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:1109.0412 · Physical Review B

Bond disorder and breakdown of ballistic heat transport in the spin- 12 antiferromagnetic Heisenberg chain as seen in Ca-doped SrCuO2

N. Hlubek, Patrick Ribeiro, R. Saint-Martin, Satoshi Nishimoto, A. Revcolevschi, S.‐L. Drechsler, Günther Behr, Jan Trinckauf, J. E. Hamann-Borrero, J. Geck, Bernd Büchner, Christian Heß

Published Dec 9, 2011• 20 citations
arXivHTMLPDF

Abstract

We study the impact of a weak bond disorder on the spinon heat transport in the $S=1/2$ antiferromagnetic (AFM) Heisenberg chain material ${\mathrm{Sr}}_{1\ensuremath{-}x}{\mathrm{Ca}}_{x}{\mathrm{CuO}}_{2}$. We observe a drastic suppression in the magnetic heat conductivity ${\ensuremath{\kappa}}_{\mathrm{mag}}$ even at tiny disorder levels (i.e., Ca-doping levels), in stark contrast to previous findings for ${\ensuremath{\kappa}}_{\mathrm{mag}}$ of $S=1/2$ two-dimensional square lattice and two-leg spin-ladder systems, where a similar bond disorder has no effect on ${\ensuremath{\kappa}}_{\mathrm{mag}}$. Hence, our results underpin the exceptional role of integrability of the $S=1/2$ AFM Heisenberg chain model and suggest that the bond disorder effectively destroys the ballistic nature of its heat transport. We further show that the suppression of ${\ensuremath{\kappa}}_{\mathrm{mag}}$ is captured by an effective spinon-impurity scattering length, which exhibits the same doping dependence as the long-distance exponential decay length of the spin-spin correlation as determined by density-matrix renormalization group calculations.

DOI
10.1103/physrevb.84.214419

Related papers

Impurities in the weakly coupled quantum spin chains Sr2CuO3 and SrCuO2

Koushik Karmakar, Rabindranath Bag, M. Skoulatos +2 more

We study the effect of nonmagnetic ${\mathrm{Zn}}^{2+}$ (spin-0) and magnetic ${\mathrm{Ni}}^{2+}$ (spin-1) impurities on the ground state and low-lying excitations of the quasi-one-dimensional spin-$1/2$ Heisenberg antiferromagnet ${\mathrm{Sr}}_{2}{\mathrm{CuO}}_{3}$ using inelastic neutron scattering, specific heat, and bulk magnetization measurements. We show that 1% ${\mathrm{Ni}}^{2+}$ doping in ${\mathrm{Sr}}_{2}{\mathrm{CuO}}_{3}$ results in a sizable spin gap in the spinon excitations, analogous to the case of Ni doped ${\mathrm{SrCuO}}_{2}$ previously reported [Simutis et al., Phys. Rev. Lett. 111, 067204 (2013)]. However, a similar level of ${\mathrm{Zn}}^{2+}$ doping in ${\mathrm{SrCuO}}_{2}$, investigated here for comparison, did not reveal any signs of a spin gap. Magnetic ordering temperature was found to be suppressed in the presence of both ${\mathrm{Zn}}^{2+}$ and ${\mathrm{Ni}}^{2+}$ impurities; however, the rate of suppression due to ${\mathrm{Ni}}^{2+}$ was found to be much more pronounced than for ${\mathrm{Zn}}^{2+}$. Effect of magnetic field on the ordering temperature is investigated. We found that with increasing magnetic field, not only the magnetic ordering temperature gradually increases but the size of specific heat anomaly associated with the magnetic ordering also progressively enhances, which can be qualitatively understood as due to the field induced suppression of quantum fluctuations.

arXiv:1706.01262•Physical review. B./Physical review. B•Jun 28, 2017•11 citations

