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/0611418 · Physical Review Letters

Impurity Induced Spin Texture in Quantum Critical 2D Antiferromagnets

Kaj H. Höglund, Anders W. Sandvik, Subir Sachdev A

Published Feb 22, 2007• 36 citations
arXivHTMLPDF

Abstract

We describe the uniform and staggered magnetization distributions around a vacancy in a quantum critical two-dimensional S=1/2 antiferromagnet. The distributions are delocalized across the entire sample with a universal functional form arising from an uncompensated Berry phase. The numerical results, obtained using quantum Monte Carlo simulations of the Heisenberg model on bilayer lattices with up to approximately equal to 10(5) spins, are in good agreement with the proposed scaling structure. We determine the exponent eta' = 0.40+/-0.02, which governs both the staggered and uniform magnetic structure away from the impurity and also controls the impurity spin dynamics.

DOI
10.1103/physrevlett.98.087203

Related papers

Impurity spin textures across conventional and deconfined quantum critical points of two-dimensional antiferromagnets

Max A. Metlitski, Subir Sachdev A

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/0703790•Physical Review B•Aug 17, 2007•10 citations

Nonmagnetic impurities in spin-gapped and gapless Heisenberg antiferromagnets

Anders W. Sandvik, Elbio R. Dagotto, Douglas J. Scalapino

We discuss the effects of nonmagnetic impurities (static holes) in the $S=1/2$ Heisenberg model on a two-dimensional (2D) square lattice, and on two- and three-leg ladders. Results of quantum Monte Carlo simulations show that a free localized moment is induced around an isolated impurity only in the spin-gapped two-leg ladder, in agreement with previous theoretical expectations. The localization length of the $S=1/2$ impurity moment in a two-leg ladder with isotropic couplings is $\ensuremath{\approx}1.5$ lattice spacings. In gapless ladders (odd number of legs) and in the 2D lattice, no free moments are induced. However, in the 2D system, which has antiferromagnetic long-range order at $T=0$ and a gap for longitudinal fluctuations, the impurity leads to a localized distortion of the magnetization in the direction of the broken symmetry, with total ${S}^{z}=1/2.$ The shape of the distortion is in close agreement with previous spin-wave calculations. For all the systems, a staggered moment is induced by the impurity. For the gapped two-leg ladder this is exponentially localized within a length equal to the spin correlation length of the ladder ($\ensuremath{\approx}3.2$ lattice spacings). For the three-leg ladder, the integrated staggered moment diverges as the system size goes to infinity, but the staggered magnetization at a given site appears to vanish. In 2D, we discuss the behavior seen in finite systems both with and without additional symmetry-breaking mechanisms. We also discuss the effect of impurities on the NMR Knight shift and the bulk magnetic susceptibility.

Physical review. B, Condensed matter•Nov 1, 1997•49 citations

Impurity spin texture at a deconfined quantum critical point

Argha Banerjee, Kedar Damle, Fabien Alet

The spin texture surrounding a nonmagnetic impurity in a quantum antiferromagnet is a sensitive probe of the novel physics of a class of quantum phase transitions between a N\'eel ordered phase and a valence-bond solid phase in square lattice $S=1/2$ antiferromagnets. Using a newly developed $T=0$ quantum Monte Carlo technique, we compute this spin texture at these transitions and find that it does not obey the universal scaling form expected at a scale invariant quantum critical point. We also identify the precise logarithmic form of these scaling violations. Our results are expected to yield important clues regarding the probable theory of these unconventional transitions.

arXiv:1002.1375•Physical Review B•Oct 26, 2010•68 citations

Edge and impurity response in two-dimensional quantum antiferromagnets

Max A. Metlitski, Subir Sachdev A

Motivated by recent Monte Carlo simulations of H\"oglund and Sandvik (arXiv:0808.0408), we study edge response in square lattice quantum antiferromagnets. We use the O(3) nonlinear $\ensuremath{\sigma}$ model to compute the decay asymptotics of the staggered magnetization, energy density, and local magnetic susceptibility away from the edge. We find that the total edge susceptibility is negative and diverges logarithmically as the temperature $T\ensuremath{\rightarrow}0$. We confirm the predictions of the continuum theory by performing a $1/S$ expansion of the microscopic Heisenberg model with the edge. We propose a qualitative explanation of the edge dimerization seen in Monte Carlo simulations by a theory of valence-bond-solid correlations in the N\'eel state. We also discuss the extension of the latter theory to the response of a single nonmagnetic impurity, and its connection to the theory of the deconfined critical point.

