Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:cond-mat/0103424 · Physical review. B, Condensed matter

Antiferromagnetically coupled alternating spin chains

A. E. Trumper, C. J. Gazza

Published Sep 4, 2001• 28 citations
arXivHTMLPDF

Abstract

The effect of antiferromagnetic interchain coupling in alternating spin-(1,1/2) chains is studied by means of spin-wave theory and density-matrix renormalization group (DMRG). In particular, two limiting cases are investigated, the two-leg ladder and its two-dimensional (2D) generalization. Results of the ground-state properties like energy, spin gap, magnetizations, and correlation functions are reported for the whole range of the interchain coupling ${J}_{\ensuremath{\perp}}.$ For the 2D case the spin-wave results predict a smooth dimensional crossover from 1D to 2D keeping the ground state always ordered. For the ladder system, the DMRG results show that any ${J}_{\ensuremath{\perp}}>0$ drives the system to a gapped ground state. Furthermore the behavior of the correlation functions closely resemble the uniform spin-1/2 ladder. For ${J}_{\ensuremath{\perp}}$ lower than 0.3, however, the gap behaves quadratically as $\ensuremath{\Delta}\ensuremath{\sim}{0.6J}_{\ensuremath{\perp}}^{2}.$ Finally, it is argued that the behavior of the spin gap for an arbitrary number of mixed coupled spin chains is analogous to that of the uniform spin-1/2 chains.

DOI
10.1103/physrevb.64.134408

Related papers

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.

arXiv:cond-mat/9806111•Physical review. B, Condensed matter•Jan 1, 1999•63 citations

Low-energy properties and magnetization plateaus in a two-leg mixed spin ladder

Jizhong Lou, Changfeng Chen, Shaojin Qin

Using the density-matrix renormalization-group technique we investigate the low-energy properties and the magnetization-plateau behavior in a two-leg mixed spin ladder consisting of a spin-1/2 chain coupled with a spin-1 chain. The calculated results show that the system is in the same universality class as the spin-3/2 chain when the interchain coupling is strongly ferromagnetic, but the similarity between the two systems is less clear under other coupling conditions. We have identified two types of magnetization-plateau phases. The calculation of the magnetization distribution on the spin-1/2 and the spin-1 chains on the ladder shows that one plateau phase is related to the partially magnetized valence-bond-solid state, and the other plateau state contains strongly coupled $S=1$ and $s=1/2$ spins on the rung.

arXiv:cond-mat/0109014•Physical review. B, Condensed matter•Aug 29, 2001•10 citations

Asymmetric spin- 12 two-leg ladders: Analytical studies supported by exact diagonalization, DMRG, and Monte Carlo simulations

D. N. Aristov, C. Brünger, Fakher F. Assaad +4 more

We consider asymmetric spin-$\frac{1}{2}$ two-leg ladders with nonequal antiferromagnetic (AF) couplings ${J}_{\ensuremath{\parallel}}$ and $\ensuremath{\kappa}{J}_{\ensuremath{\parallel}}$ along legs $(\ensuremath{\kappa}\ensuremath{\le}1)$ and ferromagnetic rung coupling, ${J}_{\ensuremath{\perp}}$. This model is characterized by a gap $\ensuremath{\Delta}$ in the spectrum of spin excitations. We show that in the large ${J}_{\ensuremath{\perp}}$ limit this gap is equivalent to the Haldane gap for the AF spin-1 chain, irrespective of the asymmetry of the ladder. The behavior of the gap at small rung coupling falls in two different universality classes. The first class, which is best understood from the case of the conventional symmetric ladder at $\ensuremath{\kappa}=1$, admits a linear scaling for the spin gap $\ensuremath{\Delta}\ensuremath{\sim}{J}_{\ensuremath{\perp}}$. The second class appears for a strong asymmetry of the coupling along legs, $\ensuremath{\kappa}{J}_{\ensuremath{\parallel}}⪡{J}_{\ensuremath{\perp}}⪡{J}_{\ensuremath{\parallel}}$ and is characterized by two energy scales: the exponentially small spin gap $\ensuremath{\Delta}\ensuremath{\sim}{J}_{\ensuremath{\perp}}\text{ }\text{exp}(\ensuremath{-}{J}_{\ensuremath{\parallel}}/{J}_{\ensuremath{\perp}})$, and the bandwidth of the low-lying excitations induced by a Suhl-Nakamura indirect exchange $\ensuremath{\sim}{J}_{\ensuremath{\perp}}^{2}/{J}_{\ensuremath{\parallel}}$. We report numerical results obtained by exact diagonalization, density-matrix renormalization group and quantum Monte Carlo simulations for the spin gap and various spin correlation functions. Our data indicate that the behavior of the string order parameter, characterizing the hidden AF order in Haldane phase, is different in the limiting cases of weak and strong asymmetries. On the basis of the numerical data, we propose a low-energy theory of effective spin-1 variables, pertaining to large blocks on a decimated lattice.