Spin gap in the single spin- 12 chain cuprate Sr1.9 Ca0.1 CuO3

Franziska Hammerath, E. M. Brüning, Samuele Sanna +7 more

We report $^{63}\mathrm{Cu}$ nuclear magnetic resonance and muon spin rotation measurements on the $S=1/2$ antiferromagnetic Heisenberg spin chain compound ${\mathrm{Sr}}_{1.9}$${\mathrm{Ca}}_{0.1}$${\mathrm{CuO}}_{3}$. An exponentially decreasing spin-lattice relaxation rate ${T}_{1}^{\ensuremath{-}1}$ indicates the opening of a spin gap. This behavior is very similar to what has been observed for the cognate zigzag spin chain compound ${\mathrm{Sr}}_{0.9}$${\mathrm{Ca}}_{0.1}$${\mathrm{CuO}}_{2}$, and it confirms that the occurrence of a spin gap upon Ca doping is independent of the interchain exchange coupling ${J}^{\ensuremath{'}}$. Our results therefore suggest that the appearance of a spin gap in an antiferromagnetic Heisenberg spin chain is induced by a local bond disorder of the intrachain exchange coupling $J$. A low-temperature upturn of ${T}_{1}^{\ensuremath{-}1}$ evidences growing magnetic correlations. However, zero-field muon spin rotation measurements down to 1.5 K confirm the absence of magnetic order in this compound, which is most likely suppressed by the opening of the spin gap.

arXiv:1403.2890•Physical Review B•May 16, 2014•18 citations

Impurity-induced staggered polarization and antiferromagnetic order in spin- 12 Heisenberg two-leg ladder compound SrCu2O3: Extensive Cu NMR and NQR studies

Shigeki Ohsugi, Y. Tokunaga, Kenji Ishida +4 more

We report characteristics of impurity-induced staggered polarization (IISP) and antiferromagnetic long-range order (AF-LRO) in the gapped spin-1/2 Heisenberg two-leg ladder compound ${\mathrm{SrCu}}_{2}{\mathrm{O}}_{3}$ (Sr123). We have carried out comprehensive NMR and NQR investigations on three impurity-doped systems, $\mathrm{Sr}({\mathrm{Cu}}_{1\ensuremath{-}x}{M}_{x}{)}_{2}{\mathrm{O}}_{3} (M=\mathrm{Z}\mathrm{n},\mathrm{}\mathrm{Ni})$ with $x<~0.02$ and ${\mathrm{Sr}}_{1\ensuremath{-}x}{\mathrm{La}}_{x}{\mathrm{Cu}}_{2}{\mathrm{O}}_{3}$ with $x<~0.03.$ Either the Zn or Ni impurity that is nonmagnetic depletes a single spin on the ladders, whereas the La impurity is believed to dope electrons onto the ladders. The width of the Lorentzian Cu NMR spectrum increases with the increase in impurity content x and follows the Curie-like temperature (T) dependence as $W/T.