arXiv:0808.0496•Physical Review B•Nov 10, 2008•12 citations

Weak Universality in the Disordered Two-Dimensional Antiferromagnetic Potts Model on a Triangular Lattice

Albert Babaevich Babaev, Akai Kurbanovich Murtazaev

The critical behavior of the disordered two-dimensional antiferromagnetic Potts model with the number of spin states q= 3 on a triangular lattice with disorder in the form of nonmagnetic impurities is studied by the Monte Carlo method. The critical exponents for the susceptibility γ, magnetization β, specific heat α, and correlation radius ν are calculated in the framework of the finite-size scaling theory at spin concentrations p = 0.90, 0.80, 0.70, and 0.65. It is found that the critical exponents increase with the degree of disorder, whereas the ratios and do not change, thus holding the scaling equality $$\frac{{2\beta }}{\nu } + \frac{\gamma }{\nu } = d$$ . Such behavior of the critical exponents is related to the weak universality of the critical behavior characteristic of disordered systems. All results are obtained using independent Monte Carlo algorithms, such as the Metropolis and Wolff algorithms.

Journal of Experimental and Theoretical Physics Letters•May 1, 2018•5 citations

Quantum Monte Carlo study on the phase transition for a generalized two-dimensional staggered dimerized Heisenberg model

Rui Zheng, Bang‐Gui Liu

In order to gain a deeper understanding of the quantum criticality in the explicitly staggered dimerized Heisenberg models, we study a generalized staggered dimer model named the J 0 — J 1 — J 2 model, which corresponds to the staggered J — J ′ model on a square lattice and a honeycomb lattice when J 1 / J 0 equals 1 and 0, respectively. Using the quantum Monte Carlo method, we investigate all the quantum critical points of these models with J 1 / J 0 changing from 0 to 1 as a function of coupling ratio α = J 2 / J 0 . We extract all the critical values of the coupling ratio α c for these models, and we also obtain the critical exponents ν, β/ν, and η using different finite-size scaling ansätz,. All these exponents are not consistent with the three-dimensional Heisenberg universality class, indicating some unconventional quantum critical points in these models.

