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Multiple magnetization plateaus induced by further neighbor interaction in an $S = 1$ two-leg Heisenberg spin ladder

Hidehiko Kohshiro, Ryui Kaneko, Satoshi Morita, Hosho Katsura, Naoki Kawashima

Published Feb 15, 2021• 0 citations
OpenAlex

Abstract

We study the magnetization process of the $S=1$ Heisenberg model on a two-leg ladder with further neighbor spin-exchange interaction. We consider the interaction that couples up to the next-nearest neighbor rungs and find an exactly solvable regime where the ground states become product states. The next-nearest neighbor interaction tends to stabilize magnetization plateaus at multiples of 1/6. In most of the exactly solvable regime, a single magnetization curve shows two series of plateaus with different periodicities.

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Multiple magnetization plateaus induced by further neighbor interaction in an S=1S = 1S=1 two-leg Heisenberg spin ladder
We study the magnetization process of the S=1S=1S=1 Heisenberg model on a two-leg ladder with further neighbor spin-exchange interaction. We consider the interaction that couples up to the next-nearest neighbor rungs and find an exactly solvable regime where the ground states become product states. The next-nearest neighbor interaction tends to stabilize magnetization plateaus at multiples of 1/6. In most of the exactly solvable regime, a single magnetization curve shows two series of plateaus with different periodicities.
We study the magnetization process of the S=1S=1S=1 Heisenberg model on a two-leg ladder with farther neighbor spin-exchange interaction. We consider the interaction that couples up to the next-nearest neighbor rungs and find an exactly solvable regime where the ground states become product states. The next-nearest neighbor interaction tends to stabilize magnetization plateaus at multiples of 1/6. In most of the exactly solvable regime, a single magnetization curve shows two series of plateaus with different periodicities.
The magnetization process of the S=1/2 antiferromagnetic spin ladder at T=0 is studied by the exact diagonalization of finite clusters and size scaling analyses. It is found that a magnetization plateau appears at half the saturation value (m=1/2) in the presence of a sufficiently large next-nearest-neighbor exchange interaction to yield the frustration, when the rung coupling is larger than the leg one. The phase diagram at m=1/2 is given by the analysis based on the conformal invariance. The magnetization curves are also presented in several cases.
We present a solvable ladder model which displays magnetization plateaus at fractional values of the total magnetization. Plateau signatures are also shown to exist along special lines. The model has isotropic Heisenberg interactions with additional many-body terms. The phase diagram can be calculated exactly for all values of the rung coupling and the magnetic field. We also derive the anomalous behavior of the susceptibility near the plateau boundaries. There is good agreement with the phase diagram obtained recently for the pure Heisenberg ladders by numerical and perturbative techniques.
The ground state, entropy, and magnetic Grüneisen parameter of the antiferromagnetic spin-1/2 Ising-Heisenberg model on a double sawtooth ladder are rigorously investigated using the classical transfer-matrix technique. The model includes the XXZ interaction between the interstitial Heisenberg dimers, the Ising coupling between nearest-neighbor spins of the legs and rungs, and additional cyclic four-spin Ising term in each square plaquette. For a particular value of the cyclic four-spin exchange, we found in the ground-state phase diagram of the Ising-Heisenberg ladder a quadruple point, at which four different ground states coexist together. During an adiabatic demagnetization process, a fast cooling accompanied with an enhanced magnetocaloric effect can be detected near this quadruple point. The ground-state phase diagram of the Ising-Heisenberg ladder is confronted with the zero-temperature magnetization process of the purely quantum Heisenberg ladder, which is calculated by using exact diagonalization based on the Lanczos algorithm for a finite-size ladder of 24 spins and the density-matrix renormalization group simulations for a finite-size ladder with up to 96 spins. Some indications of the existence of intermediate magnetization plateaus in the magnetization process of the full Heisenberg model for a small but nonzero four-spin Ising coupling were found. The DMRG results reveal that the quantum Heisenberg double sawtooth ladder exhibits some quantum Luttinger spin-liquid phase regions that are absent in the Ising-Heisenberg counterpart model. Except this difference, the magnetic behavior of the full Heisenberg model is quite analogous to its simplified Ising-Heisenberg counterpart and, hence, may bring insight into the fully quantum Heisenberg model from rigorous results for the Ising-Heisenberg model.
We study a system with spin-Peierls dimerization in next-nearest-neighbor (NNN) interaction and also the presence of nearest-neighbor (NN) interaction under a magnetic field. We predict the existence of different fractionally quantized magnetization plateaus with many interesting physical properties. The effect of the frustrating NNN interaction and the role of quantum fluctuations are also explored for different magnetization plateaus. We explain more physically the gapless state of spin spectrum for small values of the frustrating NNN interaction. The transition from commensurate gapped phase to incommensurate Luttinger liquid phase is of Mott-δ type.
We study the one-dimensional spin-1/2 model with nearest and next-to-nearest-neighbor couplings exposed to a homogeneous magnetic field h3{h}_{3}h3​ and a dimer field with period q and strength $\ensuremath{\delta}$. The latter generates a magnetization plateau at $M=(1\ensuremath{-}q/\ensuremath{\pi})/2$, which evolves with strength $\ensuremath{\delta}$ of the perturbation as ${\ensuremath{\delta}}^{\ensuremath{\epsilon}}$, where $\ensuremath{\epsilon}=\ensuremath{\epsilon}{(h}_{3},\ensuremath{\alpha})$ is related to the $\ensuremath{\eta}$ exponent which describes the critical behavior of the dimer structure factor, if the perturbation is switched off $(\ensuremath{\delta}=0)$. We also discuss the appearance of magnetization plateaus in ladder systems with l legs.