The ground-state energy and the singlet-triplet energy gap of the antiferromagnetic Heisenberg model on a ladder is investigated using a mean-field theory and the density-matrix renormalization group. Spin-wave theory shows that the corrections to the local magnetization are infinite. This indicates that no long-range order occurs in this system. A flux-phase state is used to calculate the energy gap as a function of the transverse coupling, ${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$, in the ladder. It is found that the gap is linear in ${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$ for ${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$\ensuremath{\gg}1 and goes to zero for ${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$\ensuremath{\rightarrow}0. The mean-field theory agrees well with the numerical results.The ground-state energy and the singlet-triplet energy gap of the antiferromagnetic Heisenberg model on a ladder is investigated using a mean-field theory and the density-matrix renormalization group. Spin-wave theory shows that the corrections to the local magnetization are infinite. This indicates that no long-range order occurs in this system. A flux-phase state is used to calculate the energy gap as a function of the transverse coupling, ${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$, in the ladder. It is found that the gap is linear in ${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$ for ${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$\ensuremath{\gg}1 and goes to zero for ${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$\ensuremath{\rightarrow}0. The mean-field theory agrees well with the numerical results.

arXiv:cond-mat/9404067Physical review. B, Condensed matterSep 1, 199463 citations

Generalized antiferromagnetic Heisenberg spin ladders

Yan-Chr Tsai, Chin‐Kun Hu

Physica B Condensed MatterOct 1, 20013 citations

Self-consistent mean-field theory of a spin-1 antiferromagnetic chain

Hanting Wang, Jue-Lian Shen, Kui-Ru Li +1 more

We develop an extended self-consistent mean-field approach to study a spin-1 antiferromagnetic (AF) chain with the Hamiltonian H= ${\mathit{tsum}}_{\mathit{i}}$ [ ${\mathit{S}}_{\mathit{i}}^{\mathit{x}}$ ${\mathit{S}}_{\mathit{i}+1}^{\mathit{x}}$ + ${\mathit{S}}_{\mathit{i}}^{\mathit{y}}$ ${\mathit{S}}_{\mathit{i}+1}^{\mathit{y}}$ +\ensuremath{\lambda} ${\mathit{S}}_{\mathit{i}}^{\mathit{z}}$ ${\mathit{S}}_{\mathit{i}+1}^{\mathit{z}}$ +D( ${\mathit{S}}_{\mathit{i}}^{\mathit{z}}$ ${)}^{2}$ ] based on Anderson's spin-wave theory. The ground-state energy changes little compared with the traditional spin-wave theory and the excitation spectrum shows a gap which lends support to Haldane's conjecture. At the Heisenberg point (\ensuremath{\lambda}=1,D=0), the ground-state energy and the gap are -1.3505 and 0.3914, respectively. In the Heisenberg-Ising case (\ensuremath{\lambda}>0,D=0), the gap decreases when \ensuremath{\lambda} goes down from 1 and at a critical ${\ensuremath{\lambda}}_{\mathit{c}}$>0 the gap goes to 0, while for the single-ion anisotropy (\ensuremath{\lambda}=1,D>0) the gap decreases with the increasing of D and at a critical value ${\mathit{D}}_{\mathit{c}}$ the gap goes to 0. These results agree well with those of other theoretical methods and experiments. We study the one-magnon excitation spectrum carefully and suggest an explanation for its crossing with the two-magnon excitation spectrum at low momentum. We estimate the crossing occurring at k\ensuremath{\simeq}0.3\ensuremath{\pi}. The results agree well with the very recent theoretical and experimental results. The picture of the Haldane gap is discussed from our extended self-consistent mean-field ground state and many interesting properties of the spin-1 AF chain are discussed.We develop an extended self-consistent mean-field approach to study a spin-1 antiferromagnetic (AF) chain with the Hamiltonian H=${\mathit{tsum}}_{\mathit{i}}$ [${\mathit{S}}_{\mathit{i}}^{\mathit{x}}$${\mathit{S}}_{\mathit{i}+1}^{\mathit{x}}$+${\mathit{S}}_{\mathit{i}}^{\mathit{y}}$${\mathit{S}}_{\mathit{i}+1}^{\mathit{y}}$ +\ensuremath{\lambda}${\mathit{S}}_{\mathit{i}}^{\mathit{z}}$${\mathit{S}}_{\mathit{i}+1}^{\mathit{z}}$+D(${\mathit{S}}_{\mathit{i}}^{\mathit{z}}$${)}^{2}$] based on Anderson's spin-wave theory. The ground-state energy changes little compared with the traditional spin-wave theory and the excitation spectrum shows a gap which lends support to Haldane's conjecture. At the Heisenberg point (\ensuremath{\lambda}=1,D=0), the ground-state energy and the gap are -1.3505 and 0.3914, respectively. In the Heisenberg-Ising case (\ensuremath{\lambda}>0,D=0), the gap decreases when \ensuremath{\lambda} goes down from 1 and at a critical ${\ensuremath{\lambda}}_{\mathit{c}}$>0 the gap goes to 0, while for the single-ion anisotropy (\ensuremath{\lambda}=1,D>0) the gap decreases with the increasing of D and at a critical value ${\mathit{D}}_{\mathit{c}}$ the gap goes to 0. These results agree well with those of other theoretical methods and experiments. We study the one-magnon excitation spectrum carefully and suggest an explanation for its crossing with the two-magnon excitation spectrum at low momentum. We estimate the crossing occurring at k\ensuremath{\simeq}0.3\ensuremath{\pi}. The results agree well with the very recent theoretical and experimental results. The picture of the Haldane gap is discussed from our extended self-consistent mean-field ground state and many interesting properties of the spin-1 AF chain are discussed.