Chinese Physics B•Nov 1, 2012•2 citations
We describe the uniform and staggered magnetization distributions around a vacancy in a quantum critical two-dimensional S=1/2 antiferromagnet. The distributions are delocalized across the entire sample with a universal functional form arising from an uncompensated Berry phase. The numerical results, obtained using quantum Monte Carlo simulations of the Heisenberg model on bilayer lattices with up to approximately equal to 10(5) spins, are in good agreement with the proposed scaling structure. We determine the exponent eta' = 0.40+/-0.02, which governs both the staggered and uniform magnetic structure away from the impurity and also controls the impurity spin dynamics.
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∕2S=1∕2S=1∕2 (if the system without the impurity had an even number of S=1∕2S=1∕2S=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∕2S=1∕2S=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∕2S=1∕2S=1∕2 spin per unit cell, which are described by a ``deconfined'' field theory of spinons.
We discuss the effects of nonmagnetic impurities (static holes) in the S=1/2S=1/2S=1/2 Heisenberg model on a two-dimensional (2D) square lattice, and on two- and three-leg ladders. Results of quantum Monte Carlo simulations show that a free localized moment is induced around an isolated impurity only in the spin-gapped two-leg ladder, in agreement with previous theoretical expectations. The localization length of the S=1/2S=1/2S=1/2 impurity moment in a two-leg ladder with isotropic couplings is $\ensuremath{\approx}1.5$ lattice spacings. In gapless ladders (odd number of legs) and in the 2D lattice, no free moments are induced. However, in the 2D system, which has antiferromagnetic long-range order at T=0T=0T=0 and a gap for longitudinal fluctuations, the impurity leads to a localized distortion of the magnetization in the direction of the broken symmetry, with total Sz=1/2.{S}^{z}=1/2.Sz=1/2. The shape of the distortion is in close agreement with previous spin-wave calculations. For all the systems, a staggered moment is induced by the impurity. For the gapped two-leg ladder this is exponentially localized within a length equal to the spin correlation length of the ladder ($\ensuremath{\approx}3.2$ lattice spacings). For the three-leg ladder, the integrated staggered moment diverges as the system size goes to infinity, but the staggered magnetization at a given site appears to vanish. In 2D, we discuss the behavior seen in finite systems both with and without additional symmetry-breaking mechanisms. We also discuss the effect of impurities on the NMR Knight shift and the bulk magnetic susceptibility.
The spin texture surrounding a nonmagnetic impurity in a quantum antiferromagnet is a sensitive probe of the novel physics of a class of quantum phase transitions between a N\'eel ordered phase and a valence-bond solid phase in square lattice S=1/2S=1/2S=1/2 antiferromagnets. Using a newly developed T=0T=0T=0 quantum Monte Carlo technique, we compute this spin texture at these transitions and find that it does not obey the universal scaling form expected at a scale invariant quantum critical point. We also identify the precise logarithmic form of these scaling violations. Our results are expected to yield important clues regarding the probable theory of these unconventional transitions.
Motivated by recent Monte Carlo simulations of H\"oglund and Sandvik (arXiv:0808.0408), we study edge response in square lattice quantum antiferromagnets. We use the O(3) nonlinear $\ensuremath{\sigma}$ model to compute the decay asymptotics of the staggered magnetization, energy density, and local magnetic susceptibility away from the edge. We find that the total edge susceptibility is negative and diverges logarithmically as the temperature $T\ensuremath{\rightarrow}0$. We confirm the predictions of the continuum theory by performing a 1/S1/S1/S expansion of the microscopic Heisenberg model with the edge. We propose a qualitative explanation of the edge dimerization seen in Monte Carlo simulations by a theory of valence-bond-solid correlations in the N\'eel state. We also discuss the extension of the latter theory to the response of a single nonmagnetic impurity, and its connection to the theory of the deconfined critical point.
The critical behavior of the disordered two-dimensional antiferromagnetic Potts model with the number of spin states q= 3 on a triangular lattice with disorder in the form of nonmagnetic impurities is studied by the Monte Carlo method. The critical exponents for the susceptibility γ, magnetization β, specific heat α, and correlation radius ν are calculated in the framework of the finite-size scaling theory at spin concentrations p = 0.90, 0.80, 0.70, and 0.65. It is found that the critical exponents increase with the degree of disorder, whereas the ratios and do not change, thus holding the scaling equality 2βν+γν=d\frac{{2\beta }}{\nu } + \frac{\gamma }{\nu } = dν2β​+νγ​=d . Such behavior of the critical exponents is related to the weak universality of the critical behavior characteristic of disordered systems. All results are obtained using independent Monte Carlo algorithms, such as the Metropolis and Wolff algorithms.
In order to gain a deeper understanding of the quantum criticality in the explicitly staggered dimerized Heisenberg models, we study a generalized staggered dimer model named the J 0 — J 1 — J 2 model, which corresponds to the staggered J — J ′ model on a square lattice and a honeycomb lattice when J 1 / J 0 equals 1 and 0, respectively. Using the quantum Monte Carlo method, we investigate all the quantum critical points of these models with J 1 / J 0 changing from 0 to 1 as a function of coupling ratio α = J 2 / J 0 . We extract all the critical values of the coupling ratio α c for these models, and we also obtain the critical exponents ν, β/ν, and η using different finite-size scaling ansätz,. All these exponents are not consistent with the three-dimensional Heisenberg universality class, indicating some unconventional quantum critical points in these models.