arXiv subjects

A. Sedrakyan

Publications and source records attributed to A. Sedrakyan.

At least 19 recordsLinked to original sources

arXiv2026

Critical couplings of two dimensional Ising model on various lattices

We develop a unified fermionic-field formulation of the two-dimensional Ising model on several planar lattices using the Kac--Ward representation. Grassmann fields are associated with directed lattice links, while the turning of a fermionic trajectory at a lattice vertex is encoded by the corresponding Kac--Ward phase factor. Within this approach the partition function is expressed through the determinant of a finite-dimensional momentum-space matrix, whose zeros determine the excitation spectrum and the critical coupling. We apply the method to the regular square, honeycomb, triangular, kagomé, and dual kagomé (dice or $T_3$) lattices. In all cases the known exact critical couplings are reproduced. Particular attention is given to the anisotropic kagomé lattice, for which the fermionic determinant yields the complete critical surface and the low-energy spectral equation. We also construct the fermionic action for the dual kagomé lattice and derive its anisotropic critical condition. In the isotropic dice model the spectrum reduces at low energy and momentum to a relativistic massive form, with the mass vanishing at $\cosh(2J_c)=(1+\sqrt3)/2$. The results demonstrate that the same fermionic construction provides a compact description of criticality and low-energy excitations for Ising models on lattices with different local geometries and coordination numbers.

cond-mat.stat-mech↗

arXiv2026

Thermal effect on the anomaly-induced electromechanical response in gapped graphene

Mechanical deformation of gapped graphene can act on Dirac quasiparticles as an emergent gauge field. When this deformation field couples to the same current as the electromagnetic field, the parity anomaly produces a mixed electromechanical Chern-Simons response: a phonon electric field drives a transverse electrical current, and a phonon magnetic field binds charge. Previous zero-temperature results predict a sharp change in the response when the chemical potential crosses the band edge. We show that finite temperature replaces this sharp feature by a universal smooth crossover controlled only by the ratios of temperature, gap, and chemical potential. The response remains almost quantized in the insulating regime, is rounded over a gate window of order temperature near the band edge, and approaches the doped Berry-curvature result with a controlled Sommerfeld correction. We apply the result to two experimentally useful drives: a traveling flexural wave, which produces a transverse second-harmonic current, and a dynamic phonon mixed with a static ripple, which produces a fundamental-frequency signal. The same gate-temperature line shape controls both signals. This gives a direct way to separate the anomaly-induced current from ordinary electromechanical backgrounds and to extract the effective gap and electronic temperature in graphene devices.

cond-mat.mes-hall↗

arXiv2025

Factorization in deep inelastic scattering at Björken limit: Reduction to (1+1)D integrable models

We investigate structure functions in deep inelastic scattering processes (DIS) at Björken limit and found that they are factorized into the longitudinal and transversal parts. We see that the longitudinal part can be linked to exact form factors calculated earlier in 1+1 dimensional integrable quantum field theories, such as sine-Gordon model. We extract asymptotic of Form-factors at small Björken parameter $x$ and compare it with experimental data of HERA and ZEUS collaborations on Deep inelastic lepton-proton scattering. We observe the factorization of the structure functions $F_2(x,q^2)$ and find out its power behavior on scaling parameter $x$.

hep-ph↗

arXiv2021

Explicit R-matrices for inhomogeneous 3D chiral Potts models: Integrability and the action formulation for

We construct the exact spectral parameter dependent vertex R-matrix for the classical 3D $\mathcal{N}$-state chiral Potts models, convenient for considering the model in context of the Bethe ansatz. The R-matrix is defined on the $\mathcal{N}^4$ dimensional space $V_\mathcal{N}\otimes V_\mathcal{N}\otimes V_\mathcal{N}\otimes V_\mathcal{N}$, appropriate for consideration by means of the cube-equations defined in [14]. We present the 2D quantum spin Hamiltonians for general case and, at $\mathcal{N}=2$, a fermionic lattice action representation corresponding to 3D Ising's statistical model.

math-ph↗

arXiv2020

Critical behavior at the integer quantum Hall transition in a network model on the Kagome lattice

