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:1009.0840 · Physical Review B

Statics and dynamics of weakly coupled antiferromagnetic spin- 1 2 ladders in a magnetic field

Pierre Bouillot, Corinna Kollath, Andreas Martin Läuchli, Mikhail B. Zvonarev, B. Thielemann, Christian Rüegg, E. Orignac, R. Citro, M. Klanjšek, C. Berthier, M. Horvatić, Thierry Giamarchi

Published Feb 9, 2011• 139 citations
arXivHTMLPDF

Abstract

We investigate weakly coupled spin-$1/2$ ladders in a magnetic field. The work is motivated by recent experiments on the compound ${(}_{\mathrm{C}}{\mathrm{H}}_{12}{\mathrm{N}}_{)}{\mathrm{CuBr}}_{4}$ (BPCB). We use a combination of numerical and analytical methods, in particular, the density-matrix renormalization group (DMRG) technique, to explore the phase diagram and the excitation spectra of such a system. We give detailed results on the temperature dependence of the magnetization and the specific heat, and the magnetic-field dependence of the nuclear-magnetic-resonance relaxation rate of single ladders. For coupled ladders, treating the weak interladder coupling within a mean-field or quantum Monte Carlo approach, we compute the transition temperature of triplet condensation and its corresponding antiferromagnetic order parameter. Existing experimental measurements are discussed and compared to our theoretical results. Furthermore, we compute, using time-dependent DMRG, the dynamical correlations of a single spin ladder. Our results allow to describe directly the inelastic neutron scattering cross section up to high energies. We focus on the evolution of the spectra with the magnetic field and compare their behavior for different couplings. The characteristic features of the spectra are interpreted using different analytical approaches such as the mapping onto a spin chain, a Luttinger liquid or onto a $t$-$J$ model. For values of parameters for which such measurements exist, we compare our results to inelastic neutron scattering experiments on the compound BPCB and find excellent agreement. We make additional predictions for the high-energy part of the spectrum that are potentially testable in future experiments.

DOI
10.1103/physrevb.83.054407

Related papers

Statics and dynamics of weakly coupled antiferromagnetic spin-1/2 ladders in a magnetic field (PhD thesis)

Pierre Bouillot

We investigate weakly coupled spin-1/2 ladders in a magnetic field. The work is motivated by recent experiments on the compound $\mathrm{(C_5H_{12}N)_2CuBr_4}$ (BPCB). We use a combination of numerical and analytical methods, in particular the density matrix renormalization group (DMRG) technique, to explore the phase diagram and the excitation spectra of such a system. We give detailed results on the temperature dependence of the magnetization and the specific heat, and the magnetic field dependence of the nuclear magnetic resonance (NMR) relaxation rate of single ladders. For coupled ladders, treating the weak interladder coupling within a mean field approach, we compute the transition temperature of triplet condensation and its corresponding antiferromagnetic order parameter. Existing experimental measurements are discussed and compared to our theoretical results. Furthermore we compute, using time dependent DMRG, the dynamical correlations of a single spin ladder. Our results allow to directly describe the inelastic neutron scattering cross section up to high energies. We focus on the evolution of the spectra with the magnetic field and compare their behavior for different couplings. The characteristic features of the spectra are interpreted using different analytical approaches such as the mapping onto a spin chain, a Luttinger liquid (LL) or onto a t-J model. For values of parameters for which such measurements exist, we compare our results to inelastic neutron scattering experiments on the compound BPCB and find excellent agreement. We make additional predictions for the high energy part of the spectrum that are potentially testable in future experiments.

arXiv:1201.5276•Jan 18, 2012•0 citations

Controlling Luttinger Liquid Physics in Spin Ladders under a Magnetic Field

M. Klanjšek, H. Mayaffre, C. Berthier +8 more

We present a 14N nuclear magnetic resonance study of a single crystal of CuBr4(C5H12N)2 (BPCB) consisting of weakly coupled spin-1/2 Heisenberg antiferromagnetic ladders. Treating ladders in the gapless phase as Luttinger liquids, we are able to fully account for (i) the magnetic field dependence of the nuclear spin-lattice relaxation rate T1(-1) at 250 mK and for (ii) the phase transition to a 3D ordered phase occurring below 110 mK due to weak interladder exchange coupling. BPCB is thus an excellent model system where the possibility to control Luttinger liquid parameters in a continuous manner is demonstrated and the Luttinger liquid model tested in detail over the whole fermion band.

