We describe the spin distribution in the vicinity of a nonmagnetic impurity in a two-dimensional antiferromagnet undergoing a transition from a magnetically ordered N\'eel state to a paramagnet with a spin gap. The quantum critical ground state in a finite system has total spin $S=1∕2$ (if the system without the impurity had an even number of $S=1∕2$ spins), and recent numerical studies in a double layer antiferromagnet [K. H. H\"oglund et al., Phys. Rev. Lett. 98, 087203 (2007)] have shown that the spin has a universal spatial form delocalized across the entire sample. We present the field theory describing the uniform and staggered magnetizations in this spin texture for two classes of antiferromagnets: (i) the transition from a N\'eel state to a paramagnet with local spin singlets, in models with an even number of $S=1∕2$ spins per unit cell, which are described by a O(3) Landau-Ginzburg-Wilson field theory; and (ii) the transition from a N\'eel state to a valence bond solid, in antiferromagnets with a single $S=1∕2$ spin per unit cell, which are described by a ``deconfined'' field theory of spinons.We describe the spin distribution in the vicinity of a nonmagnetic impurity in a two-dimensional antiferromagnet undergoing a transition from a magnetically ordered N\'eel state to a paramagnet with a spin gap. The quantum critical ground state in a finite system has total spin $S=1∕2$ (if the system without the impurity had an even number of $S=1∕2$ spins), and recent numerical studies in a double layer antiferromagnet [K. H. H\"oglund et al., Phys. Rev. Lett. 98, 087203 (2007)] have shown that the spin has a universal spatial form delocalized across the entire sample. We present the field theory describing the uniform and staggered magnetizations in this spin texture for two classes of antiferromagnets: (i) the transition from a N\'eel state to a paramagnet with local spin singlets, in models with an even number of $S=1∕2$ spins per unit cell, which are described by a O(3) Landau-Ginzburg-Wilson field theory; and (ii) the transition from a N\'eel state to a valence bond solid, in antiferromagnets with a single $S=1∕2$ spin per unit cell, which are described by a ``deconfined'' field theory of spinons.

arXiv:cond-mat/0703790Physical Review BAug 17, 200710 citations

Spin squeezed states in a two-dimensional system

Feng Peng, Dapeng Ding

Physica B Condensed MatterOct 28, 20040 citations

Quantum impurities in a two-dimensional Heisenberg antiferromagnet

O. P. Vajk

Jan 1, 20031 citation

From enhanced to reduced quantum antiferromagnetism by tuning a magnetic impurity

Julian Engel, Stefan Weßel

Based on quantum Monte Carlo simulations, we study the local-order-parameter modulations induced by a magnetic impurity that couples to a single moment of a two-dimensional quantum antiferromagnet. A strong antiferromagnetic coupling of the impurity spin reduces the antiferromagnetic order in the host beyond the next-nearest-neighbor sites of the impurity spin, whereas on the next-nearest neighbors the order increases, similar as for an embedded vacancy. We show that for weak and intermediate couplings to the impurity spin, the local antiferromagnetic order is enhanced throughout the host magnet. We compare our numerical findings to analytical results from a recent perturbative approach based on spin-wave theory.Based on quantum Monte Carlo simulations, we study the local-order-parameter modulations induced by a magnetic impurity that couples to a single moment of a two-dimensional quantum antiferromagnet. A strong antiferromagnetic coupling of the impurity spin reduces the antiferromagnetic order in the host beyond the next-nearest-neighbor sites of the impurity spin, whereas on the next-nearest neighbors the order increases, similar as for an embedded vacancy. We show that for weak and intermediate couplings to the impurity spin, the local antiferromagnetic order is enhanced throughout the host magnet. We compare our numerical findings to analytical results from a recent perturbative approach based on spin-wave theory.

Physical Review BSep 9, 20095 citations

Long-range dynamics of magnetic impurities coupled to a two-dimensional Heisenberg antiferromagnet

