Excitation spectrum of Heisenberg spin ladders

Barnes, T.; Dagotto, Elbio; Riera, J.; Swanson, Eric S.

doi:10.1103/physrevb.47.3196

Cited by 420 publications

(441 citation statements)

References 25 publications

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“…We also show for comparison the exact diagonalization results for the singlet-triplet excitations for L = 12 from Ref. [12]. A continuum of excitations can be observed above the magnon band for k y = 0.…”

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confidence: 90%

Time-step targeting methods for real-time dynamics using the density matrix renormalization group

2005

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We present a time-step targetting scheme to simulate real-time dynamics efficiently using the density matrix renormalization group (DMRG). The algorithm works on ladders and systems with interactions beyond nearest neighbors, in contrast to existing Suzuki-Trotter based approaches.PACS numbers: 71.27.+a, 71.10.Pm, 72.15.Qm, 73.63.Kv Over the last ten years the density matrix renormalization group (DMRG) [1] has proven to be remarkably effective at calculating static, ground state properties of one-dimensional strongly correlated systems. During this period there has also been substantial progress made in calculating frequency dependent spectral functions [2]. However, the most significant progress in extending DMRG since its invention has occurred in the last year or two. Through a convergence of quantum information and DMRG ideas and techniques, a number of new approaches are being developed. The first of these are highly efficient and accurate methods for real-time evolution, allowing both the calculation of spectral functions via Fourier transforming, and also novel time development studies of systems out of equilibrium.The key real-time methods thus far developed [3, 4, 5] rely on the Suzuki-Trotter (S-T) break-up of the evolution operator. This approach has a number of important advantages: it is surprisingly simple and easy to implement in an existing ground state DMRG program; the time evolution is very stable and the only source of non-unitarity is the truncation error; and the number of density matrix eigenstates needed for a given truncation error is minimal. It also has two notable weaknesses: it has an error proportional to the time step τ squared, and, more importantly, it is limited to systems with nearest neighbor interactions on a single chain. As we show here, the accuracy can be improved using higher order expansions. The nearest-neighbor/single chain limitation is more problematic. In the case of narrow ladders with nearest-neighbor interactions, one can avoid the problem by lumping all sites in a rung into a single supersite. Unfortunately, this approach becomes very inefficient for wider ladders, and is not applicable to general long-range interaction terms.In this paper we propose a new time evolution scheme which produces a basis which targets the states needed to represent one time step. Once this basis is complete enough, the time step is taken and the algorithm proceeds to the next time step. This targetting is intermediate to previous approaches: the Trotter methods target precisely one instant in time at any DMRG step, while Luo, Xiang, and Wang's approach [7] targetted the entire range of time to be studied. Targetting a wider range of time requires more density matrix eigenstates be kept, slowing the calculation. By targetting only a small interval of time, our approach is nearly as efficient as the Trotter methods. In exchange for the small loss of efficiency, we gain the ability to treat longer range interactions, ladder systems, and narrow two-dimensional strips. In addition, ...

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confidence: 90%

Time-step targeting methods for real-time dynamics using the density matrix renormalization group

2005

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“…The numerical results for the Heisenberg ladder [35] would thus correspond to J ⊥ /J ≈ 1 which is a reasonable value in the undoped ladder limit. This is consistent with the anisotropy ratio which has been derived from the interpretation of the neutron scattering data in La6 introducing a smaller four-spin exchange interaction [38].…”

Section: Knight Shiftsmentioning

confidence: 99%

( Sr / Ca ) 14 Cu 24 O 41 spin ladders studied by NMR under pressure

et al. 2001

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63 Cu-NMR measurements have been performed on two-leg hole-doped spin ladders Sr14−xCaxCu24O41 single crystals 0 ≤ x ≤ 12 at several pressures up to the pressure domain where the stabilization of a superconducting ground state can be achieved. The data reveal a marked decrease of the spin gap derived from Knight shift measurements upon Ca substitution and also under pressure and confirm the onset of low lying spin excitations around Pc as previously reported. The spin gap in Sr2Ca12Cu24O41 is strongly reduced above 20kbar. However, the data of an experiment performed at P = 36kbar where superconductivity has been detected at 6.7K by an inductive technique have shown that a significant amount of spin excitations remains gapped at 80K when superconductivity sets in. The standard relaxation model with two and three-magnon modes explains fairly well the activated relaxation data in the intermediate temperature regime corresponding to gapped spin excitations using the spin gap data derived from Knight shift experiments.The data of Gaussian relaxation rates of heavily doped samples support the limitation of the coherence lenght at low temperature by the average distance between doped holes. We discuss the interplay between superconductivity and the spin gap and suggest that these new results support the exciting prospect of superconductivity induced by the interladder tunnelling of preformed pairs as long as the pressure remains lower than the pressure corresponding to the maximum of the superconducting critical temperature.

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“…The q y = π correlation couples then to states with an odd number of triplet excitations with rung parity P = −1 and total spin S = 1, M z = ±1,0 (see Table I spectral weight is concentrated in a very sharp peak, whose dispersion relation can be approximated using a strong coupling expansion in γ . Up to first order it is simply given by a cosine dispersion, 12 i.e., ω t (q)/J ⊥ ≈ 1 + γ cos q. Further corrections up to third order in γ have been determined in Ref.…”

Section: Single-triplet Excitationsmentioning

confidence: 99%

“…It has been seen previously that in this system both single-triplet excitations and two-triplet excitations play an important role. [12][13][14][15][16] We discuss these excitations in the following, focusing on the ones that can be created by the symmetric S αα 0 = 2S ±∓ 0 and the antisymmetric S αα π = 2S ±∓ π correlations (see Fig. 11) for the BPCB parameters (39).…”

Section: B Excitations In the Spin Liquidmentioning

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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Excitation spectrum of Heisenberg spin ladders

Cited by 420 publications

References 25 publications

Time-step targeting methods for real-time dynamics using the density matrix renormalization group

Time-step targeting methods for real-time dynamics using the density matrix renormalization group

( Sr / Ca ) 14 Cu 24 O 41 spin ladders studied by NMR under pressure

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

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