arXiv:0804.2639•Physical Review Letters•Sep 26, 2008•217 citations

Magnetic-Field-Induced Bound States in Spin- 1 2 Ladders

Mithilesh Nayak, D. Blosser, A. Zheludev +1 more

Motivated by the recently observed intriguing mode splittings in a magnetic field with inelastic neutron scattering in the spin ladder compound (C_{5}H_{12}N)_{2}CuBr_{4} (BPCB), we investigate the nature of the spin ladder excitations using a density matrix renormalization group and analytical arguments. Starting from the fully frustrated ladder, for which we derive the low-energy spectrum, we show that bound states are generically present close to k=0 in the dynamical structure factor of spin ladders above H_{c1}, and that they are characterized by a field-independent binding energy and an intensity that grows with H-H_{c1}. These predictions are shown to explain quantitatively the split modes observed in BPCB.

arXiv:1912.01576•Physical Review Letters•Feb 26, 2020•10 citations

Spin dynamics of coupled spin ladders near quantum criticality in Ba 2 CuTeO 6

David Macdougal, Alexandra S. Gibbs, Tao Ying +6 more

We report inelastic neutron scattering measurements of the magnetic excitations in ${\mathrm{Ba}}_{2}{\mathrm{CuTeO}}_{6}$, proposed by ab initio calculations to magnetically realize weakly coupled antiferromagnetic two-leg spin-$\frac{1}{2}$ ladders. Isolated ladders are expected to have a singlet ground state protected by a spin gap. ${\mathrm{Ba}}_{2}{\mathrm{CuTeO}}_{6}$ orders magnetically, but with a small N\'eel temperature relative to the exchange strength, suggesting that the interladder couplings are relatively small and only just able to stabilize magnetic order, placing ${\mathrm{Ba}}_{2}{\mathrm{CuTeO}}_{6}$ close in parameter space to the critical point separating the gapped phase and N\'eel order. Through comparison of the observed spin dynamics with linear spin wave theory and quantum Monte Carlo calculations, we propose values for all relevant intra- and interladder exchange parameters, which place the system on the ordered side of the phase diagram in proximity to the critical point. We also compare high field magnetization data with quantum Monte Carlo predictions for the proposed model of coupled ladders.

arXiv:1806.04052•Physical review. B./Physical review. B•Nov 7, 2018•18 citations

Luttinger liquid physics in the spin ladder material CuBr4(C5H12N)2

M. Klanjšek, H. Mayaffre, C. Berthier +8 more

Abstract We present a 14N nuclear magnetic resonance study of a single crystal of CuBr4(C5H12N)2 consisting of weakly coupled spin‐1/2 Heisenberg antiferromagnetic ladders. When placed in a magnetic field, such a ladder is theoretically predicted to exhibit a quantum critical Luttinger liquid (LL) behaviour in the gapless phase, i.e. between the two critical fields. Treating ladders as LLs and interaction between them as a perturbation, we are indeed able to fully account for (i) the spin dynamics accessed by measuring the spin–lattice relaxation rate $T_1^{ - 1}$ , and for (ii) the phase transition to a 3D ordered phase occurring below 110 mK due to the weak interladder coupling.