$ The W's for the Zn- and Ni-doped samples (M doping) are larger than for the La-doped one (La doping). The NMR spectra were fit by assuming that unpaired spin ${S}_{0}=1/2$ induced next to impurity on the rung for the Zn and Ni doping ${(S}_{0}=1/4$ for the La doping) creates the staggered spin polarization along the leg, which decreases exponentially from ${S}_{0}.$ In Sr123, an instantaneous spin-correlation length ${\ensuremath{\xi}}_{0}$ was theoretically predicted as ${\ensuremath{\xi}}_{0}/a\ensuremath{\sim}3\ensuremath{-}8,$ where a is the lattice spacing between the Cu sites along the leg. However, a correlation length ${\ensuremath{\xi}}_{s}/a$ estimated from the IISP along the leg was found to be much longer than ${\ensuremath{\xi}}_{0}/a$ in $x=0.001$ and 0.005. The notable result is that ${\ensuremath{\xi}}_{s}/a$ that was found to be T independent is scaled to mean distances ${D}_{\mathrm{AV}}=1/(2x)$ between the Zn and Ni impurities and ${D}_{\mathrm{AV}}=1/x$ between the La impurities. When ${D}_{\mathrm{AV}}=500$ for $x=0.001$ (Zn doping), ${\ensuremath{\xi}}_{s}/a\ensuremath{\sim}50$ is estimated. The significantly broadened NQR spectrum has provided unambiguous evidence for the AF-LRO in the Zn and Ni doping (x=0.01 and 0.02). Rather uniform AF moments at the middle Cu sites between the impurities are estimated to be about $0.04{\ensuremath{\mu}}_{B}$ at 1.4 K along the a axis. By assuming that exponential decay constants of AF moments are equivalent to ${\ensuremath{\xi}}_{s}/a$'s for the IISP, the size of an AF moment next to the impurity is deduced as ${S}_{\mathrm{AF}}\ensuremath{\sim}1/4.$ We propose that these exponential distributions of IISP and AF moments along the two-leg suggest that an interladder interaction is in a weakly coupled quasi-one-dimensional (WC-Q1D) regime. The formula of ${T}_{N}{=J}_{0}\mathrm{exp}(\ensuremath{-}{D}_{\mathrm{AV}}/({\ensuremath{\xi}}_{s}/a))$ based on the WC-Q1D model explains ${T}_{N}(\mathrm{exp})=3$ K $(x=0.01)$ and 5.8 K $(x=0.02)$ quantitatively and predicts to be as small as ${T}_{N}=0.09$ K for $x=0.001$ using ${J}_{0}=2000$ K. On the other hand, there is no evidence of AF-LRO for the La doping $(x=0.02$ and 0.03) down to 1.4 K, nevertheless their ${\ensuremath{\xi}}_{s}/a$'s are almost equivalent to those in the Zn and Ni doping $(x=0.01$ and 0.02). We remark that the Q1D-IISP is dramatically enhanced by the interladder interaction even though so weak, once the impurity breaks up the quantum coherence in the short-range resonating valence bond (RVB) state with the gap. On the one hand, we propose that ${T}_{N}$ is determined by a strength of the interladder interaction and a size of ${S}_{0}.$

