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

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 Néel 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 Néel 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 Néel order vanishes for $J_1 > 4.5$. The static spin structure factor further corroborates the nature of the ordered phases.

Figures (8)

• Figure 1: This picture represents a schematic representation of the model Hamiltonian \ref{['eq:model_hamiltonian']} on a coupled ladder system or equivalently on a square lattice ($J_D:$ double red lines, $J_1:$ blue lines, $J_2:$ green lines, $J_3:$ dotted black lines)
• Figure 2: This figure illustrates the spin gap using both mean-field theory and DMRG and for both frustrated and unfrustrated system.
• Figure 3: This figure illustrates the singlet condensation on dimers for the case of frustrated and unfrustrated lattice.
• Figure 4: This figure illustrates the dispersion of quasi-particles in $\mathbf{k}$-space derived from BOMFT for double period striped phase at $J_1=0.0$ and Neel order at $J_1=2.0$ away from the exact point.
• Figure 5: This figure illustrates the spin gap ($\omega_k$) obtained from the mean-field theory and triplet condensation density with different scales on the y-axis. Dashed lines are for the system without frustration, and solid line is for the model with frustrated interactions. The ordering wave vector for which the gap closes and $n_c$ increases is same for both cases, i.e. ($\frac{\pi}{2},\pi$) and ($0,0$)