Bulletin of the American Physical Society

Ground states of a J-Q model with long-range antiferromagnetic interactions

Sibin Yang, Dao‐Xin Yao, Anders W. Sandvik

Published Mar 6, 2019• 0 citations

OpenAlex

Related papers

Ground states of one-dimensional antiferromagnetic models with long-range interaction

Azer Kerimov

Theoretical and Mathematical PhysicsMar 1, 198411 citations

Off-diagonal long-range order in the ground state of the two-dimensional antiferromagnetic Heisenberg model

Biao Hao, Chang-De Gong

Physics Letters ANov 1, 19922 citations

Ising models with long-range antiferromagnetic and short-range ferromagnetic interactions

Alessandro Giuliani, Joel L. Lebowitz, Élliott H. Lieb

arXiv:cond-mat/0604668Physical Review BAug 25, 200670 citations

Absence of phase transitions in one-dimensional antiferromagnetic models with long-range interactions

Azer Kerimov

Journal of Statistical PhysicsAug 1, 199323 citations

Ground-state phase diagram of the spin- 12 square-lattice J1 - J2 model with plaquette structure

Oliver Götze, Sven E. Krüger, F. Fleck +2 more

arXiv:1205.0681Physical Review BJun 21, 201216 citations

Long range order in the ground state of two-dimensional antiferromagnets

Eduardo Jordão Neves, J.Fernando Perez

Physics Letters AMar 1, 1986155 citations

Bulletin of the American Physical Society

Ground states of a J-Q model with long-range antiferromagnetic interactions

Sibin Yang, Dao‐Xin Yao, Anders W. Sandvik

Published Mar 6, 2019• 0 citations

OpenAlex

Related papers

Ground states of one-dimensional antiferromagnetic models with long-range interaction

Azer Kerimov

Theoretical and Mathematical PhysicsMar 1, 198411 citations

Off-diagonal long-range order in the ground state of the two-dimensional antiferromagnetic Heisenberg model

Biao Hao, Chang-De Gong

Physics Letters ANov 1, 19922 citations

Ising models with long-range antiferromagnetic and short-range ferromagnetic interactions

Alessandro Giuliani, Joel L. Lebowitz, Élliott H. Lieb

We study the ground state of a $d$ -dimensional Ising model with both long-range (dipole-like) and nearest-neighbor ferromagnetic (FM) interactions. The long-range interaction is equal to ${r}^{\ensuremath{-}p}$, $p>d$ , while the FM interaction has strength $J$ . If $p>d+1$ and $J$ is large enough the ground state is FM, while if $d<p\ensuremath{\leqslant}d+1$ the FM state is not the ground state for any choice of $J$ . In $d=1$ we show that for any $p>1$ the ground state has a series of transitions from an antiferromagnetic state of period 2 to $2h$ -periodic states of blocks of sizes $h$ with alternating sign, the size $h$ growing when the FM interaction strength $J$ is increased (a generalization of this result to the case $0<p\ensuremath{\leqslant}1$ is also discussed). In $d\ensuremath{\geqslant}2$ we prove, for $d<p\ensuremath{\leqslant}d+1$, that the dominant asymptotic behavior of the ground-state energy agrees for large $J$ with that obtained from a periodic striped state conjectured to be the true ground state. The geometry of contours in the ground state is discussed.We study the ground state of a $d$-dimensional Ising model with both long-range (dipole-like) and nearest-neighbor ferromagnetic (FM) interactions. The long-range interaction is equal to ${r}^{\ensuremath{-}p}$, $p>d$, while the FM interaction has strength $J$. If $p>d+1$ and $J$ is large enough the ground state is FM, while if $d<p\ensuremath{\leqslant}d+1$ the FM state is not the ground state for any choice of $J$. In $d=1$ we show that for any $p>1$ the ground state has a series of transitions from an antiferromagnetic state of period 2 to $2h$-periodic states of blocks of sizes $h$ with alternating sign, the size $h$ growing when the FM interaction strength $J$ is increased (a generalization of this result to the case $0<p\ensuremath{\leqslant}1$ is also discussed). In $d\ensuremath{\geqslant}2$ we prove, for $d<p\ensuremath{\leqslant}d+1$, that the dominant asymptotic behavior of the ground-state energy agrees for large $J$ with that obtained from a periodic striped state conjectured to be the true ground state. The geometry of contours in the ground state is discussed.

