Frustrated magnetic ladders a DMRG study

Ground states of the frustrated spin-1 Ising-Heisenberg two-leg ladder with Heisenberg intra-rung coupling and only Ising interaction along legs and diagonals are rigorously found by taking advantage of local conservation of the total spin on each rung.The constructed ground-state phase diagram of the frustrated spin-1 Ising-Heisenberg ladder is then compared with the analogous phase diagram of the fully quantum spin-1 Heisenberg two-leg ladder obtained by density matrix renormalization group (DMRG) calculations.Both investigated spin models exhibit quite similar magnetization scenarios, which involve intermediate plateaux at one-quarter, one-half and threequarters of the saturation magnetization.Ground states of the frustrated spin-1 Ising-Heisenberg two-leg ladder with Heisenberg intra-rung coupling and only Ising interaction along legs and diagonals are rigorously found by taking advantage of local conservation of the total spin on each rung.The constructed ground-state phase diagram of the frustrated spin-1 Ising-Heisenberg ladder is then compared with the analogous phase diagram of the fully quantum spin-1 Heisenberg two-leg ladder obtained by density matrix renormalization group (DMRG) calculations.Both investigated spin models exhibit quite similar magnetization scenarios, which involve intermediate plateaux at one-quarter, one-half and threequarters of the saturation magnetization.

arXiv:1305.6703Acta Physica Polonica AJun 6, 20142 citations

Ladders in a magnetic field: a strong coupling approach

Frédéric Mila

arXiv:cond-mat/9805029The European Physical Journal BNov 1, 1998191 citations

Series expansion analysis of a frustrated four-spin tube

Marcelo Arlego, Wolfram Brenig

We study the magnetism of a frustrated four-leg spin- $1/2$ ladder with transverse periodic boundary conditions: the frustrated four-spin tube (FFST). Using a combination of series expansion (SE), based on the continuous unitary transformation method and density-matrix renormalization group (DMRG) we analyze the ground-state, the one-, and the two-particle excitations in the regime of strong rung coupling. We find several marked differences of the FFST with respect to standard two-leg ladders. First, we show that frustration destabilizes the spin-gap phase of the FFST, which is adiabatically connected to the limit of decoupled rung singlets, leading to a first-order quantum phase transition at finite interrung coupling. Second, we show that apart from the well-known triplon branch of spin ladders, the FFST sustains additional elementary excitations, including a singlon and additional triplons. Finally, we find that in the two-particle sector, the FFST exhibits collective (anti)bound states similar to two-leg ladders, however, with a different ordering of the spin-quantum numbers. We show that frustration has significant impact on the FFST leading to a flattening of the ground-state energy landscape, a mass-enhancement of the excitations, and to a relative enhancement of the (anti)binding strength. Where possible, we use DMRG to benchmark the findings from our SE calculations, showing excellent agreement.We study the magnetism of a frustrated four-leg spin-$1/2$ ladder with transverse periodic boundary conditions: the frustrated four-spin tube (FFST). Using a combination of series expansion (SE), based on the continuous unitary transformation method and density-matrix renormalization group (DMRG) we analyze the ground-state, the one-, and the two-particle excitations in the regime of strong rung coupling. We find several marked differences of the FFST with respect to standard two-leg ladders. First, we show that frustration destabilizes the spin-gap phase of the FFST, which is adiabatically connected to the limit of decoupled rung singlets, leading to a first-order quantum phase transition at finite interrung coupling. Second, we show that apart from the well-known triplon branch of spin ladders, the FFST sustains additional elementary excitations, including a singlon and additional triplons. Finally, we find that in the two-particle sector, the FFST exhibits collective (anti)bound states similar to two-leg ladders, however, with a different ordering of the spin-quantum numbers. We show that frustration has significant impact on the FFST leading to a flattening of the ground-state energy landscape, a mass-enhancement of the excitations, and to a relative enhancement of the (anti)binding strength. Where possible, we use DMRG to benchmark the findings from our SE calculations, showing excellent agreement.

arXiv:1106.2101Physical Review BOct 18, 201115 citations

Magnetic properties of zig-zag ladders

D. C. Cabra, A. Honecker, Pierre Pujol

arXiv:cond-mat/9902112The European Physical Journal BJan 1, 200082 citations

Magnetization Process of anS=1 Frustrated Spin Ladder

Kiyomi Okamoto, Kouichi Okunishi, Tôru Sakai

We investigate, at T =0, the magnetization process of the S =1 frustrated two-leg spin ladder having the leg interaction ( J ), the rung interaction ( J 0 ) and the diagonal interaction ( J d ), especially focusing on the appearance and the disappearance of the magnetization plateaux. We use the degenerate perturbation theory, the level spectroscopy analysis of the numerical diagonalization data and the DMRG. When J d =0, the M s /2 plateau ( M s is the saturation magnetization) appears for J 0 / J > 1.463. Then there is no M s /2 plateau for the so-called isotropic case J = J 0 . In case of J d > 0, J d helps the M s /2 plateau. And also, the M s /4 and (3/4) M s plateaux appear when J d is sufficiently large. These two plateaux are associated with the spontaneous breaking of the translation symmetry along the leg direction. We show the plateau phase diagram on the J d versus J plane, and also the magnetic phase diagram on the H versus J d plane for fixed J .We investigate, at T =0, the magnetization process of the S =1 frustrated two-leg spin ladder having the leg interaction ( J ), the rung interaction ( J 0 ) and the diagonal interaction ( J d ), especially focusing on the appearance and the disappearance of the magnetization plateaux. We use the degenerate perturbation theory, the level spectroscopy analysis of the numerical diagonalization data and the DMRG. When J d =0, the M s /2 plateau ( M s is the saturation magnetization) appears for J 0 / J > 1.463. Then there is no M s /2 plateau for the so-called isotropic case J = J 0 . In case of J d > 0, J d helps the M s /2 plateau. And also, the M s /4 and (3/4) M s plateaux appear when J d is sufficiently large. These two plateaux are associated with the spontaneous breaking of the translation symmetry along the leg direction. We show the plateau phase diagram on the J d versus J plane, and also the magnetic phase diagram on the H versus J d plane for fixed J .

Journal of the Physical Society of JapanJan 1, 20053 citations

We study the magnetism of a frustrated four-leg spin-

1/2

ladder with transverse periodic boundary conditions: the frustrated four-spin tube (FFST). Using a combination of series expansion (SE), based on the continuous unitary transformation method and density-matrix renormalization group (DMRG) we analyze the ground-state, the one-, and the two-particle excitations in the regime of strong rung coupling. We find several marked differences of the FFST with respect to standard two-leg ladders. First, we show that frustration destabilizes the spin-gap phase of the FFST, which is adiabatically connected to the limit of decoupled rung singlets, leading to a first-order quantum phase transition at finite interrung coupling. Second, we show that apart from the well-known triplon branch of spin ladders, the FFST sustains additional elementary excitations, including a singlon and additional triplons. Finally, we find that in the two-particle sector, the FFST exhibits collective (anti)bound states similar to two-leg ladders, however, with a different ordering of the spin-quantum numbers. We show that frustration has significant impact on the FFST leading to a flattening of the ground-state energy landscape, a mass-enhancement of the excitations, and to a relative enhancement of the (anti)binding strength. Where possible, we use DMRG to benchmark the findings from our SE calculations, showing excellent agreement.