arXiv:1211.7078 · Physical Review B

Bond disorder in even-leg Heisenberg ladders

Kien Trinh, Stephan Haas

Published Feb 22, 2013• 4 citations

Abstract

Random bond disorder in antiferromagnetic spin-1/2 Heisenberg ladders is investigated using the stochastic series expansion quantum Monte Carlo method. We find that the effects of individual bond impurities vary strongly, depending on their positions on legs and rungs. We initially focus on how the distribution of local bond energies depends on the impurity concentration. Then we study how the phase diagram of even-leg ladders is affected by random bond doping. We observe Bose glass phases in two regimes (${h}^{\ensuremath{'}}<h\ensuremath{\lesssim}{h}_{c1}$ and ${h}^{\ensuremath{'}\ensuremath{'}}<h<{h}_{c2}$) and a Bose-Einstein Condensate in between. Their presence is discussed in relation to the local bond energies.

DOI: 10.1103/physrevb.87.075137

Related papers

Thermal properties of rung-disordered two-leg quantum spin ladders: Quantum Monte Carlo study

Ulvi Kanbur, Hamza Polat, Erol Vatansever

arXiv:2009.07942Physical review. EOct 6, 20206 citations

Correlations in quantum spin ladders with site and bond dilution

Kien Trinh, Stephan Haas, Rong Yu +1 more

arXiv:1105.0056Physical Review BJan 31, 20126 citations

Quantum Monte Carlo Calculation for Spin Systems in Two-Leg Ladders with Alternating Heisenberg-Bond Chains

Takafumi Momose, Toshihiko Suzuki, Yuhei Natsume

Journal of the Physical Society of JapanJun 15, 19970 citations

Thermodynamic properties of disordered quantum spin ladders

Erol Vatansever, Georgi Georgiev Grahovski, Nikolaos G. Fytas

arXiv:2312.12834The European Physical Journal BMar 1, 20241 citation

Quantum Monte Carlo simulations for stacked spin-ladder systems containing low concentrations of nonmagnetic impurities: Application to the low-temperature broadening of NMR spectra in SrCu 2 O 3

Robert Achleitner, Hans Gerd Evertz, Masatoshi Imada +2 more

arXiv:1310.1697Physical Review BDec 23, 20133 citations

Quantum Phases of a Strongly Disordered Two-Legged Josephson Ladder

Eyal Walach, Efrat Shimshoni

arXiv:2512.19808Dec 22, 20250 citations

arXiv:1211.7078 · Physical Review B

Bond disorder in even-leg Heisenberg ladders

Kien Trinh, Stephan Haas

Published Feb 22, 2013• 4 citations

arXiv HTML PDF

Abstract

{h}^{\ensuremath{'}}<h\ensuremath{\lesssim}{h}_{c1}

and

{h}^{\ensuremath{'}\ensuremath{'}}<h<{h}_{c2}

) and a Bose-Einstein Condensate in between. Their presence is discussed in relation to the local bond energies.

DOI: 10.1103/physrevb.87.075137

Related papers

Thermal properties of rung-disordered two-leg quantum spin ladders: Quantum Monte Carlo study

Ulvi Kanbur, Hamza Polat, Erol Vatansever

A two-leg quenched random bond disordered antiferromagnetic spin-1/2 Heisenberg ladder system is investigated by means of stochastic series expansion quantum Monte Carlo (QMC) method. Thermal properties of the uniform and staggered susceptibilities, the structure factor, the specific heat, and the spin gap are calculated over a large number of random realizations in a wide range of disorder strength. According to our QMC simulation results, the considered system has a special temperature point at which the specific heat takes the same value regardless of the strength of the disorder. Moreover, the uniform susceptibility is shown to display the same character except for a small difference in the location of the special point. Finally, the spin gap values are found to decrease with increasing disorder parameter and the smallest gap value found in this study is well above the weak coupling limit of the clean case.A two-leg quenched random bond disordered antiferromagnetic spin-1/2 Heisenberg ladder system is investigated by means of stochastic series expansion quantum Monte Carlo (QMC) method. Thermal properties of the uniform and staggered susceptibilities, the structure factor, the specific heat, and the spin gap are calculated over a large number of random realizations in a wide range of disorder strength. According to our QMC simulation results, the considered system has a special temperature point at which the specific heat takes the same value regardless of the strength of the disorder. Moreover, the uniform susceptibility is shown to display the same character except for a small difference in the location of the special point. Finally, the spin gap values are found to decrease with increasing disorder parameter and the smallest gap value found in this study is well above the weak coupling limit of the clean case.

