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

Abstract

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.

Accepted in Physica B: Condensed Matter