arXiv:cond-mat/0604668Physical Review BAug 25, 200670 citations

Absence of phase transitions in one-dimensional antiferromagnetic models with long-range interactions

Azer Kerimov

Journal of Statistical PhysicsAug 1, 199323 citations

Ground-state phase diagram of the spin- 12 square-lattice J1 - J2 model with plaquette structure

Oliver Götze, Sven E. Krüger, F. Fleck +2 more

Using the coupled-cluster method for high orders of approximation and Lanczos exact diagonalization we study the ground-state phase diagram of a quantum spin- $\frac{1}{2}$ ${J}_{1}$ - ${J}_{2}$ model on the square lattice with plaquette structure. We consider antiferromagnetic ( ${J}_{1}>0$ ) as well as ferromagnetic ( ${J}_{1}<0$ ) nearest-neighbor interactions together with frustrating antiferromagnetic next-nearest-neighbor interaction ${J}_{2}>0$ . The strength of interplaquette interaction $\ensuremath{\lambda}$ varies between $\ensuremath{\lambda}=1$ (which corresponds to the uniform ${J}_{1}$ - ${J}_{2}$ model) and $\ensuremath{\lambda}=0$ (which corresponds to isolated frustrated 4-spin plaquettes). While on the classical level ($s\ensuremath{\rightarrow}\ensuremath{\infty}$) both versions of models (i.e., with ferro- and antiferromagnetic ${J}_{1}$ ) exhibit the same ground-state behavior, the ground-state phase diagram differs basically for the quantum case $s=1/2$ . For the antiferromagnetic case ( ${J}_{1}>0$ ) N\'eel antiferromagnetic long-range order at small ${J}_{2}/{J}_{1}$ and $\ensuremath{\lambda}\ensuremath{\gtrsim}0.47$ as well as collinear striped antiferromagnetic long-range order at large ${J}_{2}/{J}_{1}$ and $\ensuremath{\lambda}\ensuremath{\gtrsim}0.30$ appear which correspond to their classical counterparts. Both semiclassical magnetic phases are separated by a nonmagnetic quantum paramagnetic phase. The parameter region, where this nonmagnetic phase exists, increases with decreasing $\ensuremath{\lambda}$. For the ferromagnetic case ( ${J}_{1}<0$ ) we have the trivial ferromagnetic ground state at small ${J}_{2}/|{J}_{1}|$ . By increasing ${J}_{2}$ this classical phase gives way for a semiclassical plaquette phase, where the plaquette block spins of length $s=2$ are antiferromagnetically long-range ordered. Further increasing of ${J}_{2}$ then yields collinear striped antiferromagnetic long-range order for $\ensuremath{\lambda}\ensuremath{\gtrsim}0.38$, but a nonmagnetic quantum paramagnetic phase $\ensuremath{\lambda}\ensuremath{\lesssim}0.38$.Using the coupled-cluster method for high orders of approximation and Lanczos exact diagonalization we study the ground-state phase diagram of a quantum spin-$\frac{1}{2}$ ${J}_{1}$-${J}_{2}$ model on the square lattice with plaquette structure. We consider antiferromagnetic (${J}_{1}>0$) as well as ferromagnetic (${J}_{1}<0$) nearest-neighbor interactions together with frustrating antiferromagnetic next-nearest-neighbor interaction ${J}_{2}>0$. The strength of interplaquette interaction $\ensuremath{\lambda}$ varies between $\ensuremath{\lambda}=1$ (which corresponds to the uniform ${J}_{1}$-${J}_{2}$ model) and $\ensuremath{\lambda}=0$ (which corresponds to isolated frustrated 4-spin plaquettes). While on the classical level ($s\ensuremath{\rightarrow}\ensuremath{\infty}$) both versions of models (i.e., with ferro- and antiferromagnetic ${J}_{1}$) exhibit the same ground-state behavior, the ground-state phase diagram differs basically for the quantum case $s=1/2$. For the antiferromagnetic case (${J}_{1}>0$) N\'eel antiferromagnetic long-range order at small ${J}_{2}/{J}_{1}$ and $\ensuremath{\lambda}\ensuremath{\gtrsim}0.47$ as well as collinear striped antiferromagnetic long-range order at large ${J}_{2}/{J}_{1}$ and $\ensuremath{\lambda}\ensuremath{\gtrsim}0.30$ appear which correspond to their classical counterparts. Both semiclassical magnetic phases are separated by a nonmagnetic quantum paramagnetic phase. The parameter region, where this nonmagnetic phase exists, increases with decreasing $\ensuremath{\lambda}$. For the ferromagnetic case (${J}_{1}<0$) we have the trivial ferromagnetic ground state at small ${J}_{2}/|{J}_{1}|$. By increasing ${J}_{2}$ this classical phase gives way for a semiclassical plaquette phase, where the plaquette block spins of length $s=2$ are antiferromagnetically long-range ordered. Further increasing of ${J}_{2}$ then yields collinear striped antiferromagnetic long-range order for $\ensuremath{\lambda}\ensuremath{\gtrsim}0.38$, but a nonmagnetic quantum paramagnetic phase $\ensuremath{\lambda}\ensuremath{\lesssim}0.38$.

