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P. N. Bibikov

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

At least 19 recordsLinked to original sources
arXiv2026

The competition between low-temperature kinks and magnons at the vicinity of the deconfinement transition point in 1D easy-axis XXZ ferromagnet

Studying the ordered phases and quantum supercritical low-temperature regime at the vicinity of the deconfinement transition point in 1D easy-axis XXZ ferromagnet, we suggest their interpretations according to the corresponding dominant lowest-energy excitations. We show, that the two ordered phases are governed by magnons, while the quantum supercritical regime is governed by kinks. Within this framework the Ising model is treated in detail.

cond-mat.str-el↗
arXiv2025

Thermodynamics of the XX spin chain in the QTM approach

The free energy density of the XX chain in magnetic field is obtained in two alternative ways within the Quantum Transfer Matrix approach. In both the cases the proofs are complete and self-consistent. All the intermediate constructions are presented explicitly in detail.

cond-mat.stat-mech↗
arXiv2024

R-matrix for the XX spin chain in a staggered magnetic field

We suggest the elliptic $16\times16$ R-matrix for the XX spin chain in a staggered magnetic field. This integrable model is a special case of the more general one, studied long ago within the alternative approach by V. M. Kontorovich and V. M. Tsukernik. The Yang-Baxter equation is verified with the full rigorous only in the two special degenerate trigonometric cases. For the general one, studying the first terms of the Taylor expansions for the $R$-matrix entries, we give the strong evidence for implementation of the Yang-Baxter equation.

nlin.SI↗
arXiv2024

R-matrix for the XX spin chain at the special imaginary value of staggered magnetic field

It is pointed, that the $16\times16$ Hamiltonian density matrix, corresponding to XX spin chain in a staggered magnetic field, satisfies the Reshetikhin condition as well, as the two higher ones. All of them are necessary for the existence of the corresponding $R$-matrix. At the special imaginary value of the staggered field, the $R$-matrix is obtained explicitly. It is shown that the corresponding Hamiltonian has purely imaginary spectrum.

nlin.SI↗
arXiv2024

Magnon peak lineshape in the transverse dynamical structure factor of a magnetically polarized easy-axis $XXZ$ chain at low temperatures

The ferromagnetically polarized gapped XXZ spin chain is studied at low temperatures. Utilizing only the one- and two-magnon spectrums and focusing on the magnon-creation contribution to the transverse dynamical susceptibility, we represent the latter in the form of the Dyson equation. Then, following the well known correspondence between the imaginary part of magnetic susceptibility and dynamical structure factor, we get the low-temperature formula for the magnon-peak lineshape. The suggested approach is effective only if the processes related to magnon creations and to transitions from magnons to coupled magnon pairs are energetically separated. As it is shown in the paper, such separation is inherent in the easy-axis chains with rather strong anisotropy. We present several plots and discuss their lineshapes. As the supplemental result we obtain integral representations for the temperature-dependent magnon resonance shift and the parameter which is usually associated with the decay rate. The low-temperature behavior of the resonance shift is studied in details. All calculations are performed up to {\it controllable} error $o({\rm e}^{-βE_{gap}})$.

cond-mat.str-el↗
arXiv2022

Low-temperature asymptotics for transverse autocorrelator of the magnetically polarized Ising chain studied by ordinary and nested Dyson equations

Suggesting two versions for the Plakida-Tserkovnikov algorithm breakdown in the low-temperature regime, we derive ordinary and nested Dyson equations for the transverse autocorrelator of the magnetically polarized Ising chain. Using them we get the corresponding low-temperature asymptotics for the autocorrelator. We show that the ordinary Dyson equation results in a correct $o({\rm e}^{-βE_{gap}})$ account of the magnon creation process, while the nested Dyson equation additionally gives the correct $o({\rm e}^{-βE_{gap}})$ contribution associated with transitions from magnons to bound two-magnon states. The obtained result may be useful for the extension of the suggested approach on the polarized $XXZ$-chain.

