Asymmetric spin-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mstyle scriptlevel="1"><mml:mfrac bevelled="false"><mml:mn>1</mml:mn><mml:mn>2</mml:mn></mml:mfrac></mml:mstyle></mml:mrow></mml:math>two-leg ladders: Analytical studies supported by exact diagonalization, DMRG, and Monte Carlo simulations

Aristov, D. N.; Brünger, C.; Assaad, Fakher F.; Kiselev, M. N.; Weichselbaum, Andreas; Capponi, Sylvain; Alet, Fabien

doi:10.1103/physrevb.82.174410

Cited by 17 publications

(16 citation statements)

References 55 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Firstly, it creates finite magnetization of the nuclear spins, m z = 0, and this leads to a decrease in the mass gap (21). Secondly, as we discuss below, for fields above the threshold, µ B B > Λ 1 , the magnetization appears in the Heisenberg spin sector.…”

Section: Extracting the Resultsmentioning

confidence: 99%

See 1 more Smart Citation

Heisenberg necklace model in a magnetic field

Tsvelik

Zaliznyak

2016

Phys. Rev. B

View full text Add to dashboard Cite

We study the low-energy sector of the Heisenberg Necklace model. Using the field theory methods, we estimate how the coupling of the electronic spins with the paramagnetic Kondo spins affects the overall spins dynamics and evaluate its dependence on a magnetic field. We are motivated by the experimental realizations of the spin-1/2 Heisenberg chains in SrCuO 2 and Sr 2 CuO 3 cuprates, which remain one-dimensional Luttinger liquids down to temperatures much lower than the inchain exchange coupling, J. We consider the perturbation of the energy spectrum caused by the interaction, γ, with nuclear spins (I = 3/2) present on the same sites. We find that the resulting Necklace model has a characteristic energy scale, Λ ∼ J 1/3 (γI) 2/3 , at which the coupling between (nuclear) spins of the necklace and the spins of the Heisenberg chain becomes strong. This energy scale is insensitive to a magnetic field, B. For µ B B > Λ we find two gapless bosonic modes that have different velocities, whose ratio at strong fields approaches a universal number, √ 2 + 1.

show abstract

Section: Extracting the Resultsmentioning

confidence: 99%

“…This model, which is an extension of the Kondo necklace model, [18] was previously considered in the context of the Haldane gap problem, where authors tagged it a spin-rotator chain, [20,21].…”

Section: Introductionmentioning

confidence: 99%

Heisenberg necklace model in a magnetic field

Tsvelik

Zaliznyak

2016

Phys. Rev. B

View full text Add to dashboard Cite

show abstract

“…The ME method has an appealing footing in probability theory, but in many cases the entropic prior regularizes the spectrum too heavily, leading to excessive broadening and distortions. To avoid this, an alternative line of methods has been developed [6][7][8][9][10] (and applied to diverse systems [11][12][13][14]) which do not impose the entropic prior, instead using stochastic sampling of A(ω) with the probability distribution…”

mentioning

confidence: 99%

Constrained sampling method for analytic continuation

2016

View full text Add to dashboard Cite

A method for analytic continuation of imaginary-time correlation functions (here obtained in quantum Monte Carlo simulations) to real-frequency spectral functions is proposed. Stochastically sampling a spectrum parametrized by a large number of delta-functions, treated as a statisticalmechanics problem, it avoids distortions caused by (as demonstrated here) configurational entropy in previous sampling methods. The key development is the suppression of entropy by constraining the spectral weight to within identifiable optimal bounds and imposing a set number of peaks. As a test case, the dynamic structure factor of the S = 1/2 Heisenberg chain is computed. Very good agreement is found with Bethe Ansatz results in the ground state (including a sharp edge) and with exact diagonalization of small systems at elevated temperatures. Obtaining real-frequency dynamic response functions from imaginary-time correlations remains one of the outstanding challenges for quantum Monte Carlo (QMC) and related simulation methods (e.g., lattice QCD). The general form of the problem is to invert the relationshipwhere a QMC estimateG(τ ) of the correlation function G(τ ) is available, A(ω) is the spectral function sought, and the kernel K(τ, ω) depends on the type of spectral function. Similar to an inverse Laplace transform, there is no closed form for A(ω). Only broad features of A(ω) can be resolved in numerical analytic continuation, because information on fine structure is only present at a level of precision of G(τ ) which is not attainable in practice. Nevertheless, one can extract important dynamical features and the key question is how to do that with the maximum fidelity, givenG(τ ) and its statistical errors. Significant progress will be presented here. The Maximum Entropy (ME) method [1] was adapted to the particulars of QMC some time ago [2]. Overcoming problems of previous approaches [3,4], it quickly became a standard tool [5]. The ME method has an appealing footing in probability theory, but in many cases the entropic prior regularizes the spectrum too heavily, leading to excessive broadening and distortions. To avoid this, an alternative line of methods has been developed [6][7][8][9][10] (and applied to diverse systems [11-14]) which do not impose the entropic prior, instead using stochastic sampling of A(ω) with the probability distributionwhere χ 2 is the standard measure of the goodness of the fit of G(τ ) obtained from A(ω) according to Eq. (1) to the QMC-computedG(τ ) with its full covariance matrix [5,8] for a set {τ i }. The spectrum is typically parametrized as a sum of a large number of δ-functions, though other forms have also been used [10]. The sampling temperature Θ in Eq. (2) acts as a regularizing parameter.An important insight was gained by Beach [7], showing that a mean-field treatment of the sampling approach gives the ME method, with Θ corresponding to the entropic weight. Subsequently, Syljuåsen argued for fixing Θ = 1 [8] (as had also been done by White in earlier work Here a previously overlook...

show abstract

“…All systems analyzed exhibit smoothly changing incommensurate behavior for finite J ′ < J For comparison, also the spin-gap ∆ S was calculated for the systems up to width-8 with rudimentary finite-size scaling only. 31 The spin-gap ∆ S was obtained by calculating the ground state energy E S 0 for increasing total spin S of a system with plain cylindrical boundary conditions, i. e. in the absence of pinning fields or smoothing of the boundary. In avoiding fully periodic boundary conditions for numerical but also physical reasons [i. e. accounting for incommensurate behavior], the open boundary at the end of the cylinder can carry spinful edge excitations.…”

mentioning

confidence: 99%

“…The energy of this state relative to the global ground state was used to estimate the spin-gap ∆ S . 31 …”

mentioning

confidence: 99%

Incommensurate correlations in the anisotropic triangular Heisenberg lattice

Weichselbaum

White

2011

Phys. Rev. B

View full text Add to dashboard Cite

We study the anisotropic spin-half antiferromagnetic triangular Heisenberg lattice in two dimensions, seen as a set of chains with couplings J (J ′ ) along (in between) chains, respectively. Our focus is on the incommensurate correlation that emerges in this system in a wide parameter range due to the intrinsic frustration of the spins. We study this system with traditional DMRG using cylindrical boundary conditions to least constrain possible incommensurate order. Despite that the limit of essentially decoupled chains J ′ /J 0.5 is not very accessible numerically, it appears that the spin-spin correlations remain incommensurate for any finite 0 < J ′ < J

show abstract

Asymmetric spin-12two-leg ladders: Analytical studies supported by exact diagonalization, DMRG, and Monte Carlo simulations

Cited by 17 publications

References 55 publications

Heisenberg necklace model in a magnetic field

Heisenberg necklace model in a magnetic field

Constrained sampling method for analytic continuation

Incommensurate correlations in the anisotropic triangular Heisenberg lattice

Contact Info

Product

Resources

About