Physical review. B, Condensed matter•Aug 1, 1999•37 citations

Transport properties of low-dimensional quantum spin systems

Fabian Heidrich‐Meisner

This thesis studies transport properties of low-dimensional quantum spin systems with a particular focus on the transport of heat and spin. While the integrable anisotropic spin-1/2 chain exhibits ballistic transport (finite Drude weights), the numerical results of this work show that heat and spin transport of non-integrable models (spin ladder, frustrated and dimerized chain) is not ballistic, characterized by vanishing Drude weights in the thermodynamic limit. The results for the thermal conductivity of spin ladders are compared to experimental data. For the case of the spin-1/2 Heisenberg chain, this work contains detailed results for the temperature and magnetic field dependence of the Drude weights. Finally, bond-disordered spin systems are considered, namely the spin-1/2 chain and the spin ladder. In the first case, the transport coefficients are computed by means of exact diagonalization and discussed as a function of frequency, temperature, and magnetic field. In the second case, spectral properties of the elementary excitation of disordered spin ladders are analyzed using diagrammatic perturbation theory and numerical techniques.

•Mar 18, 2005•5 citations

Spin- S impurities with XXZ anisotropy in a spin- 12 Heisenberg chain

Ayushi Singhania, Masahiro Kadosawa, Y. Ohta +2 more

We study the effect of anisotropy of spin-$S$ impurities on an antiferromagnetic SU(2) Heisenberg chain. The magnetic impurities are assumed to have an XXZ-type anisotropic exchange with their neighboring sites. First, using density-matrix renormalization group technique, we examine spin-spin correlation function, instability of N\'eel order, and local spin susceptibility in the presence of a single spin-$S$ impurity. Based on the results, we find that the types of spin-$S$ impurities are classified into two groups: (i) nonmagnetic and $S=1$ impurities enhance only short-range antiferromagnetic correlation and (ii) $S=\frac{1}{2}$ and $S>1$ impurities can, in contrast, stabilize a long-range N\'eel order in the disordered SU(2) Heisenberg chain. Then, we focus on the case of $S=\frac{1}{2}$ impurity as a representative of (ii) and investigate the evolution of some experimentally observable quantities such as magnetization, specific heat, and magnetic susceptibility, as a function of concentration and XXZ anisotropy strength of the impurity. We confirm that the N\'eel order is induced in the bulk spin chain in the presence of finite amount of easy-axis XXZ $S=\frac{1}{2}$ impurities. Furthermore, we recover some of the aforementioned features using cluster mean-field theory, which allows us to present results on experimentally accessible quantities at finite temperatures. Interestingly, in the presence of uniform magnetic field, the total magnetization exhibits a pseudogap behavior for low values of applied field. We also discuss the dependence of NMR spectrum on various XXZ impurities and identify that the spin state of Co impurity in ${\mathrm{SrCu}}_{0.99}{\mathrm{Co}}_{0.01}{\mathrm{O}}_{2}$ is $S=\frac{3}{2}$.

arXiv:2109.00777•Physical review. B./Physical review. B•Dec 6, 2021•0 citations

Correlations in quantum spin ladders with site and bond dilution

Kien Trinh, Stephan Haas, Rong Yu +1 more

We investigate the effects of quenched disorder, in the form of site and bond dilution, on the physics of the $S=1/2$ antiferromagnetic Heisenberg model on even-leg ladders. Site dilution is found to prune rung singlets and thus create localized moments which interact via a random, unfrustrated network of effective couplings, realizing a random-exchange Heisenberg model in one spatial dimension. This system exhibits a power-law diverging correlation length as the temperature decreases. Contrary to previous claims, we observe that the scaling exponent is nonuniversal, i.e., doping dependent. This finding can be explained by the discrete nature of the values taken by the effective exchange couplings in the doped ladder. Bond dilution on even-leg ladders leads to a more complex evolution with doping of correlations, which are weakly enhanced in 2-leg ladders, and are even suppressed for low dilution in the case of 4-leg and 6-leg ladders. We clarify the different aspects of correlation enhancement and suppression due to bond dilution by isolating the contributions of rung-bond dilution and leg-bond dilution.

