arXiv subjects

S. B. Rutkevich

Publications and source records attributed to S. B. Rutkevich.

At least 19 recordsLinked to original sources

arXiv2024

Confinement of spinons in the XXZ spin-1/2 chain in presence of the transverse magnetic field

We study the tuning effect of a transverse magnetic field on the confinement of spinons in the infinite XXZ spin-1/2 chain. The spinon confinement in this model takes place in the gapped antiferromagnetic phase upon application of a staggered longitudinal magnetic field. The tuning transverse magnetic field has mutually orthogonal uniform and staggered components. The energy spectra of the two-spinon bound states (the `mesons') in the confinement regime are analytically calculated in this model using two different perturbative schemes. The first one applies in the extreme anisotropic (Ising) limit and employs the inverse anisotropy constant as a small parameter. The second perturbative scheme, which applies at any anisotropy in the gapped antiferromagnetic domain, exploits the integrability of the XXZ spin chain at zero magnetic field. The small parameters in the second technique are the components of the transverse, and staggered longitudinal magnetic fields. It is shown, that the weak transverse magnetic field mixes the transverse and longitudinal meson modes, and leads to an avoided crossing of their energies upon increase of its strength. The explicit formulas for the two-spinon contribution to the dynamical structure factors of local spin operators are obtained as well in this model in the weak confinement regime for wave-vectors close to the points k = 0 and k = π.

cond-mat.str-el↗

arXiv2023

Soliton confinement in the double sine-Gordon model

The double sine-Gordon field theory in the weak confinement regime is studied. It represents the small non-integrable deformation of the standard sine-Gordon model caused by the cosine perturbation with the frequency reduced by the factor of 2. This perturbation leads to the confinement of the sine-Gordon solitons, which become coupled into the 'meson' bound states. We classify the meson states in the weak confinement regime, and obtain three asymptotic expansions for their masses, which can be used in different regions of the model parameters. It is shown, that the sine-Gordon breathers, slightly deformed by the perturbation term, transform into the mesons upon increase of the sine-Gordon coupling constant.

hep-th↗

arXiv2022

Spinon confinement in the gapped antiferromagnetic XXZ spin-1/2 chain

The infinite Heisenberg XXZ spin-(1/2) chain in the gapped antiferromagnetic regime has two degenerate vacua and kink topological excitations (which are also called spinons) interpolating between these vacua as elementary excitations. Application of an arbitrary weak staggered longitudinal magnetic field h induces a long-range attractive potential between two adjacent spinons leading to their confinement into 'meson' bound states. Exploiting the integrability of the XXZ model in the deconfined phase h = 0, we perform perturbative calculations of the energy spectra of the two-spinon bound states in the weak confinement regime at h \to +0, using the strength of the staggered magnetic field h as a small parameter. Both transverse and longitudinal dynamical structure factors of the local spin operators are calculated as well in the two-spinon approximation in the weak confinement regime to the leading order in h.

cond-mat.str-el↗

arXiv2020

On the ground-state energy of the finite sine-Gordon ring

The Casimir scaling function characterising the ground-state energy of the sine-Gordon model in a finite circle has been studied analytically and numerically both in the repulsive and attractive regimes. The numerical calculations of the scaling function at several values of the coupling constant were performed by the iterative solution of the Destri-de Vega nonlinear integral equations. The ultraviolet asymptotics of the Casimir scaling functions was calculated by perturbative solution of these equations, and by means of the perturbed conformal field-theory technique, and compared with numerical results.

cond-mat.stat-mech↗

arXiv2020

Scaling in the massive antiferromagnetic XXZ spin-1/2 chain near the isotropic point