Andreas Lüscher, Oleg P. Sushkov

We consider a two-dimensional Heisenberg antiferromagnet on a square lattice with weakly coupled impurities, i.e., additional spins interacting with the host magnet by a small dimensionless coupling constant $g⪡1$ . Using linear spin-wave theory, we find that the magnetization disturbance at distance $r$ from a single impurity behaves as $\ensuremath{\delta}{S}^{z}\ensuremath{\propto}g∕r$ for $1⪡r⪡1∕g$ and as $\ensuremath{\delta}{S}^{z}\ensuremath{\propto}1∕(g{r}^{3})$ for $r⪢1∕g$ . Surprisingly the magnetization disturbance is inversely proportional to the coupling constant. The interaction between two impurities separated by a distance $r$ is $\ensuremath{\delta}ϵ\ensuremath{\propto}{g}^{2}∕r$ for $1⪡r⪡1∕g$ and $\ensuremath{\delta}ϵ\ensuremath{\propto}1∕{r}^{3}$ for $r⪢1∕g$ . For large distances, the interaction is therefore universal and independent of the coupling constant. We have also found that the frequency of Rabi oscillations between two impurities is logarithmically enhanced compared to the decay width ${\ensuremath{\omega}}_{\mathrm{Rabi}}\ensuremath{\propto}{g}^{2}\phantom{\rule{0.2em}{0ex}}\mathrm{ln}(1∕\mathit{gr})$ at $1⪡r⪡1∕g$ . This leads to a logarithmic enhancement for NMR and EPR line broadening. All these astonishing results are due to the gapless spectrum of magnetic excitations in the quantum antiferromagnet.We consider a two-dimensional Heisenberg antiferromagnet on a square lattice with weakly coupled impurities, i.e., additional spins interacting with the host magnet by a small dimensionless coupling constant $g⪡1$. Using linear spin-wave theory, we find that the magnetization disturbance at distance $r$ from a single impurity behaves as $\ensuremath{\delta}{S}^{z}\ensuremath{\propto}g∕r$ for $1⪡r⪡1∕g$ and as $\ensuremath{\delta}{S}^{z}\ensuremath{\propto}1∕(g{r}^{3})$ for $r⪢1∕g$. Surprisingly the magnetization disturbance is inversely proportional to the coupling constant. The interaction between two impurities separated by a distance $r$ is $\ensuremath{\delta}ϵ\ensuremath{\propto}{g}^{2}∕r$ for $1⪡r⪡1∕g$ and $\ensuremath{\delta}ϵ\ensuremath{\propto}1∕{r}^{3}$ for $r⪢1∕g$. For large distances, the interaction is therefore universal and independent of the coupling constant. We have also found that the frequency of Rabi oscillations between two impurities is logarithmically enhanced compared to the decay width ${\ensuremath{\omega}}_{\mathrm{Rabi}}\ensuremath{\propto}{g}^{2}\phantom{\rule{0.2em}{0ex}}\mathrm{ln}(1∕\mathit{gr})$ at $1⪡r⪡1∕g$. This leads to a logarithmic enhancement for NMR and EPR line broadening. All these astonishing results are due to the gapless spectrum of magnetic excitations in the quantum antiferromagnet.

arXiv:cond-mat/0408598Physical Review BFeb 23, 200516 citations

Ground States of Quantum Antiferromagnets in Two Dimensions

Subir Sachdev A, Kwon Park

arXiv:cond-mat/0108214Annals of PhysicsMay 1, 2002102 citations

S=1∕2

(if the system without the impurity had an even number of

S=1∕2

spins), and recent numerical studies in a double layer antiferromagnet [K. H. H\"oglund et al., Phys. Rev. Lett. 98, 087203 (2007)] have shown that the spin has a universal spatial form delocalized across the entire sample. We present the field theory describing the uniform and staggered magnetizations in this spin texture for two classes of antiferromagnets: (i) the transition from a N\'eel state to a paramagnet with local spin singlets, in models with an even number of

S=1∕2

spins per unit cell, which are described by a O(3) Landau-Ginzburg-Wilson field theory; and (ii) the transition from a N\'eel state to a valence bond solid, in antiferromagnets with a single

S=1∕2

spin per unit cell, which are described by a ``deconfined'' field theory of spinons.

g⪡1

. Using linear spin-wave theory, we find that the magnetization disturbance at distance

r

from a single impurity behaves as $\ensuremath{\delta}{S}^{z}\ensuremath{\propto}g∕r$ for

1⪡r⪡1∕g

and as $\ensuremath{\delta}{S}^{z}\ensuremath{\propto}1∕(g{r}^{3})$ for

r⪢1∕g

. Surprisingly the magnetization disturbance is inversely proportional to the coupling constant. The interaction between two impurities separated by a distance

r

is $\ensuremath{\delta}ϵ\ensuremath{\propto}{g}^{2}∕r$ for

1⪡r⪡1∕g

and $\ensuremath{\delta}ϵ\ensuremath{\propto}1∕{r}^{3}$ for

r⪢1∕g

. For large distances, the interaction is therefore universal and independent of the coupling constant. We have also found that the frequency of Rabi oscillations between two impurities is logarithmically enhanced compared to the decay width ${\ensuremath{\omega}}_{\mathrm{Rabi}}\ensuremath{\propto}{g}^{2}\phantom{\rule{0.2em}{0ex}}\mathrm{ln}(1∕\mathit{gr})$ at

1⪡r⪡1∕g

. This leads to a logarithmic enhancement for NMR and EPR line broadening. All these astonishing results are due to the gapless spectrum of magnetic excitations in the quantum antiferromagnet.