We study a network model on the Kagome lattice (NMKL). This model generalizes the Chalker-Coddington (CC) network model for the integer quantum Hall transition. Unlike random network models we studied earlier, the geometry of the Kagome lattice is regular. Therefore, we expect that the critical behavior of the NMKL should be the same as that of the CC model. We numerically compute the localization length index $ν$ in the NKML. Our result $ν= 2.658 \pm 0.046$ is close to CC model values obtained in a number of recent papers. We also map the NMKL to the Dirac fermions in random potentials and in a fixed periodic curvature background. The background turns out irrelevant at long scales. Our numerical and analytical results confirm our expectation of the universality of critical behavior on regular network models.

cond-mat.dis-nn↗

arXiv2015

Integrability of three dimensional models: cubic equations

We extend basic properties of two dimensional integrable models within the Algebraic Bethe Ansatz approach to 2+1 dimensions and formulate the sufficient conditions for the commutativity of transfer matrices of different spectral parameters, in analogy with Yang-Baxter or tetrahedron equations. The basic ingredient of our models is the R-matrix, which describes the scattering of a pair of particles over another pair of particles, the quark-anti-quark (meson) scattering on another quark-anti-quark state. We show that the Kitaev model belongs to this class of models and its R-matrix fulfills well-defined equations for integrability.

math-ph↗

arXiv2014

A matrix model for strings beyond the c=1 barrier: the spin-s Heisenberg model on random surfaces

We consider a spin-s Heisenberg model coupled to two-dimensional quantum gravity. We quantize the model using the Feynman path integral, summing over all possible two-dimensional geometries and spin configurations. We regularize this path integral by starting with the R-matrices defining the spin-s Heisenberg model on a regular 2d Manhattan lattice. 2d quantum gravity is included by defining the R-matrices on random Manhattan lattices and summing over these, in the same way as one sums over 2d geometries using random triangulations in non-critical string theory. We formulate a random matrix model where the partition function reproduces the annealed average of the spin-s Heisenberg model over all random Manhattan lattices. A technique is presented which reduces the random matrix integration in partition function to an integration over their eigenvalues.

hep-th↗

arXiv2014

Localization length index in a Chalker-Coddington model: a numerical study

We calculated numerically the localization length index $ν$ for the Chalker-Coddington model of the plateau-plateau transitions in the quantum Hall effect. By taking into account finite size effects we have obtained $ν= 2.593 \pm 0.0297$. The calculations were carried out by two different programs that produced close results, each one within the error bars of the other. We also checked the possibility of logarithmic corrections to finite size effects and found, that they come with much larger error bars for $ν$.

cond-mat.mes-hall↗

arXiv2014

Effective QCD string beyond Nambu-Goto

We consider the QCD string as an effective string, whose action describes long-range stringy fluctuations. The leading infrared contribution to the ground state energy is given by the Alvarez-Arvis formula, usually derived using the Nambu-Goto action. Here we rederive it by a saddle point calculation using the Polyakov formulation of the free string, where the world sheet metric and the target space coordinates are treated as independent variables. The next order relevant in the infrared term in the effective action is the extrinsic curvature term. We show that the spectrum does not change order by order in the inverse string length, but may change at intermediate distances.

hep-th↗

arXiv2013

The XXZ Heisenberg model on random surfaces

We consider integrable models, or in general any model defined by an $R$-matrix, on random surfaces, which are discretized using random Manhattan lattices. The set of random Manhattan lattices is defined as the set dual to the lattice random surfaces embedded on a regular d-dimensional lattice. They can also be associated with the random graphs of multiparticle scattering nodes. As an example we formulate a random matrix model where the partition function reproduces the annealed average of the XXZ Heisenberg model over all random Manhattan lattices. A technique is presented which reduces the random matrix integration in partition function to an integration over their eigenvalues.

hep-th↗

arXiv2012

On the solutions of the Yang-Baxter equations with general inhomogeneous eight-vertex $R$-matrix: Relations with Zamolodchikov's tetrahedral algebra

