Three-leg Antiferromagnetic Heisenberg Ladder with Frustrated Boundary Condition; Ground State Properties

TL;DR

This study investigates the ground state properties of a three-leg antiferromagnetic Heisenberg ladder with frustrated boundary conditions, revealing a gapped, dimerized ground state and extending findings to ladders with more legs.

Contribution

It demonstrates that the three-leg ladder has a gapped, dimerized ground state and introduces an exactly solvable model with next-nearest neighbor coupling, supported by numerical DMRG results.

Findings

The system has an excitation gap of approximately 0.28J_1 in the strong coupling limit.

Ground states are dimerized and break translational symmetry.

The model with next-nearest neighbor coupling is exactly solvable and shares properties with the original model.

Abstract

The antiferromagnetic Heisenberg spin systems on the three-leg ladder are investigated. Periodic boundary condition is imposed in the rung direction. The system has an excitation gap for all antiferromagnetic inter-chain coupling ($J_{\perp}>0$). The estimated gap for the strong coupling limit ($J_{\perp}/J_1 \to \infty$) is 0.28$J_1$. Although the interaction is homogeneous and only nearest-neighbor, the ground states of the system are dimerized and break the translational symmetry in the thermodynamic limit. Introducing the next-nearest neighbor coupling ($J_2$), we can see that the system is solved exactly. The ground state wave function is completely dimer-ordered. Using density matrix renomalization group algorithm, we show numerically that the original model ($J_2=0$) has the same nature with the exactly solvable model. The ground state properties of the ladder with a higher odd number of legs are also discussed.