arXiv:1008.1644•Physical Review B•Nov 8, 2010•13 citations

Ground-state phase diagram of the dimerized spin-1/2 two-leg ladder*

Cong Fu, Hui Zhao, Yuguang Chen +1 more

Dimerized spin-1/2 ladders exhibit a variety of phase structures, which depend on the intra-chain and inter-chain spin exchange energies as well as on the dimerization pattern of the ladder. Using the density matrix renormalization group (DMRG) algorithm, we study critical properties of the bond-alternating two-leg Heisenberg spin ladder with diagonal interaction J ×. Two types of spin systems, staggered dimerized antiferromagnetic ladder and columnar dimerized ferro-antiferromagnetic couplings ladder, are investigated. To clarify the phase transition behaviors, we simultaneously analyze the string order parameter (SOP), the twisted order parameter (TOP), as well as a measurement of the quantum information analysis. Based on measuring this different observables, we establish the phase diagram accurately and give the fitting functions of the phase boundaries. In addition, the phase transition of cross-coupled spin ladder (in the absence of intrinsic dimerization) is also discussed.

Chinese Physics B•Mar 5, 2021•2 citations

Size-dependent low-energy excitations in an alternating spin-1/spin- 12 antiferromagnetic chain: Spin-wave theory and density-matrix renormalization-group studies

Sasmita Mohakud, Swapan Kumar Pati, Seiji Miyashita

We study the properties of the ground state and the low-lying excited states of an alternating spin-1 and spin-$\frac{1}{2}$ antiferromagnetic chain with ferromagnetic next-nearest-neighbor coupling with a variety of methods, namely, spin-wave analysis, density-matrix renormalization-group (DMRG) method, and exact-diagonalization method. The ground state of this model with $2N$ spins is ferrimagnetic with the total spin ${S}_{G}=N∕2$ for all parameter values. In the long chain limit, a gapless excitation is found with characteristics of goldstone mode of the ferromagnetic order with total spin $S={S}_{G}\ensuremath{-}1$. The lowest gapped excitation, however, exists in the total spin $S={S}_{G}+1$ sector. Interestingly, we find that with the increase in ferromagnetic coupling, spin-wave gapped excitation becomes lower than the massless mode for the large wave numbers. Correspondingly, from DMRG analysis we find that the excitation in the total spin $S={S}_{G}+1$ is lower than that in the total spin $S={S}_{G}\ensuremath{-}1$ when the size of the chain is short and the ferromagnetic interaction is large. Characteristics of these excitations are also reflected in the low temperature thermodynamic quantities, where the low-energy properties are strongly affected by the system size and the coupling strength.

