to lie along the sides of the diamond cells and the monomers form a 1D Heisenberg chain.…”

Topological approach to microcanonical thermodynamics and phase transition of interacting classical spins

“…for positive (negative) h. These unstable solutions, also illustrated by dashed lines, start at T = 0 with M = −h (filled squares) and meet the metastable solutions at T h max ( ). In fact, the metastable and unstable solutions are the corresponding van der Waals loops in the M versus T diagram 6 . Notice that T h 1 0 max ( ) = = and for h 1 | | > only stable solutions, emerging from = ± M 1, exist in any T-regime.…”

“…Moreover, the relevance of the singularities associated with the stationary points (critical points) of the potential energy has been emphasized [4] by the following condition: at a PT the density of the Jacobian's critical points diverges in the thermodynamic limit, or, by the same token, the determinant (D) of the Hessian matrix of the potential should be asymptotically flat at the transition. The two abovementioned conditions were shown to be fulfilled in several MF models: XY and k-trigonometric [4]; XY on AB 2 chains under frustration-or field-induced PT's [5,6] 3 ; and in a model of self-gravitating particles [7]. In addition, it has been proposed [5] that in the models mentioned the following property holds: the simultaneous occurrence of the two necessary conditions-namely the D-flatness condition and the discontinuity or cusp-like pattern exhibited by E ( ) χ at E c , emerges as a necessary and sucient condition for the occurrence of a finite temperature PT.…”

MAGNETIC PHASE DIAGRAM OF THE HUBBARD MODEL ON THE AB2 CHAIN

“…The unit cell of the AB 2 chain contains two kinds of atoms, A and B, where each atom A is connected to four atoms B, each linked to two atoms A. Despite this chain has been extensively studied, [9][10][11][12][13][14][15][16][17][18][19][20][21][22] a detailed analysis of the full magnetic phase diagram and its relationship with the intra-atomic interaction and number of particles per site has not been performed and this is the purpose of the present paper. The magnetic system is described by the Hubbard Hamiltonian 23 and we apply the Green's function method within the Hartree-Fock approximation 24 (HFA) to obtain the physical quantities of interest.…”