arXiv:1205.0681Physical Review BJun 21, 201216 citations

Long range order in the ground state of two-dimensional antiferromagnets

Eduardo Jordão Neves, J.Fernando Perez

Physics Letters AMar 1, 1986155 citations

We study the ground state of a

d

-dimensional Ising model with both long-range (dipole-like) and nearest-neighbor ferromagnetic (FM) interactions. The long-range interaction is equal to ${r}^{\ensuremath{-}p}$,

p>d

, while the FM interaction has strength

J

. If

p>d+1

and

J

is large enough the ground state is FM, while if $d<p\ensuremath{\leqslant}d+1$ the FM state is not the ground state for any choice of

J

. In

d=1

we show that for any

p>1

the ground state has a series of transitions from an antiferromagnetic state of period 2 to

2h

-periodic states of blocks of sizes

h

with alternating sign, the size

h

growing when the FM interaction strength

J

is increased (a generalization of this result to the case $0<p\ensuremath{\leqslant}1$ is also discussed). In $d\ensuremath{\geqslant}2$ we prove, for $d<p\ensuremath{\leqslant}d+1$, that the dominant asymptotic behavior of the ground-state energy agrees for large

J

with that obtained from a periodic striped state conjectured to be the true ground state. The geometry of contours in the ground state is discussed.

Using the coupled-cluster method for high orders of approximation and Lanczos exact diagonalization we study the ground-state phase diagram of a quantum spin-

\frac{1}{2}

{J}_{1}

{J}_{2}

model on the square lattice with plaquette structure. We consider antiferromagnetic (

{J}_{1}>0

) as well as ferromagnetic (

{J}_{1}<0

) nearest-neighbor interactions together with frustrating antiferromagnetic next-nearest-neighbor interaction

{J}_{2}>0

. The strength of interplaquette interaction $\ensuremath{\lambda}$ varies between $\ensuremath{\lambda}=1$ (which corresponds to the uniform

{J}_{1}

{J}_{2}

model) and $\ensuremath{\lambda}=0$ (which corresponds to isolated frustrated 4-spin plaquettes). While on the classical level ($s\ensuremath{\rightarrow}\ensuremath{\infty}$) both versions of models (i.e., with ferro- and antiferromagnetic

{J}_{1}

) exhibit the same ground-state behavior, the ground-state phase diagram differs basically for the quantum case

s=1/2

. For the antiferromagnetic case (

{J}_{1}>0

) N\'eel antiferromagnetic long-range order at small

{J}_{2}/{J}_{1}

and $\ensuremath{\lambda}\ensuremath{\gtrsim}0.47$ as well as collinear striped antiferromagnetic long-range order at large

{J}_{2}/{J}_{1}

and $\ensuremath{\lambda}\ensuremath{\gtrsim}0.30$ appear which correspond to their classical counterparts. Both semiclassical magnetic phases are separated by a nonmagnetic quantum paramagnetic phase. The parameter region, where this nonmagnetic phase exists, increases with decreasing $\ensuremath{\lambda}$. For the ferromagnetic case (

{J}_{1}<0

) we have the trivial ferromagnetic ground state at small

{J}_{2}/|{J}_{1}|

. By increasing

{J}_{2}

this classical phase gives way for a semiclassical plaquette phase, where the plaquette block spins of length

s=2

are antiferromagnetically long-range ordered. Further increasing of

{J}_{2}

then yields collinear striped antiferromagnetic long-range order for $\ensuremath{\lambda}\ensuremath{\gtrsim}0.38$, but a nonmagnetic quantum paramagnetic phase $\ensuremath{\lambda}\ensuremath{\lesssim}0.38$.