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/9606170 · Journal of the Physical Society of Japan

Low-Temperature Properties of the Randomly Depleted Heisenberg Ladder

Manfred Sigrist, Akira Furusaki

Published Aug 15, 1996• 92 citations
arXivHTMLPDF

Abstract

Low-temperature thermodynamic properties of the spin-1/2 Heisenberg ladder system with non-magnetic impurities are discussed using an effective Hamiltonian for the impurity-induced spins in the background of a spin liquid with a gap. It is shown that the uniform susceptibility shows Curie-like behavior in high-, intermediate-, and low-temperature regimes, with three different Curie constants. The ratio of specific heat to temperature, C/T, is divergent in the low-temperature limit, reflecting a singular distribution of the effective couplings among the impurity spins.

DOI
10.1143/jpsj.65.2385

Related papers

Effects of Nonmagnetic Impurity Doping on Spin Ladder System

Youichirou Iino, Masatoshi Imada

Effects of nonmagnetic impurity doping on an AF spin-1/2 Heisenberg ladder system are studied by the QMC method. A single nonmagnetic impurity induces a localized spin-1/2 moment accompanied by "static" and enhanced AF correlations around it. Small and finite concentration of impurities induces a remarkable change of magnetic and thermodynamic properties with gapless excitations. It also shows rather sharp but continuous crossover around the concentration of about 4%. Above the crossover concentration, all the spins are strongly coupled participating in the enhanced and rather uniform power-law decay of the antiferromagnetic correlation. Below the crossover, each impurity forms an antiferromagnetic cluster only weakly coupled each other. For random distribution of impurities, large Curie-like susceptibility accompanied with small residual entropy is obtained at low temperatures in agreement with recent experimental observation in Zn-doped $SrCu_{2}O_{3}$. Temperature dependence of AF susceptibility shows power-law-like but weaker divergence than the single chain AFH in the temperature range studied.

arXiv:cond-mat/9609038•Journal of the Physical Society of Japan•Dec 15, 1996•39 citations

Boundary Susceptibility in the Spin- 1/2 Chain: Curie-Like Behavior without Magnetic Impurities

Satoshi Fujimoto, Sebastian Eggert

We investigate the low-temperature thermodynamics of the spin-1/2 Heisenberg chain with open ends. On the basis of boundary conformal field theory arguments and numerical density matrix renormalization group calculations, it is established that in the isotropic case the impurity susceptibility exhibits a Curie-like divergent behavior as the temperature decreases, even in the absence of magnetic impurities. A similar singular temperature dependence is also found in the boundary contributions of the specific heat coefficient. In the anisotropic case, for 1/2<Delta<1, these boundary quantities still show a singular temperature dependence obeying a power law with an anomalous dimension. Experimental consequences will be discussed.

arXiv:cond-mat/0310230•Physical Review Letters•Jan 23, 2004•45 citations

Magnetic responses of randomly depleted spin ladders

Arthur Lavarélo, Guillaume Roux, Nicolas Laflorencie

The magnetic responses of a spin-$1/2$ ladder doped with nonmagnetic impurities are studied combining both analytical and numerical methods. The regime where frustration induces incommensurability is taken into account. Several improvements are made on the results of the seminal work by Sigrist and Furusaki [M. Sigrist and A. Furusaki, J. Phys. Soc. Jpn. 65, 2385 (1996)] and deviations from the Brillouin magnetization curve due to interactions are also analyzed. We first discuss the magnetic profile around a single impurity and the effective interactions between impurities within the bond-operator mean-field theory. The results are compared to density-matrix renormalization group calculations. In particular, these quantities are shown to be sensitive to the transition to the incommensurate regime. We then focus on the behavior of the zero-field susceptibility through an effective Curie constant. At zero temperature, we give doping-dependent corrections to the results of Sigrist and Furusaki on general bipartite lattices and compute exactly the distribution of ladder clusters due to chain breaking effects. Solving the effective model with exact diagonalization and quantum Monte Carlo simulations gives the temperature dependence of the Curie constant. Its high-temperature limit is understood within a random dimer model, while the low-temperature tail is compatible with a real-space renormalization group scenario. Interestingly, solving the full microscopic model does not show a plateau corresponding to the saturation of the impurities in isotropic ladders. The second magnetic response that is analyzed is the magnetic curve. Below fields of the order of the spin gap, the magnetization process is controlled by the physics of interacting impurity spins. The random dimer model is shown to capture the bulk of the curve, accounting for the deviation from a Brillouin behavior due to interactions. The effective model calculations agree rather well with density-matrix renormalization group calculations at zero temperature and with quantum Monte Carlo simulations at finite temperature. In all, the effect of incommensurability does not display a strong qualitative effect on both the magnetic susceptibility and the magnetic curve. Consequences for experiments on the BiCu${}_{2}$PO${}_{6}$ compound and other spin-gapped materials are briefly mentioned.