physica status solidi (b)•Feb 8, 2010•8 citations

Spin correlations in the two-leg antiferromagnetic ladder in a magnetic field

Takashi Hikihara, Akira Furusaki

We study the ground-state spin correlations in the gapless incommensurate regime of a $S=1/2$ $\mathrm{XXZ}$ chain and a two-leg antiferromagnetic ladder under a magnetic field, in which the gapless excitations form a Tomonaga-Luttinger (TL) liquid. We calculate numerically the two-spin correlation functions and the local magnetization in the two models using the density-matrix renormalization-group method. By fitting the numerical results for an open $\mathrm{XXZ}$ chain of 100 spins to correlation functions of a Gaussian model, we determine the TL-liquid parameter K and the amplitudes of the correlation functions. The value of K estimated from the fits is in excellent agreement with the exact value obtained from the Bethe ansatz. We apply the same method to the open ladder consisting of 200 spins and determine the dependence of K on the magnetization M. The $K\ensuremath{-}M$ relation changes drastically depending on the ratio of the coupling constants in the leg and rung directions. We also discuss implications of these results to experiments on the nuclear spin relaxation rate ${1/T}_{1}$ and dynamical spin structure factors.

arXiv:cond-mat/0011320•Physical review. B, Condensed matter•Mar 15, 2001•71 citations
We investigate weakly coupled spin-1/21/21/2 ladders in a magnetic field. The work is motivated by recent experiments on the compound (CH12N)CuBr4{(}_{\mathrm{C}}{\mathrm{H}}_{12}{\mathrm{N}}_{)}{\mathrm{CuBr}}_{4}(C​H12​N)​CuBr4​ (BPCB). We use a combination of numerical and analytical methods, in particular, the density-matrix renormalization group (DMRG) technique, to explore the phase diagram and the excitation spectra of such a system. We give detailed results on the temperature dependence of the magnetization and the specific heat, and the magnetic-field dependence of the nuclear-magnetic-resonance relaxation rate of single ladders. For coupled ladders, treating the weak interladder coupling within a mean-field or quantum Monte Carlo approach, we compute the transition temperature of triplet condensation and its corresponding antiferromagnetic order parameter. Existing experimental measurements are discussed and compared to our theoretical results. Furthermore, we compute, using time-dependent DMRG, the dynamical correlations of a single spin ladder. Our results allow to describe directly the inelastic neutron scattering cross section up to high energies. We focus on the evolution of the spectra with the magnetic field and compare their behavior for different couplings. The characteristic features of the spectra are interpreted using different analytical approaches such as the mapping onto a spin chain, a Luttinger liquid or onto a ttt-JJJ model. For values of parameters for which such measurements exist, we compare our results to inelastic neutron scattering experiments on the compound BPCB and find excellent agreement. We make additional predictions for the high-energy part of the spectrum that are potentially testable in future experiments.
We investigate weakly coupled spin-1/2 ladders in a magnetic field. The work is motivated by recent experiments on the compound (C5H12N)2CuBr4\mathrm{(C_5H_{12}N)_2CuBr_4}(C5​H12​N)2​CuBr4​ (BPCB). We use a combination of numerical and analytical methods, in particular the density matrix renormalization group (DMRG) technique, to explore the phase diagram and the excitation spectra of such a system. We give detailed results on the temperature dependence of the magnetization and the specific heat, and the magnetic field dependence of the nuclear magnetic resonance (NMR) relaxation rate of single ladders. For coupled ladders, treating the weak interladder coupling within a mean field approach, we compute the transition temperature of triplet condensation and its corresponding antiferromagnetic order parameter. Existing experimental measurements are discussed and compared to our theoretical results. Furthermore we compute, using time dependent DMRG, the dynamical correlations of a single spin ladder. Our results allow to directly describe the inelastic neutron scattering cross section up to high energies. We focus on the evolution of the spectra with the magnetic field and compare their behavior for different couplings. The characteristic features of the spectra are interpreted using different analytical approaches such as the mapping onto a spin chain, a Luttinger liquid (LL) or onto a t-J model. For values of parameters for which such measurements exist, we compare our results to inelastic neutron scattering experiments on the compound BPCB and find excellent agreement. We make additional predictions for the high energy part of the spectrum that are potentially testable in future experiments.
