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P. N. Bibikov

Publications and source records attributed to P. N. Bibikov.

35 records · Page 2Linked to original sources
arXiv2009

Ground state fluctuations in rung-dimerised spin ladders

Treating an exactly rung-dimerized spin ladder as a reference model we study perturbatively zero temperature quantum fluctuations in spin ladders with slightly destroyed rung-dimerization. Analytic expressions are obtained for the gas parameter (density of rung-triplets) and the ground state energy per rung. At a strong diagonal frustration as well as at a rather strong antiferromagnetic rung coupling these results well agree with the previous numerical calculations.

cond-mat.str-el↗
arXiv2009

Three-magnon problem for exactly rung-dimerized spin ladders: from general outlook to Bethe Ansatze

Three-magnon problem for exactly rung-dimerized spin ladder is brought up separately at all total spin sectors. At first a special duality transformation of the $\rm Schr\ddot odinger$ equation is found within general outlook. Then the problem is treated within Coordinate Bethe Ansatze. A straightforward approach is developed to obtain pure scattering states. At values S=0 and S=3 of total spin the $\rm Schr\ddot odinger$ equation has the form inherent in the $XXZ$ chain. For $S=1,2$ solvability holds only in five previously found {\it completely integrable} cases. Nevertheless a partial S=1 Bethe solution always exists even for general non integrable model. Pure scattering states for all total spin sectors are presented explicitly.

cond-mat.str-el↗
arXiv2008

Quantum mechanics not on manifold

The free scalar field is studied on the Y-junction of three semi infinite axes which is the simplest example of a non-manifold space. It is shown that under an assumption that the junction point can not gain a macroscopic amount of energy and charge the transmission rules for this system uniquely follow from conservation of energy and charge. This result is also obtained in the discrete version of the model. Some alternative approaches to the problem based on quantum mechanics of Hamiltonian systems with constrains are discussed.

quant-ph↗
arXiv2007

Magnon mode truncation in a rung-dimerized asymmetric spin ladder

An exactly solvable effective model is suggested for an asymmetric spin ladder with dimerized rungs. Magnon mode truncation originated from magnon decay (recently observed in the 1D compound ${\rm IPA-CuCl}_3$) is naturally described within this model. Using Bethe Ansatze we described a one-magnon sector and obtained relations between interaction constants of the model and experimentally observable quantities such as the gap and truncation energies, spin velocity and the truncation wave vector. It is also shown that structure factor turns to zero at the truncation point.

cond-mat.str-el↗
arXiv2007

R-matrices for integrable $SU(2)\times U(1)$-symmetric S=1/2 spin-orbital chains

The Yang-Baxter equation for a $SU(2)\times U(1)$-symmetric $S=1/2$ spin-orbital chain was solved using the special computer algorithm developed by the author. The 8 new $R$-matrices separated on 5 groups are presented. Among the obtained integrable models there are special cases related to 1D ferromagnet ${\rm TDAE-C}_{60}$, 1D superconductors ${\rm AC}_{60}$ (A=K, Cs, Rb), the quarter filled ladder compound ${\rm NaV}_2{\rm O}_5$ and the model of correlated electrons on a chain of Berry phase molecules.

cond-mat.str-el↗
arXiv2007

Origin of the second coherent peak in the dynamical structure factor of an asymmetric spin-ladder

Appearance of the second coherent peak in the dynamical structure factor of an asymmetric spin ladder is suggested. The general arguments are confirmed by the first order (with respect to the asymmetry) calculation for a spin ladder with singlet-rung ground state. Basing on this result a new interpretation is proposed for the inelastic neutron scattering data in the spin gap compound CuHpCl.

cond-mat.str-el↗
arXiv2007

Defining relations on the Hamiltonians of $XXX$ and $XXZ$ $R$-matrices and new integrable spin-orbital chains

Several complete systems of integrability conditions on a spin chain Hamiltonian density matrix are presented. The corresponding formulas for $R$-matrices are also given. The latter is expressed via the local Hamiltonian density in the form similar to spin one half $XXX$ and $XXZ$ models. The result is applied to the problem of integrability of $SU(2)\times SU(2)$- and $SU(2)\times U(1)$-invariant spin-orbital chains (the Kugel-Homskii-Inagaki model). The eight new integrable cases are found. One of them corresponds to the Temperley-Lieb algebra, the others three to the algebra associated with the $XXX$, $XXZ$ and graded $XXZ$ models. The last two $R$-matrices are also presented.

nlin.SI↗
arXiv2006

Zero-temperature magnetic-field-induced phase transition between two ordered gapped phases in spin-ladders with ferromagnetic legs

We suggest that under an increase of a magnetic field a spin-ladder with ferromagnetic legs does not pass without fail through an incommensurate phase but possibly in a straight way turns into a fully polarized ferromagnetic phase. The spin gap remains finite at the transition point. This scenario is demonstrated for the special spin-ladder model with exact singlet-rung ground state. We suppose that this kind of behavior realizes for the spin-ladder material (5IAP)_2CuBr_4*H_2O

cond-mat.str-el↗
arXiv2005

Two-magnon Raman scattering in spin-ladders with exact singlet-rung ground state

We suggest a family of spin-ladder models with exact singlet-rung vacuum. In addition to the terms describing interactions along legs and rungs the Hamiltonian has frustration and cyclic terms. Using coordinate Bethe ansatze all one- and two-dimensional states are constructed. The explicit formula for zero-temperature Raman scattering cross section is derived. The corresponding line-shapes are strongly asymmetric and have no more than one van-Hove singularity. The results are in good agreement with experimental data.

cond-mat.str-el↗
arXiv2005

One-magnon states and electron spin resonance in spin-ladders with singlet-rung ground statein a staggered magnetic field

One-magnon problem for spin-ladders with exact singlet-rung ground state in arbitrary oriented constant and staggered magnetic fields is studied. For two special configurations when the both fields are parallel or perpendicular to each other the exact formulas for eigenstates and eigenvectors are presented. In the parallel case the one-magnon contribution to the ESR absorption line shape is obtained. The latter is non-Lorentzian, has finite range and a gap around resonance. For low fields both the range of the spectrum and the width of the gap are controlled by the width of the one-magnon zone in zero magnetic field. Some other interactions usually contributing to the ESR line shape are also briefly discussed.

cond-mat.str-el↗
arXiv2000

Derivation of R-matrix from local Hamiltonian density

A computer algebra algoritm for solving the quantum Yang-Baxter equation is presented. It is based on the Taylor expansion of R-matrix which is developed up to the order λ^6. As an example the classification of 4x4 R-matrices is given.

nlin.SI↗