arXiv:1307.6613•Physical Review B•Oct 21, 2013•14 citations

Zero Modes and Thermodynamics of Disordered Spin-1/2 Ladders

Alexander O. Gogolin, A. A. Nersesyan, Alexei M. Tsvelik +1 more

The influence of nonmagnetic doping on the thermodynamic properties of two-leg S = 1/2 spin ladders is studied in this paper. It is shown that, for a weak interchain coupling, the problem can be mapped onto a model of random mass Dirac (Majorana) fermions. We investigate in detail the structure of the fermionic states localized at an individual mass kink (zero modes) in the framework of a generalized Dirac model. The low-temperature thermodynamic properties are dominated by these zero modes. We use the single-fermion density of states, known to exhibit the Dyson singularity in the zero-energy limit, to construct the thermodynamics of the spin ladder. In particular, we find that the magnetic susceptibility $χ$ diverges at $T\to 0$ as $1/T\ln^2(1/T)$, and the specific heat behaves as $C\propto 1/\ln^3(1/T)$. The predictions on magnetic susceptibility are consistent with the most recent results of quantum Monte Carlo simulations on doped ladders with randomly distributed impurities. We also calculate the average staggered magnetic susceptibility induced in the system by such defects.

arXiv:cond-mat/9707341•Jul 31, 1997•3 citations

Spin ladders with nonmagnetic impurities

H.-J. Mikeska, U. Neugebauer, Ulrich Schollwöck

We investigate antiferromagnetic spin ladders with nonmagnetic impurities by variational and numerical [Lanczos and density matrix renormalization group (DMRG)] methods. The interaction between the two unpaired spins opposite to the impurities is described by an effective exchange interaction ${\mathrm{J}}_{\mathrm{eff}}$, the magnitude of which depends on the impurity distance. The magnitude of ${\mathrm{J}}_{\mathrm{eff}}$ is different for unpaired spins at the edges of an open ladder and in the bulk. This difference is related to the different distributions of the unpaired spin into the bulk of the ladder. The numerical results are interpreted using matrix product states. Using the DMRG we calculate the spectrum of low-lying energy levels for up to six impurities and find that these spectra can be reproduced assuming pair interactions with an accuracy of better than 10%. We discuss the filling of the ladder gap with impurity states and argue that in the thermodynamic limit the spin ladder with a finite concentration of impurities always shows a Curie susceptibility at low temperatures.

arXiv:cond-mat/9608100•Physical review. B, Condensed matter•Feb 1, 1997•39 citations

Exact Thermodynamics of Disordered Impurities in Quantum Spin Chains

Andreas Klümper, Andrei A. Zvyagin

Exact results for the thermodynamic properties of ensembles of magnetic impurities with randomly distributed host-impurity couplings in the quantum antiferromagnetic Heisenberg model are presented. Exact calculations are done for arbitrary values of temperature and external magnetic field. We have shown that for strong disorder the quenching of the impurity moments is absent. For weak disorder the screening persists, but with the critical non-Fermi-liquid behaviors of the magnetic susceptibility and specific heat. A comparison with disordered Kondo effect experiments in dirty metallic alloys is performed.