We present a 14N nuclear magnetic resonance study of a single crystal of CuBr4(C5H12N)2 (BPCB) consisting of weakly coupled spin-1/2 Heisenberg antiferromagnetic ladders. Treating ladders in the gapless phase as Luttinger liquids, we are able to fully account for (i) the magnetic field dependence of the nuclear spin-lattice relaxation rate T1(-1) at 250 mK and for (ii) the phase transition to a 3D ordered phase occurring below 110 mK due to weak interladder exchange coupling. BPCB is thus an excellent model system where the possibility to control Luttinger liquid parameters in a continuous manner is demonstrated and the Luttinger liquid model tested in detail over the whole fermion band.
Motivated by the recently observed intriguing mode splittings in a magnetic field with inelastic neutron scattering in the spin ladder compound (C_{5}H_{12}N)_{2}CuBr_{4} (BPCB), we investigate the nature of the spin ladder excitations using a density matrix renormalization group and analytical arguments. Starting from the fully frustrated ladder, for which we derive the low-energy spectrum, we show that bound states are generically present close to k=0 in the dynamical structure factor of spin ladders above H_{c1}, and that they are characterized by a field-independent binding energy and an intensity that grows with H-H_{c1}. These predictions are shown to explain quantitatively the split modes observed in BPCB.
We report inelastic neutron scattering measurements of the magnetic excitations in Ba2CuTeO6{\mathrm{Ba}}_{2}{\mathrm{CuTeO}}_{6}Ba2​CuTeO6​, proposed by ab initio calculations to magnetically realize weakly coupled antiferromagnetic two-leg spin-12\frac{1}{2}21​ ladders. Isolated ladders are expected to have a singlet ground state protected by a spin gap. Ba2CuTeO6{\mathrm{Ba}}_{2}{\mathrm{CuTeO}}_{6}Ba2​CuTeO6​ orders magnetically, but with a small N\'eel temperature relative to the exchange strength, suggesting that the interladder couplings are relatively small and only just able to stabilize magnetic order, placing Ba2CuTeO6{\mathrm{Ba}}_{2}{\mathrm{CuTeO}}_{6}Ba2​CuTeO6​ close in parameter space to the critical point separating the gapped phase and N\'eel order. Through comparison of the observed spin dynamics with linear spin wave theory and quantum Monte Carlo calculations, we propose values for all relevant intra- and interladder exchange parameters, which place the system on the ordered side of the phase diagram in proximity to the critical point. We also compare high field magnetization data with quantum Monte Carlo predictions for the proposed model of coupled ladders.
Abstract We present a 14N nuclear magnetic resonance study of a single crystal of CuBr4(C5H12N)2 consisting of weakly coupled spin‐1/2 Heisenberg antiferromagnetic ladders. When placed in a magnetic field, such a ladder is theoretically predicted to exhibit a quantum critical Luttinger liquid (LL) behaviour in the gapless phase, i.e. between the two critical fields. Treating ladders as LLs and interaction between them as a perturbation, we are indeed able to fully account for (i) the spin dynamics accessed by measuring the spin–lattice relaxation rate T1−1T_1^{ - 1}T1−1​ , and for (ii) the phase transition to a 3D ordered phase occurring below 110 mK due to the weak interladder coupling.
We study the ground-state spin correlations in the gapless incommensurate regime of a S=1/2S=1/2S=1/2 XXZ\mathrm{XXZ}XXZ chain and a two-leg antiferromagnetic ladder under a magnetic field, in which the gapless excitations form a Tomonaga-Luttinger (TL) liquid. We calculate numerically the two-spin correlation functions and the local magnetization in the two models using the density-matrix renormalization-group method. By fitting the numerical results for an open XXZ\mathrm{XXZ}XXZ chain of 100 spins to correlation functions of a Gaussian model, we determine the TL-liquid parameter K and the amplitudes of the correlation functions. The value of K estimated from the fits is in excellent agreement with the exact value obtained from the Bethe ansatz. We apply the same method to the open ladder consisting of 200 spins and determine the dependence of K on the magnetization M. The $K\ensuremath{-}M$ relation changes drastically depending on the ratio of the coupling constants in the leg and rung directions. We also discuss implications of these results to experiments on the nuclear spin relaxation rate 1/T1{1/T}_{1}1/T1​ and dynamical spin structure factors.