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

TL;DR

This paper investigates a coupled spin-1/2 ladder model with frustration and anisotropy, revealing an exact dimer ground state and multiple quantum phase transitions through analytical and numerical methods.

Contribution

It introduces a specific coupled spin ladder model with an exact dimer ground state and maps out its quantum phase diagram using BOMFT and DMRG.

Findings

Exact dimer ground state identified

Critical points for phase transitions determined

Multiple ordered and disordered phases characterized

Abstract

Spin ladders are key models that act as intermediaries between one-dimensional and two-dimensional spin systems. In this study, we examine a coupled spin-$1/2$ ladder, where frustrated ladders with leg, rung, and diagonal interactions are linked through a horizontal coupling. By introducing a spatially anisotropic third-nearest-neighbor interaction along the horizontal direction, the model was found to possess an exact dimer ground state, characterized by a product of singlets forming a columnar dimer phase. The model is analyzed using bond-operator mean-field theory (BOMFT) and the density matrix renormalization group (DMRG). BOMFT reveals three distinct phases: a double-stripe ordered phase, a N\'eel ordered phase, and a quantum disordered dimerized phase. The critical points for the transitions are $J_1 = -0.81$ (double-stripe to dimerized) and $J_1 = 2.81$ (dimerized to N\'eel phase). 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 N\'eel order vanishes for $J_1 > 4.5$. The static spin structure factor further corroborates the nature of the ordered phases.