arXiv:1105.0056•Physical Review B•Jan 31, 2012•6 citations
We study the impact of a weak bond disorder on the spinon heat transport in the S=1/2S=1/2S=1/2 antiferromagnetic (AFM) Heisenberg chain material Sr1\ensuremath−xCaxCuO2{\mathrm{Sr}}_{1\ensuremath{-}x}{\mathrm{Ca}}_{x}{\mathrm{CuO}}_{2}Sr1\ensuremath−x​Cax​CuO2​. We observe a drastic suppression in the magnetic heat conductivity \ensuremathκmag{\ensuremath{\kappa}}_{\mathrm{mag}}\ensuremathκmag​ even at tiny disorder levels (i.e., Ca-doping levels), in stark contrast to previous findings for \ensuremathκmag{\ensuremath{\kappa}}_{\mathrm{mag}}\ensuremathκmag​ of S=1/2S=1/2S=1/2 two-dimensional square lattice and two-leg spin-ladder systems, where a similar bond disorder has no effect on \ensuremathκmag{\ensuremath{\kappa}}_{\mathrm{mag}}\ensuremathκmag​. Hence, our results underpin the exceptional role of integrability of the S=1/2S=1/2S=1/2 AFM Heisenberg chain model and suggest that the bond disorder effectively destroys the ballistic nature of its heat transport. We further show that the suppression of \ensuremathκmag{\ensuremath{\kappa}}_{\mathrm{mag}}\ensuremathκmag​ is captured by an effective spinon-impurity scattering length, which exhibits the same doping dependence as the long-distance exponential decay length of the spin-spin correlation as determined by density-matrix renormalization group calculations.
We study the effect of nonmagnetic Zn2+{\mathrm{Zn}}^{2+}Zn2+ (spin-0) and magnetic Ni2+{\mathrm{Ni}}^{2+}Ni2+ (spin-1) impurities on the ground state and low-lying excitations of the quasi-one-dimensional spin-1/21/21/2 Heisenberg antiferromagnet Sr2CuO3{\mathrm{Sr}}_{2}{\mathrm{CuO}}_{3}Sr2​CuO3​ using inelastic neutron scattering, specific heat, and bulk magnetization measurements. We show that 1% Ni2+{\mathrm{Ni}}^{2+}Ni2+ doping in Sr2CuO3{\mathrm{Sr}}_{2}{\mathrm{CuO}}_{3}Sr2​CuO3​ results in a sizable spin gap in the spinon excitations, analogous to the case of Ni doped SrCuO2{\mathrm{SrCuO}}_{2}SrCuO2​ previously reported [Simutis et al., Phys. Rev. Lett. 111, 067204 (2013)]. However, a similar level of Zn2+{\mathrm{Zn}}^{2+}Zn2+ doping in SrCuO2{\mathrm{SrCuO}}_{2}SrCuO2​, investigated here for comparison, did not reveal any signs of a spin gap. Magnetic ordering temperature was found to be suppressed in the presence of both Zn2+{\mathrm{Zn}}^{2+}Zn2+ and Ni2+{\mathrm{Ni}}^{2+}Ni2+ impurities; however, the rate of suppression due to Ni2+{\mathrm{Ni}}^{2+}Ni2+ was found to be much more pronounced than for Zn2+{\mathrm{Zn}}^{2+}Zn2+. Effect of magnetic field on the ordering temperature is investigated. We found that with increasing magnetic field, not only the magnetic ordering temperature gradually increases but the size of specific heat anomaly associated with the magnetic ordering also progressively enhances, which can be qualitatively understood as due to the field induced suppression of quantum fluctuations.
We report 63Cu^{63}\mathrm{Cu}63Cu nuclear magnetic resonance and muon spin rotation measurements on the S=1/2S=1/2S=1/2 antiferromagnetic Heisenberg spin chain compound Sr1.9{\mathrm{Sr}}_{1.9}Sr1.9​Ca0.1{\mathrm{Ca}}_{0.1}Ca0.1​CuO3{\mathrm{CuO}}_{3}CuO3​. An exponentially decreasing spin-lattice relaxation rate ${T}_{1}^{\ensuremath{-}1}$ indicates the opening of a spin gap. This behavior is very similar to what has been observed for the cognate zigzag spin chain compound Sr0.9{\mathrm{Sr}}_{0.9}Sr0.9​Ca0.1{\mathrm{Ca}}_{0.1}Ca0.1​CuO2{\mathrm{CuO}}_{2}CuO2​, and it confirms that the occurrence of a spin gap upon Ca doping is independent of the interchain exchange coupling ${J}^{\ensuremath{'}}$. Our results therefore suggest that the appearance of a spin gap in an antiferromagnetic Heisenberg spin chain is induced by a local bond disorder of the intrachain exchange coupling JJJ. A low-temperature upturn of ${T}_{1}^{\ensuremath{-}1}$ evidences growing magnetic correlations. However, zero-field muon spin rotation measurements down to 1.5 K confirm the absence of magnetic order in this compound, which is most likely suppressed by the opening of the spin gap.
