We study the behavior of bipartite, as well as genuine multipartite, entanglement of a resonating valence bond state on a ladder. Although there is negligible bipartite entanglement (BE) present in the rails, as is the case for isotropic lattices in two and higher dimensions, we show that the system possesses significant amounts of BE in the steps of the ladder. However, we find that the genuine multipartite entanglement in the system is substantially low. Therefore, both the properties of bipartite as well as multipartite entanglement in the ladder are contrary to the behavior of entanglement in isotropic lattices, indicating that the geometry of the lattice can play a significant role in quantum information processing tasks. Our results also indicate that numerical and analytical investigations obtained on ladders cannot infer the same on two-dimensional lattices.We study the behavior of bipartite, as well as genuine multipartite, entanglement of a resonating valence bond state on a ladder. Although there is negligible bipartite entanglement (BE) present in the rails, as is the case for isotropic lattices in two and higher dimensions, we show that the system possesses significant amounts of BE in the steps of the ladder. However, we find that the genuine multipartite entanglement in the system is substantially low. Therefore, both the properties of bipartite as well as multipartite entanglement in the ladder are contrary to the behavior of entanglement in isotropic lattices, indicating that the geometry of the lattice can play a significant role in quantum information processing tasks. Our results also indicate that numerical and analytical investigations obtained on ladders cannot infer the same on two-dimensional lattices.

arXiv:1003.4401Journal of Physics A Mathematical and TheoreticalOct 26, 201123 citations

New Variational States for t - J Ladders

J. C. Amadon, Steven R. White

Springer proceedings in physicsJan 1, 20020 citations

Magnetization properties of some quantum spin ladders

Kunj Tandon, Siddhartha Lal, Swapan Kumar Pati +2 more

The experimental realization of various spin ladder systems has prompted their detailed theoretical investigations. Here we study the evolution of ground-state magnetization with an external magnetic field for two different antiferromagnetic systems: a three-legged spin- $1/2$ ladder, and a two-legged spin- $1/2$ ladder with an additional diagonal interaction. The finite system density-matrix renormalization-group method is employed for numerical studies of the three-chain system, and an effective low-energy Hamiltonian is used in the limit of strong interchain coupling to study the two- and three-chain systems. The three-chain system has a magnetization plateau at one-third of the saturation magnetization. The two-chain system has a plateau at zero magnetization due to a gap above the singlet ground state. It also has a plateau at half of the saturation magnetization for a certain range of values of the couplings. We study the regions of transitions between plateaus numerically and analytically, and find that they are described, at first order in a strong-coupling expansion, by an $\mathrm{XXZ}$ spin- $1/2$ chain in a magnetic field; the second-order terms give corrections to the $\mathrm{XXZ}$ model. We also study numerically some low-temperature properties of the three-chain system, such as the magnetization, magnetic susceptibility and specific heat.The experimental realization of various spin ladder systems has prompted their detailed theoretical investigations. Here we study the evolution of ground-state magnetization with an external magnetic field for two different antiferromagnetic systems: a three-legged spin-$1/2$ ladder, and a two-legged spin-$1/2$ ladder with an additional diagonal interaction. The finite system density-matrix renormalization-group method is employed for numerical studies of the three-chain system, and an effective low-energy Hamiltonian is used in the limit of strong interchain coupling to study the two- and three-chain systems. The three-chain system has a magnetization plateau at one-third of the saturation magnetization. The two-chain system has a plateau at zero magnetization due to a gap above the singlet ground state. It also has a plateau at half of the saturation magnetization for a certain range of values of the couplings. We study the regions of transitions between plateaus numerically and analytically, and find that they are described, at first order in a strong-coupling expansion, by an $\mathrm{XXZ}$ spin-$1/2$ chain in a magnetic field; the second-order terms give corrections to the $\mathrm{XXZ}$ model. We also study numerically some low-temperature properties of the three-chain system, such as the magnetization, magnetic susceptibility and specific heat.

arXiv:cond-mat/9806111Physical review. B, Condensed matterJan 1, 199963 citations

1/2

ladder, and a two-legged spin-

1/2

ladder with an additional diagonal interaction. The finite system density-matrix renormalization-group method is employed for numerical studies of the three-chain system, and an effective low-energy Hamiltonian is used in the limit of strong interchain coupling to study the two- and three-chain systems. The three-chain system has a magnetization plateau at one-third of the saturation magnetization. The two-chain system has a plateau at zero magnetization due to a gap above the singlet ground state. It also has a plateau at half of the saturation magnetization for a certain range of values of the couplings. We study the regions of transitions between plateaus numerically and analytically, and find that they are described, at first order in a strong-coupling expansion, by an

\mathrm{XXZ}

spin-

1/2

chain in a magnetic field; the second-order terms give corrections to the

\mathrm{XXZ}

model. We also study numerically some low-temperature properties of the three-chain system, such as the magnetization, magnetic susceptibility and specific heat.