arXiv:2009.07942Physical review. EOct 6, 20206 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.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:1105.0056Physical Review BJan 31, 20126 citations

Quantum Monte Carlo Calculation for Spin Systems in Two-Leg Ladders with Alternating Heisenberg-Bond Chains

Takafumi Momose, Toshihiko Suzuki, Yuhei Natsume

Thermodynamic properties of spin=1/2 two-leg ladders with alternating chains including ferromagnetic and antiferromagnetic interactions are discussed on the basis of the numerical results obtained by quantum Monte Carlo simulations. As well as the role of exchange interaction of rungs, the essential role of the bond alternation in the chain on ladder systems is investigated in connection with the appearance of characteristic properties in magnetic susceptibilities and heat capacities. Furthermore, quantum effects on the ground-state energy are obtained. On the basis of calculated results, the relationship between singlet dimer phases and Haldane states is discussed.Thermodynamic properties of spin=1/2 two-leg ladders with alternating chains including ferromagnetic and antiferromagnetic interactions are discussed on the basis of the numerical results obtained by quantum Monte Carlo simulations. As well as the role of exchange interaction of rungs, the essential role of the bond alternation in the chain on ladder systems is investigated in connection with the appearance of characteristic properties in magnetic susceptibilities and heat capacities. Furthermore, quantum effects on the ground-state energy are obtained. On the basis of calculated results, the relationship between singlet dimer phases and Haldane states is discussed.

Journal of the Physical Society of JapanJun 15, 19970 citations

Thermodynamic properties of disordered quantum spin ladders

Erol Vatansever, Georgi Georgiev Grahovski, Nikolaos G. Fytas

Abstract In this paper, we study the thermodynamic properties of spin-1/2 antiferromagnetic Heisenberg ladders by means of the stochastic series expansion quantum Monte Carlo technique. This includes the thermal properties of the specific heat, uniform and staggered susceptibilities, spin gap, and structure factor. Our numerical simulations are probed over a large ensemble of random realizations in a wide range of disorder strengths r, from the clean ( $r=0$ r = 0 ) case up to the diluted ( $r \rightarrow 1$ r → 1 ) limit, and for selected choices of number of legs $L_y$ L y per site. Our results show some interesting phenomena, like the presence of crossing points in the temperature plane for both the specific heat and uniform susceptibility curves which appear to be universal in r, as well as a variable dependence of the spin gap in the amount of disorder upon increasing $L_y$ L y . Graphical AbstractAbstract In this paper, we study the thermodynamic properties of spin-1/2 antiferromagnetic Heisenberg ladders by means of the stochastic series expansion quantum Monte Carlo technique. This includes the thermal properties of the specific heat, uniform and staggered susceptibilities, spin gap, and structure factor. Our numerical simulations are probed over a large ensemble of random realizations in a wide range of disorder strengths r, from the clean ( $$r=0$$ r = 0 ) case up to the diluted ( $$r \rightarrow 1$$ r → 1 ) limit, and for selected choices of number of legs $$L_y$$ L y per site. Our results show some interesting phenomena, like the presence of crossing points in the temperature plane for both the specific heat and uniform susceptibility curves which appear to be universal in r, as well as a variable dependence of the spin gap in the amount of disorder upon increasing $$L_y$$ L y . Graphical Abstract

arXiv:2312.12834The European Physical Journal BMar 1, 20241 citation

Quantum Monte Carlo simulations for stacked spin-ladder systems containing low concentrations of nonmagnetic impurities: Application to the low-temperature broadening of NMR spectra in SrCu 2 O 3