The scaling limit of the Heisenberg XXZ spin chain at zero magnetic field is studied in the gapped antiferromagnetic phase. For a spin-chain ring having $N_x$ sites, the universal Casimir scaling function, which characterises the leading finite-size correction term in the large-$N_x$ expansion of the ground state energy, is calculated by numerical solution of the nonlinear integral equation of the convolution type. It is shown, that the same scaling function describes the temperature dependence of the free energy of the infinite XXZ chain at low enough temperatures in the gapped scaling regime.

cond-mat.stat-mech↗

arXiv2018

A formula for eigenvalues of Jacobi matrices with a reflection symmetry

The spectral properties of two special classes of Jacobi operators are studied. For the first class represented by the $2M$-dimensional real Jacobi matrices whose entries are symmetric with respect to the secondary diagonal, a new polynomial identity relating the eigenvalues of such matrices with their matrix { entries} is obtained. In the limit $M\to\infty$ this identity induces some requirements, which should satisfy the scattering data of the resulting infinite-dimensional Jacobi operator in the half-line, which super- and sub-diagonal matrix elements are equal to -1. We obtain such requirements in the simplest case of the discrete Schrödinger operator acting in ${l}^2( \mathbb{N})$, which does not have bound and semi-bound states, and which potential has a compact support.

math-ph↗

arXiv2018

Kink confinement in the antiferromagnetic XXZ spin-1/2 chain in a weak staggered magnetic field

The Heisenberg XXZ spin-1/2 chain is considered in the massive antiferromagnetic regime in the presence of a staggered longitudinal magnetic field. The Hamiltonian of the model is characterised by the anisotropy parameter $Δ<-1$, and by the magnetic field strength h. At zero magnetic field, the model is exactly solvable. In the thermodynamic limit, it has two degenerate vacua and the kinks (which are also called spinons) interpolating between these vacua, as elementary excitations. Application of the staggered magnetic field breaks integrability of the model and induces the long-range attractive potential between two adjacent kinks leading to their confinement into the bound states. The energy spectra of the resulting two-kink bound states are perturbatively calculated in the extreme anisotropic (Ising) limit $Δ\to-\infty$ to the first order in the inverse anisotropy constant $|Δ|^{-1}$, and also for generic values of $Δ<-1$ to the first order in the weak magnetic field h.

cond-mat.stat-mech↗

arXiv2017

Radiative corrections to the quark masses in the ferromagnetic Ising and Potts field theories

We consider the Ising Field Theory (IFT), and the 3-state Potts Field Theory (PFT), which describe the scaling limits of the two- dimensional lattice q-state Potts model with q=2, and q=3, respectively. At zero magnetic field h=0, both field theories are integrable away from the critical point, have q degenerate vacua in the ferromagnetic phase, and q(q-1) particles of the same mass - the kinks interpolating between two different vacua. Application of a weak magnetic field induces confinement of kinks into bound states - the mesons (for q =2,3) consisting predominantly of two kinks, and baryons (for q=3), which are essentially the three-kink excitations. The kinks in the confinement regime are also called the quarks. We review and refine the Form Factor Perturbation Theory (FFPT), adapting it to the analysis of the confinement problem in the limit of small h, and apply it to calculate the corrections to the kink (quark) masses induced by the multi-kink fluctuations caused by the weak magnetic field. It is shown that the subleading third-order correction to the kink mass vanishes in the IFT. The leading second order correction to the kink mass in the 3-state PFT is estimated by truncation the infinite form factor expansion at the first term representing contribution of the two-kink fluctuations into the kink self energy.

cond-mat.stat-mech↗

arXiv2014

Baryon masses in the three-state Potts field theory in a weak magnetic field

The 3-state Potts field theory describes the scaling limit of the 3-state Potts model on the two-dimensional lattice near its continuous phase transition point. In the presence of thermal and magnetic field perturbations, the 3-state Potts field theory in the ordered phase exhibits confinement of kinks, which allows both mesons and baryons. We calculate the masses of light baryons in this model in the weak confinement regime in leading order of the small magnetic field. In leading order of perturbation theory, the light baryons can be viewed as bound states of three quantum particles - the kinks, which move on a line and interact via a linear potential. We determine the masses of the lightest baryons by numerical solution of the associated non-relativistic one-dimensional quantum three-body problem.

