Valence bond phases inS= 1/2 Kane–Mele–Heisenberg model

Abstract

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.

Quantum phase diagram of distortedJ1 − J2HeisenbergS = 1/2 antiferromagnet in honeycomb lattice: a modified spin wave study

“…Furthermore, analysis of the ground state properties by defining appropriate structure factors, suggests a plaquette valence bond solid (PVBS) ground state for 0.2 J 2 /J 1 0.35 which transforms to a valence bond solid (VBS) state with staggered dimerization at J 2 /J 1 ≈ 0.35 20,21 . The existence of plaquette valence bond solid has been verified by different methods, such as functional renormalization group 22 , coupled cluster method (CCM) 23,24 , mean-field plaquette valence bond theory 25,37 and density matrix renormalization group (DMRG) 26,27 . However, other methods such as Schwinger boson mean-field approach 28,29,32,33 , Schwinger fermion mean-field theory 30 and variational Monte Carlo 31 propose a Z 2 quantum spin liquid (QSL) for the disordered region.…”

“…ED calculations in both S z = 0, and a nearest neighbor valence bond (NNVB) basis, show that the NNVB basis provides a very good description of the ground state for J J 0.2 0.3 / ≈ [20,21]. The existence of a plaquette VBS has been verified by different methods, such as the functional renormalization group [22], the coupled cluster method (CCM) [23,24], mean-field plaquette valence bond theory [25,37] and the density matrix renormalization group (DMRG) [26,27]. However, other methods such as the Schwinger boson mean-field approach [28,29,32,33], Schwinger fermion mean-field theory [30] and variational Monte Carlo [31] propose a Z 2 QSL for the disordered region.…”

Spin liquid in twisted homobilayers group-VI gichalcogenides

“…Due to the suppression of charge fluctuations in the limit of the strong on-site Coulomb repulsion, we try to obtain the effective spin Hamiltonian using second-order perturbation theory. The perturba-tion to second-order in t 1 /U (t 2 /U ), we find an effective spin Hamiltonian for the half-filling case including the Kane-Mele Heisenberg [93,94] and Dzyaloshinskii-Moriya (DM) terms as follows:…”