We report characteristics of impurity-induced staggered polarization (IISP) and antiferromagnetic long-range order (AF-LRO) in the gapped spin-1/2 Heisenberg two-leg ladder compound SrCu2O3{\mathrm{SrCu}}_{2}{\mathrm{O}}_{3}SrCu2​O3​ (Sr123). We have carried out comprehensive NMR and NQR investigations on three impurity-doped systems, $\mathrm{Sr}({\mathrm{Cu}}_{1\ensuremath{-}x}{M}_{x}{)}_{2}{\mathrm{O}}_{3} (M=\mathrm{Z}\mathrm{n},\mathrm{}\mathrm{Ni})$ with x< 0.02x<~0.02x< 0.02 and ${\mathrm{Sr}}_{1\ensuremath{-}x}{\mathrm{La}}_{x}{\mathrm{Cu}}_{2}{\mathrm{O}}_{3}$ with x< 0.03.x<~0.03.x< 0.03. Either the Zn or Ni impurity that is nonmagnetic depletes a single spin on the ladders, whereas the La impurity is believed to dope electrons onto the ladders. The width of the Lorentzian Cu NMR spectrum increases with the increase in impurity content x and follows the Curie-like temperature (T) dependence as W/T.W/T.W/T. The W's for the Zn- and Ni-doped samples (M doping) are larger than for the La-doped one (La doping). The NMR spectra were fit by assuming that unpaired spin S0=1/2{S}_{0}=1/2S0​=1/2 induced next to impurity on the rung for the Zn and Ni doping (S0=1/4{(S}_{0}=1/4(S0​=1/4 for the La doping) creates the staggered spin polarization along the leg, which decreases exponentially from S0.{S}_{0}.S0​. In Sr123, an instantaneous spin-correlation length ${\ensuremath{\xi}}_{0}$ was theoretically predicted as ${\ensuremath{\xi}}_{0}/a\ensuremath{\sim}3\ensuremath{-}8,$ where a is the lattice spacing between the Cu sites along the leg. However, a correlation length ${\ensuremath{\xi}}_{s}/a$ estimated from the IISP along the leg was found to be much longer than ${\ensuremath{\xi}}_{0}/a$ in x=0.001x=0.001x=0.001 and 0.005. The notable result is that ${\ensuremath{\xi}}_{s}/a$ that was found to be T independent is scaled to mean distances DAV=1/(2x){D}_{\mathrm{AV}}=1/(2x)DAV​=1/(2x) between the Zn and Ni impurities and DAV=1/x{D}_{\mathrm{AV}}=1/xDAV​=1/x between the La impurities. When DAV=500{D}_{\mathrm{AV}}=500DAV​=500 for x=0.001x=0.001x=0.001 (Zn doping), ${\ensuremath{\xi}}_{s}/a\ensuremath{\sim}50$ is estimated. The significantly broadened NQR spectrum has provided unambiguous evidence for the AF-LRO in the Zn and Ni doping (x=0.01 and 0.02). Rather uniform AF moments at the middle Cu sites between the impurities are estimated to be about $0.04{\ensuremath{\mu}}_{B}$ at 1.4 K along the a axis. By assuming that exponential decay constants of AF moments are equivalent to ${\ensuremath{\xi}}_{s}/a$'s for the IISP, the size of an AF moment next to the impurity is deduced as ${S}_{\mathrm{AF}}\ensuremath{\sim}1/4.$ We propose that these exponential distributions of IISP and AF moments along the two-leg suggest that an interladder interaction is in a weakly coupled quasi-one-dimensional (WC-Q1D) regime. The formula of ${T}_{N}{=J}_{0}\mathrm{exp}(\ensuremath{-}{D}_{\mathrm{AV}}/({\ensuremath{\xi}}_{s}/a))$ based on the WC-Q1D model explains TN(exp)=3{T}_{N}(\mathrm{exp})=3TN​(exp)=3 K (x=0.01)(x=0.01)(x=0.01) and 5.8 K (x=0.02)(x=0.02)(x=0.02) quantitatively and predicts to be as small as TN=0.09{T}_{N}=0.09TN​=0.09 K for x=0.001x=0.001x=0.001 using J0=2000{J}_{0}=2000J0​=2000 K. On the other hand, there is no evidence of AF-LRO for the La doping (x=0.02(x=0.02(x=0.02 and 0.03) down to 1.4 K, nevertheless their ${\ensuremath{\xi}}_{s}/a$'s are almost equivalent to those in the Zn and Ni doping (x=0.01(x=0.01(x=0.01 and 0.02). We remark that the Q1D-IISP is dramatically enhanced by the interladder interaction even though so weak, once the impurity breaks up the quantum coherence in the short-range resonating valence bond (RVB) state with the gap. On the one hand, we propose that TN{T}_{N}TN​ is determined by a strength of the interladder interaction and a size of S0.{S}_{0}.S0​.