cond-mat.str-el↗
arXiv2021

Thermodynamics of an Ising-like XXZ chain in a longitudinal magnetic field in the framework of the Quantum Transfer Matrix approach

Taking the Ising chain as a reference model we have derived a perturbative expression for the free energy density of the Heisenberg-Ising chain with strong easy-axis anisotropy. All calculations are performed on the ground of the Quantum Transfer Matrix approach. The obtained result agrees with the direct high-temperature expansion. It also agrees with the low-temperature cluster expansion in the special subregime when quantum fluctuations are weak against thermodynamical ones.

cond-mat.str-el↗
arXiv2020

Low-temperature asymptotics for the transverse dynamical structure factor for a magnetically polarized $XX$ chain at small and negative frequencies

Using the truncated form factor expansion the low-temperature asymptotics for the transverse dynamical structure factor of the magnetically polarized $XX$ chain is studied. Unlike the previous paper we do not use the representation of structure factor in terms of the corresponding magnetic susceptibility. This enables to obtain correct results at small and negative frequencies.

cond-mat.str-el↗
arXiv2020

Low-temperature asymptotic of the transverse dynamical structure factor for a magnetically polarized XX chain

Dyson equation for the real two-time commutator retarded one-magnon Green function of the ferromagnetically polarized XX chain is suggested following the Plakida-Tserkovnikov algorithm. Starting from this result a low-temperature integral representation for the corresponding magnon self energy is obtained by the truncated form factor expansion however without any resummations. Within the suggested approach the low-temperature asymptotics of the transverse dynamical structure factor may be readily studied. Some obtained line shapes are presented.

cond-mat.str-el↗
arXiv2018

Bethe Ansatz for two-magnon scattering states in 2D and 3D Heisenberg-Ising ferromagnets

Various versions of the Bethe ansatz are suggested for evaluation of scattering two-magnon states in 2D and 3D Heisenberg-Ising ferromagnets. It is shown that for 2D square (3D qubic) finite-periodic or infinite lattices about a half (3/4) of states have a correctly 2D- (3D-) generalized Bethe form. The remaining scattering states are treated (on the infinite lattices only) within the degenerative discrete-diffractive modification of the Bethe ansatz previously suggested by the author.

cond-mat.str-el↗
arXiv2015

Second cluster integral from the spectrum of an infinite XXZ spin chain

First and second terms of the low-temperature cluster expansion for the free energy density of a magnetically polarized $XXZ$ spin chain is obtained within the propagator approach suggested by E. W. Montroll and J. C. Ward. All the calculations employ only one- and two-magnon infinite-chain spectrums. In the $XXX$-point the result reproduces the well known S. Katsura's formula obtained 50 years ago by finite-chain calculations.

cond-mat.str-el↗
arXiv2012

On the ground state energy scaling in quasi-rung-dimerized spin ladders

On the basis of periodic boundary conditions we study perturbatively a large N asymptotics (N is the number of rungs) for the ground state energy density and gas parameter of a spin ladder with slightly destroyed rung-dimerization. Exactly rung-dimerized spin ladder is treated as the reference model. Explicit perturbative formulas are obtained for three special classes of spin ladders.

cond-mat.str-el↗
arXiv2010

Three-magnon bound states in exactly rung-dimerized spin ladders

Three magnon bound states in all total spin sectors of general nonintegrable exactly rung-dimerized spin ladder are obtained by Bethe Ansatz. Basing on this result a dispersion law for $m$-magnon ($m>3$) bound states is conjectured. It is suggested that (depending on correlations between coupling constants) a behavior of the gas parameter (density of rung-triplets) on the boundary of the rung-dimerized phase may either be smooth or have a leap.

cond-mat.str-el↗
arXiv2009

A model with generalized Y-junction

The Klein-Fock-Gordon equation is studied on the generalized Y-junction of $N$ strings with a massive center. The corresponding formulas for wave scattering and normal modes are obtained.

math-ph↗