arXiv:cond-mat/9811115•Physical Review Letters•Nov 30, 1998•22 citations
Low-temperature thermodynamic properties of the spin-1/2 Heisenberg ladder system with non-magnetic impurities are discussed using an effective Hamiltonian for the impurity-induced spins in the background of a spin liquid with a gap. It is shown that the uniform susceptibility shows Curie-like behavior in high-, intermediate-, and low-temperature regimes, with three different Curie constants. The ratio of specific heat to temperature, C/T, is divergent in the low-temperature limit, reflecting a singular distribution of the effective couplings among the impurity spins.
Effects of nonmagnetic impurity doping on an AF spin-1/2 Heisenberg ladder system are studied by the QMC method. A single nonmagnetic impurity induces a localized spin-1/2 moment accompanied by "static" and enhanced AF correlations around it. Small and finite concentration of impurities induces a remarkable change of magnetic and thermodynamic properties with gapless excitations. It also shows rather sharp but continuous crossover around the concentration of about 4%. Above the crossover concentration, all the spins are strongly coupled participating in the enhanced and rather uniform power-law decay of the antiferromagnetic correlation. Below the crossover, each impurity forms an antiferromagnetic cluster only weakly coupled each other. For random distribution of impurities, large Curie-like susceptibility accompanied with small residual entropy is obtained at low temperatures in agreement with recent experimental observation in Zn-doped SrCu2O3SrCu_{2}O_{3}SrCu2​O3​. Temperature dependence of AF susceptibility shows power-law-like but weaker divergence than the single chain AFH in the temperature range studied.
We investigate the low-temperature thermodynamics of the spin-1/2 Heisenberg chain with open ends. On the basis of boundary conformal field theory arguments and numerical density matrix renormalization group calculations, it is established that in the isotropic case the impurity susceptibility exhibits a Curie-like divergent behavior as the temperature decreases, even in the absence of magnetic impurities. A similar singular temperature dependence is also found in the boundary contributions of the specific heat coefficient. In the anisotropic case, for 1/2<Delta<1, these boundary quantities still show a singular temperature dependence obeying a power law with an anomalous dimension. Experimental consequences will be discussed.
The magnetic responses of a spin-1/21/21/2 ladder doped with nonmagnetic impurities are studied combining both analytical and numerical methods. The regime where frustration induces incommensurability is taken into account. Several improvements are made on the results of the seminal work by Sigrist and Furusaki [M. Sigrist and A. Furusaki, J. Phys. Soc. Jpn. 65, 2385 (1996)] and deviations from the Brillouin magnetization curve due to interactions are also analyzed. We first discuss the magnetic profile around a single impurity and the effective interactions between impurities within the bond-operator mean-field theory. The results are compared to density-matrix renormalization group calculations. In particular, these quantities are shown to be sensitive to the transition to the incommensurate regime. We then focus on the behavior of the zero-field susceptibility through an effective Curie constant. At zero temperature, we give doping-dependent corrections to the results of Sigrist and Furusaki on general bipartite lattices and compute exactly the distribution of ladder clusters due to chain breaking effects. Solving the effective model with exact diagonalization and quantum Monte Carlo simulations gives the temperature dependence of the Curie constant. Its high-temperature limit is understood within a random dimer model, while the low-temperature tail is compatible with a real-space renormalization group scenario. Interestingly, solving the full microscopic model does not show a plateau corresponding to the saturation of the impurities in isotropic ladders. The second magnetic response that is analyzed is the magnetic curve. Below fields of the order of the spin gap, the magnetization process is controlled by the physics of interacting impurity spins. The random dimer model is shown to capture the bulk of the curve, accounting for the deviation from a Brillouin behavior due to interactions. The effective model calculations agree rather well with density-matrix renormalization group calculations at zero temperature and with quantum Monte Carlo simulations at finite temperature. In all, the effect of incommensurability does not display a strong qualitative effect on both the magnetic susceptibility and the magnetic curve. Consequences for experiments on the BiCu2{}_{2}2​PO6{}_{6}6​ compound and other spin-gapped materials are briefly mentioned.
The influence of nonmagnetic doping on the thermodynamic properties of two-leg S = 1/2 spin ladders is studied in this paper. It is shown that, for a weak interchain coupling, the problem can be mapped onto a model of random mass Dirac (Majorana) fermions. We investigate in detail the structure of the fermionic states localized at an individual mass kink (zero modes) in the framework of a generalized Dirac model. The low-temperature thermodynamic properties are dominated by these zero modes. We use the single-fermion density of states, known to exhibit the Dyson singularity in the zero-energy limit, to construct the thermodynamics of the spin ladder. In particular, we find that the magnetic susceptibility χχχ diverges at T→0T\to 0T→0 as 1/Tln⁡2(1/T)1/T\ln^2(1/T)1/Tln2(1/T), and the specific heat behaves as C∝1/ln⁡3(1/T)C\propto 1/\ln^3(1/T)C∝1/ln3(1/T). The predictions on magnetic susceptibility are consistent with the most recent results of quantum Monte Carlo simulations on doped ladders with randomly distributed impurities. We also calculate the average staggered magnetic susceptibility induced in the system by such defects.
We investigate antiferromagnetic spin ladders with nonmagnetic impurities by variational and numerical [Lanczos and density matrix renormalization group (DMRG)] methods. The interaction between the two unpaired spins opposite to the impurities is described by an effective exchange interaction Jeff{\mathrm{J}}_{\mathrm{eff}}Jeff​, the magnitude of which depends on the impurity distance. The magnitude of Jeff{\mathrm{J}}_{\mathrm{eff}}Jeff​ is different for unpaired spins at the edges of an open ladder and in the bulk. This difference is related to the different distributions of the unpaired spin into the bulk of the ladder. The numerical results are interpreted using matrix product states. Using the DMRG we calculate the spectrum of low-lying energy levels for up to six impurities and find that these spectra can be reproduced assuming pair interactions with an accuracy of better than 10%. We discuss the filling of the ladder gap with impurity states and argue that in the thermodynamic limit the spin ladder with a finite concentration of impurities always shows a Curie susceptibility at low temperatures.
Exact results for the thermodynamic properties of ensembles of magnetic impurities with randomly distributed host-impurity couplings in the quantum antiferromagnetic Heisenberg model are presented. Exact calculations are done for arbitrary values of temperature and external magnetic field. We have shown that for strong disorder the quenching of the impurity moments is absent. For weak disorder the screening persists, but with the critical non-Fermi-liquid behaviors of the magnetic susceptibility and specific heat. A comparison with disordered Kondo effect experiments in dirty metallic alloys is performed.