cond-mat.stat-mech↗

arXiv2014

The O(n) $ϕ^4$ model with free surfaces in the large-$n$ limit: Some exact results for boundary critical behaviour, fluctuation-induced forces and distant-wall corrections

The $O(n)$ $ϕ^4$ model on a slab $\mathbb{R}^{d-1}\times[0,L]$ bounded by free surfaces is studied for $2<d<4$ in the limit $n\to\infty$. The self-consistent potential $V(z)$ which the exact $n\to\infty$ solution of the model involves is analysed by means of boundary operator expansions. Building on the known exact $n\to\infty$ solution for $V(z)$ in the semi-infinite case $L=\infty$ at the bulk critical point, we exactly determine two types of corrections to this potential: (i) those linear in the temperature scaling field $t$ at $L=\infty$, and (ii) the leading $L$-dependent (distant-wall) corrections at the critical point. From (i) exact analytical results at $d=3$ are obtained for the leading temperature singularity of the excess surface free energy and the implied asymptotic behaviours of the scaling functions $Θ_3(x)$ and $\vartheta_3(x)$ of the residual free energy $f_{\rm res} =L^{1-d}\,Θ_d(tL)$ and the critical Casimir force $β\mathcal{F}_{\rm C}(T,L)=L^{-d}\,\vartheta_d(tL)$ in the limit $x\to 0\pm$. The second derivative $\vartheta_3''(0)$ is computed exactly.

cond-mat.stat-mech↗

arXiv2013

Non-Linear Spin Dynamics Of The Electron Liquid In Nanosystems

We investigate the dynamics of spin-nonequilibrium electron systems in the hydrodynamic flow regime, when the normal scattering processes, which conserve the total quasi-momentum of the system of electrons and quasi-particles that interact with them, dominate over other scattering processes. We obtain a set of spin-hydrodynamic equations for the case of an arbitrary electron spectrum that varies slowly with the coordinates. Solving the one-dimensional non-linear problem we found the exact solutions both for the electrical potential in the open-ends circuit and for the spin-electrical oscillation in an inhomogeneous conducting ring. As we demonstrate, the oscillation characteristics are different in the cases of a magnetic ring and a non-magnetic ring to which the spin polarization was injected. We found also that a voltage between the ends of the open circuit may reveal the presence of an inhomogeneous spin polarization of the electron density.

cond-mat.mes-hall↗

arXiv2012

Partial thermalization in the quantum chain of harmonic oscillators

This preprint contains the English translation of the paper "Relaxation dynamics of a quantum chain of harmonic oscillators", which was published by the author in 1980 in the Ukrainian Physical Journal. Comments describing its motivations, background ideas and results are presented as well. This paper addressed to the problem of approach to the thermal equilibrium in an isolated macroscopic quantum system, which was studied on the example of the quantum chain of weakly interacting harmonic oscillators. In the initial state, macroscopic energy was supplied to one oscillator (atom) in the chain. Subsequent evolution of the quantum state of the whole chain was determined due to the model integrability. The main subject of interest was the time evolution of the reduced density operators characterizing the quantum state of a particular atom. On the short time-scale, the energy perturbation expands along the chain with the velocity of the fastest phonon mode. On the long-time scale, the single-atom density operators display strong fluctuations around the canonical Gibbs distribution. These fluctuations are caused by the degeneracy of the energy level differences (presence of resonances) in the model of coupled harmonic oscillators. After lifting this degeneracy, fluctuations are suppressed providing, that the reduced density operator of each atom in the chain becomes very close to the Gibbs distribution at almost any time moment.

cond-mat.stat-mech↗

arXiv2010

On the weak confinement of kinks in the one-dimensional quantum ferromagnet CoNb2O6