Robert Achleitner, Hans Gerd Evertz, Masatoshi Imada +2 more

We present a quantum Monte Carlo study for Heisenberg spin- $\frac{1}{2}$ two-leg ladder systems doped with nonmagnetic impurities. The simulations are applied to the doped spin-ladder compound Sr(Cu${}_{1\ensuremath{-}x}$Zn ${}_{x}$ ) ${}_{2}$ O ${}_{3}$ , where a large broadening of the ${}^{65}$ Cu NMR lines has been observed in experiment at low temperatures but far above the N\'eel temperature. We find that interladder couplings with a sizable coupling in the stacking direction are required to describe the line broadening, which cannot be explained by considering a single ladder only. Around a single impurity, spin correlations cause an exponentially decaying antiferromagnetic local magnetization in a magnetic field. We develop an effective model for the local magnetization of systems with many randomly distributed impurities, with few parameters which can be extracted out of quantum Monte Carlo calculations with a single impurity. The broadening arises from a drag effect, where the magnetization around an impurity works as an effective field for spins on the neighboring ladders, causing a nonexponentially decaying magnetization cloud around the impurity. Our results show that even for impurity concentrations as small as $x=0.001$ and $x=0.0025$ , the broadening effect is large, in good quantitative agreement with experiment. We also develop a simple model for the effective interaction of two impurity spins.We present a quantum Monte Carlo study for Heisenberg spin-$\frac{1}{2}$ two-leg ladder systems doped with nonmagnetic impurities. The simulations are applied to the doped spin-ladder compound Sr(Cu${}_{1\ensuremath{-}x}$Zn${}_{x}$)${}_{2}$O${}_{3}$, where a large broadening of the ${}^{65}$Cu NMR lines has been observed in experiment at low temperatures but far above the N\'eel temperature. We find that interladder couplings with a sizable coupling in the stacking direction are required to describe the line broadening, which cannot be explained by considering a single ladder only. Around a single impurity, spin correlations cause an exponentially decaying antiferromagnetic local magnetization in a magnetic field. We develop an effective model for the local magnetization of systems with many randomly distributed impurities, with few parameters which can be extracted out of quantum Monte Carlo calculations with a single impurity. The broadening arises from a drag effect, where the magnetization around an impurity works as an effective field for spins on the neighboring ladders, causing a nonexponentially decaying magnetization cloud around the impurity. Our results show that even for impurity concentrations as small as $x=0.001$ and $x=0.0025$, the broadening effect is large, in good quantitative agreement with experiment. We also develop a simple model for the effective interaction of two impurity spins.