Physical review. B, Condensed matterMay 1, 19947 citations

Theory of Spin Correlations in Antiferromagnetic Spin Ladders

Alexei M. Tsvelik

APSMar 1, 19970 citations

A novel basis for the study of Heisenberg spin ladders

J. Piekarewicz, James R. Shepard

Revista Mexicana de FísicaJan 1, 19981 citation

From one to two dimensions: Magnetic phases in weakly coupled spin ladders

Mateo Cárdenes Wuttig, Andrew J. Millis

A large variety of materials can be approximately described by means of spin-1/2 Heisenberg ladders. Here, the Density Matrix Renormalization Group (DMRG) algorithm together with a previously established numerical self-consistent mean-field approximation is used to investigate the magnetic properties of spin ladders coupled in a second dimension. The full ground state phase diagram including spin-gapped, antiferromagnetic, ferrimagnetic and fully polarized phases is presented as a function of interladder and intraladder coupling and magnetic field. Measurement of the dependence of magnetization on applied magnetic field is shown to enable location of a material on the phase diagram and determination of the Hamiltonian parameters. These results provide a practical route toward identifying and characterizing magnetic materials composed of coupled spin ladders.A large variety of materials can be approximately described by means of spin-1/2 Heisenberg ladders. Here, the Density Matrix Renormalization Group (DMRG) algorithm together with a previously established numerical self-consistent mean-field approximation is used to investigate the magnetic properties of spin ladders coupled in a second dimension. The full ground state phase diagram including spin-gapped, antiferromagnetic, ferrimagnetic and fully polarized phases is presented as a function of interladder and intraladder coupling and magnetic field. Measurement of the dependence of magnetization on applied magnetic field is shown to enable location of a material on the phase diagram and determination of the Hamiltonian parameters. These results provide a practical route toward identifying and characterizing magnetic materials composed of coupled spin ladders.

arXiv:2511.10503Physical review. B./Physical review. BFeb 2, 20260 citations

We develop an extended self-consistent mean-field approach to study a spin-1 antiferromagnetic (AF) chain with the Hamiltonian H=

{\mathit{tsum}}_{\mathit{i}}

[

{\mathit{S}}_{\mathit{i}}^{\mathit{x}}

{\mathit{S}}_{\mathit{i}+1}^{\mathit{x}}

{\mathit{S}}_{\mathit{i}}^{\mathit{y}}

{\mathit{S}}_{\mathit{i}+1}^{\mathit{y}}

+\ensuremath{\lambda}

{\mathit{S}}_{\mathit{i}}^{\mathit{z}}

{\mathit{S}}_{\mathit{i}+1}^{\mathit{z}}

+D(

{\mathit{S}}_{\mathit{i}}^{\mathit{z}}

{)}^{2}

] based on Anderson's spin-wave theory. The ground-state energy changes little compared with the traditional spin-wave theory and the excitation spectrum shows a gap which lends support to Haldane's conjecture. At the Heisenberg point (\ensuremath{\lambda}=1,D=0), the ground-state energy and the gap are -1.3505 and 0.3914, respectively. In the Heisenberg-Ising case (\ensuremath{\lambda}>0,D=0), the gap decreases when \ensuremath{\lambda} goes down from 1 and at a critical ${\ensuremath{\lambda}}_{\mathit{c}}$>0 the gap goes to 0, while for the single-ion anisotropy (\ensuremath{\lambda}=1,D>0) the gap decreases with the increasing of D and at a critical value

{\mathit{D}}_{\mathit{c}}

the gap goes to 0. These results agree well with those of other theoretical methods and experiments. We study the one-magnon excitation spectrum carefully and suggest an explanation for its crossing with the two-magnon excitation spectrum at low momentum. We estimate the crossing occurring at k\ensuremath{\simeq}0.3\ensuremath{\pi}. The results agree well with the very recent theoretical and experimental results. The picture of the Haldane gap is discussed from our extended self-consistent mean-field ground state and many interesting properties of the spin-1 AF chain are discussed.