Physical Review B•Jul 27, 2007•15 citations

Mixed-spin Heisenberg ladders in a magnetic field

D. S. Almeida, Anderson S. Bibiano-Filho, W. M. da Silva +1 more

In this work, we study alternating mixed-spin (s,S) Heisenberg ladders in the magnetic field h density matrix renormalization group and linear spin-wave calculations. The h versus interchain coupling J_{⊥} phase diagram for the (1/2,1) case is investigated in detail. In particular, we demonstrate the compatibility between the critical line estimates and magnetic ordering by analyzing chains with variable values of J_{⊥} and of h along the chain, J_{⊥} and h scans, and considering the usual case of chains with uniform couplings. The magnetization plateau at 1/3 of saturation magnetization, 1/3 plateau, is observed for J_{⊥}>0 and in a limited range for J_{⊥}<0. The critical Kosterlitz-Thouless transition point, where the 1/3 plateau closes, is identified through a finite-size analysis of the transverse spin correlation functions.

arXiv:2606.28521•Physical review. E•Jan 27, 2025•2 citations
The effect of antiferromagnetic interchain coupling in alternating spin-(1,1/2) chains is studied by means of spin-wave theory and density-matrix renormalization group (DMRG). In particular, two limiting cases are investigated, the two-leg ladder and its two-dimensional (2D) generalization. Results of the ground-state properties like energy, spin gap, magnetizations, and correlation functions are reported for the whole range of the interchain coupling J\ensuremath⊥.{J}_{\ensuremath{\perp}}.J\ensuremath⊥​. For the 2D case the spin-wave results predict a smooth dimensional crossover from 1D to 2D keeping the ground state always ordered. For the ladder system, the DMRG results show that any J\ensuremath⊥>0{J}_{\ensuremath{\perp}}>0J\ensuremath⊥​>0 drives the system to a gapped ground state. Furthermore the behavior of the correlation functions closely resemble the uniform spin-1/2 ladder. For J\ensuremath⊥{J}_{\ensuremath{\perp}}J\ensuremath⊥​ lower than 0.3, however, the gap behaves quadratically as \ensuremathΔ\ensuremath∼0.6J\ensuremath⊥2.\ensuremath{\Delta}\ensuremath{\sim}{0.6J}_{\ensuremath{\perp}}^{2}.\ensuremathΔ\ensuremath∼0.6J\ensuremath⊥2​. Finally, it is argued that the behavior of the spin gap for an arbitrary number of mixed coupled spin chains is analogous to that of the uniform spin-1/2 chains.
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-1/21/21/2 ladder, and a two-legged spin-1/21/21/2 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 XXZ\mathrm{XXZ}XXZ spin-1/21/21/2 chain in a magnetic field; the second-order terms give corrections to the XXZ\mathrm{XXZ}XXZ model. We also study numerically some low-temperature properties of the three-chain system, such as the magnetization, magnetic susceptibility and specific heat.
Using the density-matrix renormalization-group technique we investigate the low-energy properties and the magnetization-plateau behavior in a two-leg mixed spin ladder consisting of a spin-1/2 chain coupled with a spin-1 chain. The calculated results show that the system is in the same universality class as the spin-3/2 chain when the interchain coupling is strongly ferromagnetic, but the similarity between the two systems is less clear under other coupling conditions. We have identified two types of magnetization-plateau phases. The calculation of the magnetization distribution on the spin-1/2 and the spin-1 chains on the ladder shows that one plateau phase is related to the partially magnetized valence-bond-solid state, and the other plateau state contains strongly coupled S=1S=1S=1 and s=1/2s=1/2s=1/2 spins on the rung.
We consider asymmetric spin-12\frac{1}{2}21​ two-leg ladders with nonequal antiferromagnetic (AF) couplings ${J}_{\ensuremath{\parallel}}$ and $\ensuremath{\kappa}{J}_{\ensuremath{\parallel}}$ along legs $(\ensuremath{\kappa}\ensuremath{\le}1)$ and ferromagnetic rung coupling, ${J}_{\ensuremath{\perp}}$. This model is characterized by a gap $\ensuremath{\Delta}$ in the spectrum of spin excitations. We show that in the large ${J}_{\ensuremath{\perp}}$ limit this gap is equivalent to the Haldane gap for the AF spin-1 chain, irrespective of the asymmetry of the ladder. The behavior of the gap at small rung coupling falls in two different universality classes. The first class, which is best understood from the case of the conventional symmetric ladder at $\ensuremath{\kappa}=1$, admits a linear scaling for the spin gap $\ensuremath{\Delta}\ensuremath{\sim}{J}_{\ensuremath{\perp}}$. The second class appears for a strong asymmetry of the coupling along legs, $\ensuremath{\kappa}{J}_{\ensuremath{\parallel}}⪡{J}_{\ensuremath{\perp}}⪡{J}_{\ensuremath{\parallel}}$ and is characterized by two energy scales: the exponentially small spin gap $\ensuremath{\Delta}\ensuremath{\sim}{J}_{\ensuremath{\perp}}\text{ }\text{exp}(\ensuremath{-}{J}_{\ensuremath{\parallel}}/{J}_{\ensuremath{\perp}})$, and the bandwidth of the low-lying excitations induced by a Suhl-Nakamura indirect exchange $\ensuremath{\sim}{J}_{\ensuremath{\perp}}^{2}/{J}_{\ensuremath{\parallel}}$. We report numerical results obtained by exact diagonalization, density-matrix renormalization group and quantum Monte Carlo simulations for the spin gap and various spin correlation functions. Our data indicate that the behavior of the string order parameter, characterizing the hidden AF order in Haldane phase, is different in the limiting cases of weak and strong asymmetries. On the basis of the numerical data, we propose a low-energy theory of effective spin-1 variables, pertaining to large blocks on a decimated lattice.
Dimerized spin-1/2 ladders exhibit a variety of phase structures, which depend on the intra-chain and inter-chain spin exchange energies as well as on the dimerization pattern of the ladder. Using the density matrix renormalization group (DMRG) algorithm, we study critical properties of the bond-alternating two-leg Heisenberg spin ladder with diagonal interaction J ×. Two types of spin systems, staggered dimerized antiferromagnetic ladder and columnar dimerized ferro-antiferromagnetic couplings ladder, are investigated. To clarify the phase transition behaviors, we simultaneously analyze the string order parameter (SOP), the twisted order parameter (TOP), as well as a measurement of the quantum information analysis. Based on measuring this different observables, we establish the phase diagram accurately and give the fitting functions of the phase boundaries. In addition, the phase transition of cross-coupled spin ladder (in the absence of intrinsic dimerization) is also discussed.
We study the properties of the ground state and the low-lying excited states of an alternating spin-1 and spin-12\frac{1}{2}21​ antiferromagnetic chain with ferromagnetic next-nearest-neighbor coupling with a variety of methods, namely, spin-wave analysis, density-matrix renormalization-group (DMRG) method, and exact-diagonalization method. The ground state of this model with 2N2N2N spins is ferrimagnetic with the total spin SG=N∕2{S}_{G}=N∕2SG​=N∕2 for all parameter values. In the long chain limit, a gapless excitation is found with characteristics of goldstone mode of the ferromagnetic order with total spin $S={S}_{G}\ensuremath{-}1$. The lowest gapped excitation, however, exists in the total spin S=SG+1S={S}_{G}+1S=SG​+1 sector. Interestingly, we find that with the increase in ferromagnetic coupling, spin-wave gapped excitation becomes lower than the massless mode for the large wave numbers. Correspondingly, from DMRG analysis we find that the excitation in the total spin S=SG+1S={S}_{G}+1S=SG​+1 is lower than that in the total spin $S={S}_{G}\ensuremath{-}1$ when the size of the chain is short and the ferromagnetic interaction is large. Characteristics of these excitations are also reflected in the low temperature thermodynamic quantities, where the low-energy properties are strongly affected by the system size and the coupling strength.
In this work, we study alternating mixed-spin (s,S) Heisenberg ladders in the magnetic field h density matrix renormalization group and linear spin-wave calculations. The h versus interchain coupling J_{⊥} phase diagram for the (1/2,1) case is investigated in detail. In particular, we demonstrate the compatibility between the critical line estimates and magnetic ordering by analyzing chains with variable values of J_{⊥} and of h along the chain, J_{⊥} and h scans, and considering the usual case of chains with uniform couplings. The magnetization plateau at 1/3 of saturation magnetization, 1/3 plateau, is observed for J_{⊥}>0 and in a limited range for J_{⊥}<0. The critical Kosterlitz-Thouless transition point, where the 1/3 plateau closes, is identified through a finite-size analysis of the transverse spin correlation functions.