We present most general one-parametric solutions of the Yang-Baxter equations (YBE) for one spectral parameter dependent $R_{ij}(u)$-matrices of the six- and eight-vertex models, where the only constraint is the particle number conservation by mod(2). A complete classification of the solutions is performed. We have obtained also two spectral parameter dependent particular solutions $R_{ij}(u,v)$ of YBE. The application of the non-homogeneous solutions to construction of Zamolodchikov's tetrahedral algebra is discussed.

math-ph↗

arXiv2010

Optical conductivity of graphene in the presence of random lattice deformations

We study the influence of lattice deformations on the optical conductivity of a two-dimensional electron gas. Lattice deformations are taken into account by introducing a non-abelian gauge field into the Eucledian action of two-dimensional Dirac electrons. This is in analogy to the introduction of the gravitation in the four-dimensional quantum field theory. We examine the effect of these deformations on the averaged optical conductivity. Within the perturbative theory up to second order we show that corrections of the conductivity due to the deformations cancel each other exactly. We argue that these corrections vanish to any order in perturbative expansion.

cond-mat.str-el↗

arXiv2009

Numerical study of the localization length critical index in a network model of plateau-plateau transitions in the quantum Hall effect

We calculate numerically the localization length critical index within the Chalker-Coddington (CC) model for plateau-plateau transitions in the quantum Hall effect. Lyapunov exponents have been calculated with relative errors on the order $10^{-3}$. Such high precision was obtained by considering the distribution of Lyapunov exponents for large ensembles of relatively short chains and calculating the ensemble average values. We analyze thoroughly finite size effects and find the localization length critical index $ν= 2.517\pm 0.018$.

cond-mat.mes-hall↗

arXiv2009

Network Models: Action formulation

We develop a technique to formulate quantum field theory on arbitrary network, based on different, randomly disposed sets of scattering's. We define R-matrix of the whole network as a product of R-matrices attached to each of scattering nods. Then an action for a network in terms of fermionic fields is formulated, which allows to calculate the transition amplitudes as their Green functions. On so-called bubble and triangle diagrams it is shown that the method produces the same results as the one which uses the generalized star product. The approach allows to extend network models by including multiparticle interactions at the scattering nods.

cond-mat.mes-hall↗

arXiv2009

Grassmann-Gaussian integrals and generalized star products

In quantum scattering on networks there is a non-linear composition rule for on-shell scattering matrices which serves as a replacement for the multiplicative rule of transfer matrices valid in other physical contexts. In this article, we show how this composition rule is obtained using Berezin integration theory with Grassmann variables.

math-ph↗

arXiv2006

Absence of extended states in a ladder model of DNA

We consider a ladder model of DNA for describing carrier transport in a fully coherent regime through finite segments. A single orbital is associated to each base, and both interstrand and intrastrand overlaps are considered within the nearest-neighbor approximation. Conduction through the sugar-phosphate backbone is neglected. We study analytically and numerically the spatial extend of the corresponding states by means of the Landauer and Lyapunov exponents. We conclude that intrinsic-DNA correlations, arising from the natural base pairing, does not suffice to observe extended states, in contrast to previous claims.

cond-mat.dis-nn↗

arXiv2006

Hofstadter Problem on the Honeycomb and Triangular Lattices: Bethe Ansatz Solution

We consider Bloch electrons on the honeycomb lattice under a uniform magnetic field with $2 πp/q$ flux per cell. It is shown that the problem factorizes to two triangular lattices. Treating magnetic translations as Heisenberg-Weyl group and by the use of its irreducible representation on the space of theta functions, we find a nested set of Bethe equations, which determine the eigenstates and energy spectrum. The Bethe equations have simple form which allows to consider them further in the limit $p, q \to \infty$ by the technique of Thermodynamic Bethe Ansatz and analyze Hofstadter problem for the irrational flux.

cond-mat.mes-hall↗

arXiv2005

Simplified tetrahedron equations: Fermionic realization

The natural generalization of the (two-dimensional) Yang-Baxter equations to three dimensions is known as the Zamolodchikov's tetrahedron equations. We consider a simplified version of these equations which still ensures the commutativity of the transfer matrices with different spectral parameters and we present a family of free fermionic solutions.

cond-mat.stat-mech↗