In a recent paper Coldea et al (2010 Science {\bf 327} 177) report observation of the weak confinement of kinks in the Ising spin chain ferromagnet CoNb2O6 at low temperatures. To interpret the entire spectra of magnetic excitations measured via neutron scattering, they introduce a phenomenological model, which takes into account only the two-kink configurations of the spin chain. We present the exact solution of this model. The explicit expressions for the two-kink bound-state energy spectra and for the relative intensities of neutron scattering on these magnetic modes are obtained in terms of the Bessel function.

cond-mat.stat-mech↗

arXiv2010

Two-kink bound states in the magnetically perturbed Potts field theory at T<Tc

The q-state Potts field theory with $2\le q\le 4$ in the low-temperature phase is considered in presence of a weak magnetic field h. In absence of the magnetic field, the theory is integrable, but not free at q>2: its elementary excitations - the kinks - interact at small distances, and their interaction can be characterized by the factorizable scattering matrix which was found by Chim and Zamolodchikov. The magnetic field induces the long-range attraction between kinks causing their confinement into the bound-states. We calculate the masses of the two-kink bound states in the leading order in |h| -> 0 expressing them in terms of the scattering matrix of kinks at h=0.

cond-mat.stat-mech↗

arXiv2009

Formfactor perturbation expansions and confinement in the Ising field theory

We study the particle spectrum M_n(h) in the two-dimensional ferromagnetic Ising field theory in a weak external magnetic field h. According to Wu and McCoy scenario of the weak confinement, pairs of fermions (domain walls) are coupled into bosonic kink-antikink bound states at small h>0. Fluctuations with more than two fermions also contribute to the wave functions of the compound particles, leading to the multi-fermion corrections to their masses M_n(h) in higher orders in h. We describe a perturbative procedure, which allows to account both multi-fermion fluctuations, and the long-range confining interaction between fermions, and leads to the formfactor expansions for the renormalized parameters of the model. We obtain integral representations for the third-order multi-fermion correction to the mass M_n(h), which arise from the regular correction to the kernel of the Bethe-Salpeter equation.

cond-mat.stat-mech↗

arXiv2007

Energy spectrum of bound-spinons in the quantum Ising spin-chain ferromagnet

We study the excitation energy spectrum in the S=1/2 ferromagnetic Ising spin chain with the easy axis z in a magnetic field h={h_x,0,h_z}. According to Wu and McCoy's scenario of weak confinement, the fermionic spinon excitations (kinks), being free at h_z = 0 in the ordered phase, are coupled into bosonic bound states at arbitrary small h_z. We calculate the energy spectrum of such excitations in the leading order in small h_z, using different perturbative methods developed for the similar problem in the Ising field theory.

cond-mat.stat-mech↗

arXiv2005

Large-n excitations in the ferromagnetic Ising field theory in a small magnetic field: mass spectrum and decay widths

In presence of a small magnetic field h, the elementary excitations in the scaling two-dimensional Ising model are studied perturbatively in h in the ferromagnetic phase. For excitations with large numbers n, the mass spectrum is obtained in the first order in h. The decay widths of excitations with energies above the stability threshold are calculated in the leading h^3-order.

hep-th↗

arXiv2002

Monte-Carlo simulation of nucleation in the two-dimensional Potts model

Nucleation in the two-dimensional q-state Potts model has been studied by means of Monte-Carlo simulations using the heat-bath dynamics. The initial metastable state has been prepared by magnetic quench of the ordered low-temperature phase. The magnetic field dependence of the nucleation time has been measured as the function of the magnetic field for different q and lattice sizes at T=0.5 Tc. A size-dependent crossover from the coalescence to nucleation region is observed at all q. The magnetic field dependence of the nucleation time is roughly described by the classical nucleation theory. Our data show increase of the anisotropy in the shape of the critical droplets with increase of q.

cond-mat.stat-mech↗