This thesis studies transport properties of low-dimensional quantum spin systems with a particular focus on the transport of heat and spin. While the integrable anisotropic spin-1/2 chain exhibits ballistic transport (finite Drude weights), the numerical results of this work show that heat and spin transport of non-integrable models (spin ladder, frustrated and dimerized chain) is not ballistic, characterized by vanishing Drude weights in the thermodynamic limit. The results for the thermal conductivity of spin ladders are compared to experimental data. For the case of the spin-1/2 Heisenberg chain, this work contains detailed results for the temperature and magnetic field dependence of the Drude weights. Finally, bond-disordered spin systems are considered, namely the spin-1/2 chain and the spin ladder. In the first case, the transport coefficients are computed by means of exact diagonalization and discussed as a function of frequency, temperature, and magnetic field. In the second case, spectral properties of the elementary excitation of disordered spin ladders are analyzed using diagrammatic perturbation theory and numerical techniques.
We study the effect of anisotropy of spin-SSS impurities on an antiferromagnetic SU(2) Heisenberg chain. The magnetic impurities are assumed to have an XXZ-type anisotropic exchange with their neighboring sites. First, using density-matrix renormalization group technique, we examine spin-spin correlation function, instability of N\'eel order, and local spin susceptibility in the presence of a single spin-SSS impurity. Based on the results, we find that the types of spin-SSS impurities are classified into two groups: (i) nonmagnetic and S=1S=1S=1 impurities enhance only short-range antiferromagnetic correlation and (ii) S=12S=\frac{1}{2}S=21​ and S>1S>1S>1 impurities can, in contrast, stabilize a long-range N\'eel order in the disordered SU(2) Heisenberg chain. Then, we focus on the case of S=12S=\frac{1}{2}S=21​ impurity as a representative of (ii) and investigate the evolution of some experimentally observable quantities such as magnetization, specific heat, and magnetic susceptibility, as a function of concentration and XXZ anisotropy strength of the impurity. We confirm that the N\'eel order is induced in the bulk spin chain in the presence of finite amount of easy-axis XXZ S=12S=\frac{1}{2}S=21​ impurities. Furthermore, we recover some of the aforementioned features using cluster mean-field theory, which allows us to present results on experimentally accessible quantities at finite temperatures. Interestingly, in the presence of uniform magnetic field, the total magnetization exhibits a pseudogap behavior for low values of applied field. We also discuss the dependence of NMR spectrum on various XXZ impurities and identify that the spin state of Co impurity in SrCu0.99Co0.01O2{\mathrm{SrCu}}_{0.99}{\mathrm{Co}}_{0.01}{\mathrm{O}}_{2}SrCu0.99​Co0.01​O2​ is S=32S=\frac{3}{2}S=23​.
We investigate the effects of quenched disorder, in the form of site and bond dilution, on the physics of the S=1/2S=1/2S=1/2 antiferromagnetic Heisenberg model on even-leg ladders. Site dilution is found to prune rung singlets and thus create localized moments which interact via a random, unfrustrated network of effective couplings, realizing a random-exchange Heisenberg model in one spatial dimension. This system exhibits a power-law diverging correlation length as the temperature decreases. Contrary to previous claims, we observe that the scaling exponent is nonuniversal, i.e., doping dependent. This finding can be explained by the discrete nature of the values taken by the effective exchange couplings in the doped ladder. Bond dilution on even-leg ladders leads to a more complex evolution with doping of correlations, which are weakly enhanced in 2-leg ladders, and are even suppressed for low dilution in the case of 4-leg and 6-leg ladders. We clarify the different aspects of correlation enhancement and suppression due to bond dilution by isolating the contributions of rung-bond dilution and leg-bond dilution.