Spin Gap and String Order Parameter in the Ferromagnetic Spiral Staircase Heisenberg Ladder: A Quantum Monte Carlo Study

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

doi:10.1103/physrevlett.100.017202

Cited by 12 publications

(24 citation statements)

References 27 publications

(23 reference statements)

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“…While such a fit is reasonable for low J Ќ as remarked in Ref. 23, the above exponential form appears to provide a better fit in a larger J Ќ window.…”

Section: Quantum Monte Carlo Spin Gapsupporting

confidence: 54%

“…͑c͒ In our previous paper 23 we also pointed out the existence of the intermediate asymptotic, ͉i − j͉ −1/3 , in case J Ќ = 0.3J ʈ . The existence of such power-law decay is interesting on its own but the detailed description of this regime is beyond the scope of this study.…”

Section: B Quantum Monte Carlo Spin Correlationsmentioning

confidence: 74%

“…23 for J Ќ = 0.3J ʈ . We did not discuss this situation in the present paper since at these parameters the correlation length is larger than the system size and the true string order parameter is not formed, cf.…”

Section: Discussionmentioning

confidence: 99%

“…It was implied in Ref. 23 that the scaling of the gap with J Ќ changes at a critical c ϳ . The above consideration suggests that there is no critical but rather a smooth crossover between two regimes, cf.…”

Section: ͑16͒mentioning

confidence: 99%

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

et al. 2010

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We consider asymmetric spin-1 2 two-leg ladders with nonequal antiferromagnetic ͑AF͒ couplings J ʈ and J ʈ along legs ͑ Յ 1͒ and ferromagnetic rung coupling, J Ќ . This model is characterized by a gap ⌬ in the spectrum of spin excitations. We show that in the large J Ќ limit this gap is equivalent to the Haldane gap for the AF spin-1 chain, irrespective of the asymmetry of the ladder. The behavior of the gap at small rung coupling falls in two different universality classes. The first class, which is best understood from the case of the conventional symmetric ladder at = 1, admits a linear scaling for the spin gap ⌬ ϳ J Ќ . The second class appears for a strong asymmetry of the coupling along legs, J ʈ Ӷ J Ќ Ӷ J ʈ and is characterized by two energy scales: the exponentially small spin gap ⌬ ϳ J Ќ exp͑−J ʈ / J Ќ ͒, and the bandwidth of the low-lying excitations induced by a Suhl-Nakamura indirect exchange ϳJ Ќ 2 / J ʈ . We report numerical results obtained by exact diagonalization, densitymatrix renormalization group and quantum Monte Carlo simulations for the spin gap and various spin correlation functions. Our data indicate that the behavior of the string order parameter, characterizing the hidden AF order in Haldane phase, is different in the limiting cases of weak and strong asymmetries. On the basis of the numerical data, we propose a low-energy theory of effective spin-1 variables, pertaining to large blocks on a decimated lattice.

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“…While such a fit is reasonable for low J Ќ as remarked in Ref. 23, the above exponential form appears to provide a better fit in a larger J Ќ window.…”

Section: Quantum Monte Carlo Spin Gapsupporting

confidence: 54%

Section: B Quantum Monte Carlo Spin Correlationsmentioning

confidence: 74%

Section: Discussionmentioning

confidence: 99%

Section: ͑16͒mentioning

confidence: 99%

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

et al. 2010

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“…17,18 As an illustration of our generic interaction model we consider a ladder which has been compressed so that the legs form a zigzag with a constant angle , as shown in Fig. 1͑b͒.…”

Section: Introductionmentioning

confidence: 99%

Generic short-range interactions in two-leg ladders

Bunder

Lin

2009

Phys. Rev. B

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We derive a Hamiltonian for a two-leg ladder which includes an arbitrary number of charge and spin interactions. To illustrate this Hamiltonian we consider two examples and use a renormalization group technique to evaluate the ground state phases. The first example is a two-leg ladder with zigzagged legs. We find that increasing the number of interactions in such a two-leg ladder may result in a richer phase diagram, particularly at half-filling where a few exotic phases are possible when the number of interactions are large and the angle of the zigzag is small. In the second example we determine under which conditions a two-leg ladder at quarter-filling is able to support a Tomanaga-Luttinger liquid phase. We show that this is only possible when the spin interactions across the rungs are ferromagnetic. In both examples we focus on lithium purple bronze, a two-leg ladder with zigzagged legs which is though to support a Tomanaga-Luttinger liquid phase.

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Phonon transport properties of a mass–spring simple cubic nanocrystal within the harmonic approximation

Mardaani

Rabani

Keshavarz

2012

Physica E: Low-dimensional Systems and Nanostructures

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Spin Gap and String Order Parameter in the Ferromagnetic Spiral Staircase Heisenberg Ladder: A Quantum Monte Carlo Study

Cited by 12 publications

References 27 publications

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

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

Generic short-range interactions in two-leg ladders

Phonon transport properties of a mass–spring simple cubic nanocrystal within the harmonic approximation

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