Ladders in a magnetic field: a strong coupling approach

Mila, Frédéric

doi:10.1007/s100510050542

Cited by 184 publications

(257 citation statements)

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“…Within this mapping, the ground-state singlet and the low-energy component of the triplet form an effective spin S =1/ 2 on each rung of a ladder. [16][17][18] The effective Hamiltonian is…”

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confidence: 99%

Evidence for spinon localization in the heat transport of the spin-12ladder compound(C5<

et al. 2009

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We present experiments on the magnetic-field-dependent thermal transport in the spin-1 2 ladder system ͑C 5 H 12 N͒ 2 CuBr 4 . The thermal conductivity ͑B͒ is only weakly affected by the field-induced transitions between the gapless Luttinger-liquid state realized for B c1 Ͻ B Ͻ B c2 and the gapped states, suggesting the absence of a direct contribution of the spin excitations to the heat transport. We observe, however, that the thermal conductivity is strongly suppressed by the magnetic field deeply within the Luttinger-liquid state. These surprising observations are discussed in terms of localization of spinons within finite ladder segments and spinon-phonon umklapp scattering of the predominantly phononic heat transport. DOI: 10.1103/PhysRevB.80.220411 PACS number͑s͒: 75.40.Gb, 05.60.Gg, 75.47.Ϫm Studies of the heat transport in one-dimensional ͑1D͒ spin systems are of strong current interest. 1-3 From the theoretical side, there is consensus that the intrinsic spin-mediated heat transport of integrable spin models is ballistic, while the situation in nonintegrable spin models is less clear. Experimentally, such studies were stimulated by the observation of a strong anisotropy of the thermal conductivity ͑T͒ in the spin-1 2 ladder compound ͑Sr, Ca, La͒ 14 Cu 24 O 41 , which has been explained by a large spin contribution s along the ladder direction. [4][5][6] In order to relate model calculations to experimental data, theory has to incorporate the coupling between spin excitations and the underlying lattice, while experimentally it is necessary to separate s from the measured total . Here, studies of the magnetic-field dependent ͑B , T͒ can provide much more information than just the zero field ͑T͒ since strong enough magnetic fields change the spin excitation spectra and cause transitions between different quantum phases. Yet, the above-mentioned ͑Sr, Ca, La͒ 14 Cu 24 O 41 is unsuitable for such studies due to the strong exchange interaction ͑ϳ2000 K͒ in the ladders that require magnetic fields far above typical laboratory magnets. Piperidinium copper bromide ͑C 5 H 12 N͒ 2 CuBr 4 ͑Ref. 7͒ is one of the best spin-1 2 ladder compounds with weak intraladder exchange. It has a monoclinic structure ͑space group P2 1 / c͒ with the ladders running along the a axis. The rung exchange J Ќ Ӎ 13 K is about four times larger than the leg exchange J ʈ Ӎ 3.6 K. [8][9][10][11][12][13][14] The zero-field spin excitation gap ⌬ Ӎ 9.5 K decreases in an external magnetic field, so that between B c1 Ӎ 7.1 T and the full saturation field B c2 Ӎ 14.5 T ͓for B ʈ a, where g = 2.06 ͑Ref. 7͔͒ the spin excitations are gapless and the system is in the Luttinger-liquid ͑LL͒ state. The LL state extends down to the temperature of a 3D magnetic ordering transition at T N Յ 110 mK, suggesting an interladder coupling JЈ ϳ 27 mKӶ J Ќ , J ʈ . 10,12,13 In this Rapid Communication, we present measurements of the thermal conductivity of ͑C 5 H 12 N͒ 2 CuBr 4 between 0.3 and 10 K in magnetic fields up to 17 T. Surprisingly, no sign of spin-me...

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Evidence for spinon localization in the heat transport of the spin-12ladder compound(C5<

et al. 2009

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“…For small γ the ladder problem can be reduced to a simpler spin chain problem. The essence of the spin chain mapping 2,17,47,48 is to project out |t 0 and |t − bands from the Hilbert space of the model (2). The remaining states |s and |t + are identified with the spin states |↓ = |s , |↑ = |t + .…”

Section: Spin Ladder To Spin Chain Mappingmentioning

confidence: 99%

“…The local operators of the latter model are bosonized by combining Eqs. (12), (17), and (18). The analysis of the model (2) suggests 2,19,20 that the bosonization of the local spins can be performed for any values of J ⊥ and J in the gapless regime.…”

Section: Luttinger Liquid (Ll)mentioning

confidence: 99%

“…In the gapless regime, using the bosonization formalism (17), and taking into account only the most relevant term, we can compute it as described in Ref. …”

Section: Dynamical Ll Correlationsmentioning

confidence: 99%

“…Following Ref. 17, we map the two low-energy modes on the two states of a pseudospin [Eq. (11)], and replace the boson operators s † and t † + with the spin-1/2 operators,…”

Section: A Low-energy Sectormentioning

confidence: 99%

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Statics and Dynamics of Weakly Coupled Antiferromagnetic Spin-1/2 Ladders in a Magnetic Field

Bouillot

2013

Springer Theses

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We investigate weakly coupled spin-1/2 ladders in a magnetic field. The work is motivated by recent experiments on the compound (C 5 H 12 N) 2 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.

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Low Dimensional Magnets

Rice

2002

High Magnetic Fields

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Ladders in a magnetic field: a strong coupling approach

Cited by 184 publications

References 24 publications

Evidence for spinon localization in the heat transport of the spin-12ladder compound(C5<

Evidence for spinon localization in the heat transport of the spin-12ladder compound(C5<

Statics and Dynamics of Weakly Coupled Antiferromagnetic Spin-1/2 Ladders in a Magnetic Field

Low Dimensional Magnets

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