Exact columnar dimer ground state and quantum phase transitions in a frustratedcoupled spin ladder model

Manas Ranjan Mahapatra, Rakesh Kumar

S. Chen, Bao-Zhong Han

M. Mahapatra, Rakesh Kumar

We study a spin-half frustrated coupled ladder system, in which ladders with leg, rung, and diagonal interactions are linked via nearest-neighbor coupling. By introducing a leg-symmetric inter-ladder interaction that connects the left-to-left and right-to-right legs of adjacent ladders, the model is found to possess an exact dimer ground state, characterized by a product of two-spin singlets forming a columnar dimer phase. We analyze this model using bond-operator mean-field theory (BOMFT) and the density matrix renormalization group (DMRG) to probe the phase transitions that occur as one traverses the coupling space. The BOMFT reveals three distinct phases: a double-stripe ordered phase, a Néel ordered phase, and a quantum disordered dimerized phase. The critical points for the transitions are at $ J_1 = -0.81 $ (double-stripe to dimerized) and at $ J_1 = 2.81 $ (dimerized to Néel phase). Further, the DMRG results corroborate the exact ground state and refine the critical points to $ J_1 = -0.79 $ and $ J_1 = 2.29 $ for the respective transitions. Additionally, another transition is identified as the Néel order vanishes for $ J_1 \ge 4.5 $. The model can alternatively be represented as a network of orthogonal zigzag and fully frustrated spin ladders, offering a structural framework conducive to quantum materials engineering.

Rakesh Kumar, Brijesh Kumar

We construct and study the two frustrated quantum spin-$1∕2$ models on square lattice, which are like the antiferromagnetic ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ model with some additional four-spin exchange interactions. These models admit an exactly solvable case in which the ground state consists of four degenerate columnar-dimer singlet (CDS) configurations. Away from the exact case, we employ bond-operator mean-field theory to investigate the evolution of the ground state by varying the interaction parameters. The mean-field calculation reveals a quantum phase diagram in which the CDS phase undergoes a continuous phase transition to either N\'eel or collinear ordered antiferromagnetic phases.

敬吾 肘井

Hsiang-Hsuan Hung, Chang-De Gong, Yung‐Chung Chen +1 more

A two-leg spin-1/2 ladder with diagonal interactions is investigated numerically. We focus our attention on the possibility of columnar dimer phase, which was recently predicted based on a reformulated bosonization theory. By using density matrix renormalization group technique and exact diagonalization method, we calculate columnar dimer order parameter, spin correlation on a rung, string order parameters, and scaled excitation gaps. Carefully using various finite-size scaling techniques, our results show no support for the existence of columnar dimer phase in the spin ladder under consideration.