arXiv:1310.1697Physical Review BDec 23, 20133 citations

Quantum Phases of a Strongly Disordered Two-Legged Josephson Ladder

Eyal Walach, Efrat Shimshoni

Disordered superconductors in low dimensions provide an exemplary manifestation for the role of quantum fluctuations in a many-body system. Specifically in Josephson arrays with comparable Josephson and charging energies ( $E_J\sim E_C$ ), disorder tends to change the nature of the paradigmatic Superconductor-Insulator Transition (SIT) and potentially leads to formation of multiple distinct phases. We address this problem in a model of a two-legged Josephson ladder subjected to a wide spatial distribution of its parameters along the legs. In contrast, we assume the system to have a perfect $\mathbb{Z}_2$ symmetry to interchange between the legs, and investigate the effects of spatial randomness which preserves this symmetry in the strong-disorder limit. To this end, we apply a strong randomness real-space renormalization group technique and explore the resulting phase diagram. We identify three disorder-dominated phases, including an intermediate phase between a disordered superconductor and a disordered insulator. The latter insulating phase can be mapped to a XY spin-chain in a spin glass phase, while the intermediate phase turns out to be a Bose glass.Disordered superconductors in low dimensions provide an exemplary manifestation for the role of quantum fluctuations in a many-body system. Specifically in Josephson arrays with comparable Josephson and charging energies ($E_J\sim E_C$), disorder tends to change the nature of the paradigmatic Superconductor-Insulator Transition (SIT) and potentially leads to formation of multiple distinct phases. We address this problem in a model of a two-legged Josephson ladder subjected to a wide spatial distribution of its parameters along the legs. In contrast, we assume the system to have a perfect $\mathbb{Z}_2$ symmetry to interchange between the legs, and investigate the effects of spatial randomness which preserves this symmetry in the strong-disorder limit. To this end, we apply a strong randomness real-space renormalization group technique and explore the resulting phase diagram. We identify three disorder-dominated phases, including an intermediate phase between a disordered superconductor and a disordered insulator. The latter insulating phase can be mapped to a XY spin-chain in a spin glass phase, while the intermediate phase turns out to be a Bose glass.

arXiv:2512.19808Dec 22, 20250 citations

{h}^{\ensuremath{'}}<h\ensuremath{\lesssim}{h}_{c1}

and

{h}^{\ensuremath{'}\ensuremath{'}}<h<{h}_{c2}

) and a Bose-Einstein Condensate in between. Their presence is discussed in relation to the local bond energies.

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.

r=0

r = 0 ) case up to the diluted (

r \rightarrow 1

r → 1 ) limit, and for selected choices of number of legs

L_y

L y per site. Our results show some interesting phenomena, like the presence of crossing points in the temperature plane for both the specific heat and uniform susceptibility curves which appear to be universal in r, as well as a variable dependence of the spin gap in the amount of disorder upon increasing

L_y

L y . Graphical Abstract

We present a quantum Monte Carlo study for Heisenberg spin-

\frac{1}{2}

two-leg ladder systems doped with nonmagnetic impurities. The simulations are applied to the doped spin-ladder compound Sr(Cu${}_{1\ensuremath{-}x}$Zn

{}_{x}

)

{}_{2}

{}_{3}

, where a large broadening of the

{}^{65}

Cu NMR lines has been observed in experiment at low temperatures but far above the N\'eel temperature. We find that interladder couplings with a sizable coupling in the stacking direction are required to describe the line broadening, which cannot be explained by considering a single ladder only. Around a single impurity, spin correlations cause an exponentially decaying antiferromagnetic local magnetization in a magnetic field. We develop an effective model for the local magnetization of systems with many randomly distributed impurities, with few parameters which can be extracted out of quantum Monte Carlo calculations with a single impurity. The broadening arises from a drag effect, where the magnetization around an impurity works as an effective field for spins on the neighboring ladders, causing a nonexponentially decaying magnetization cloud around the impurity. Our results show that even for impurity concentrations as small as

x=0.001

and

x=0.0025

, the broadening effect is large, in good quantitative agreement with experiment. We also develop a simple model for the effective interaction of two impurity spins.

E_J\sim E_C

), disorder tends to change the nature of the paradigmatic Superconductor-Insulator Transition (SIT) and potentially leads to formation of multiple distinct phases. We address this problem in a model of a two-legged Josephson ladder subjected to a wide spatial distribution of its parameters along the legs. In contrast, we assume the system to have a perfect

\mathbb{Z}_2

symmetry to interchange between the legs, and investigate the effects of spatial randomness which preserves this symmetry in the strong-disorder limit. To this end, we apply a strong randomness real-space renormalization group technique and explore the resulting phase diagram. We identify three disorder-dominated phases, including an intermediate phase between a disordered superconductor and a disordered insulator. The latter insulating phase can be mapped to a XY spin-chain in a spin glass phase, while the intermediate phase turns out to be a Bose glass.