arXiv subjects

Shahane A. Khachatryan

Publications and source records attributed to Shahane A. Khachatryan.

5 recordsLinked to original sources

arXiv2026

Anizotropic Ising Model on 2D Kagomé Lattice as an Inhomogeneous XYZ Integrable Model

We investigate a generalized inhomogeneous two-dimensional Ising model on the kagomé lattice with two alternating couplings $J_i$ and $J'_i$, $i=1,2,3$, along the three lattice directions. The local Boltzmann weights are mapped onto a non-symmetric eight-vertex $R$-matrix satisfying the free-fermion condition for arbitrary values of the six couplings. We analyze the Yang--Baxter structure for the cases $J'_i=J_i$ and $J'_i=-J_i$ and derive the corresponding one-dimensional quantum spin chains in the anisotropic limit. The first case yields a transverse-field Ising-type Hamiltonian, while the second leads to a modified chain with a graded permutation structure and shifted partition-function zeros. For a partially anisotropic model, we also obtain the free energy and specific heat.

cond-mat.stat-mech↗

arXiv2026

Inhomogeneous Ising Model on 2D kagomé Lattice: Fermionic field approach

We investigate the two-dimensional inhomogeneous Ising model (2DIM) on the kagom'e lattice by mapping it onto a particular non-symmetric eight-vertex model and constructing the corresponding $R$-matrix. Using a fermionic representation, we evaluate the partition function and derive explicit expressions for the main thermodynamic quantities. In the thermodynamic limit, we obtain an exact equation for the critical surface determining the phase transition of the model. We also calculate the free energy, specific heat, and spontaneous magnetization in the ferromagnetic case. Furthermore, we show that when one or two coupling constants vanish, the model reduces, respectively, to the square-lattice and one-dimensional Ising models. In both limits, our results reproduce the corresponding exact critical couplings and free energies.

cond-mat.stat-mech↗

arXiv2023

$Z_3$ and $(\times Z_3)^3$ symmetry protected topological paramagnets

We identify two-dimensional three-state Potts paramagnets with gapless edge modes on a triangular lattice protected by $(\times Z_3)^3\equiv Z_3\times Z_3\times Z_3$ symmetry and smaller $Z_3$ symmetry. We derive microscopic models for the gapless edge, uncover their symmetries, and analyze the conformal properties. We study the properties of the gapless edge by employing the numerical density-matrix renormalization group (DMRG) simulation and exact diagonalization. We discuss the corresponding conformal field theory, its central charge, and the scaling dimension of the corresponding primary field. We argue that the low energy limit of our edge modes is defined by the $SU_k(3)/SU_k(2)$ coset conformal field theory with the level $k=2$. The discussed two-dimensional models realize a variety of symmetry-protected topological phases, opening a window for studies of the unconventional quantum criticalities between them.

cond-mat.str-el↗

arXiv2023

New series of multi-parametric solutions to GYBE: quantum gates and integrability

We obtain two series of spectral parameter dependent solutions to the generalized Yang-Baxter equations (GYBE), for definite types of $N_1^2\times N_2^2$ matrices with general dimensions $N_1$ and $N_2$. Appropriate extensions are presented for the inhomogeneous GYBEs. The first series of the solutions includes as particular cases the $X$-shaped trigonometric braiding matrices. For construction of the second series the colored and graded permutation operators are defined, and multi-spectral parameter Yang-Baxterization is performed. For some examples the corresponding integrable models are discussed. The unitary solutions existing in these two series can be considered as generalizations of the multipartite Bell matrices in the quantum information theory.

math-ph↗

arXiv2023

Integrability in $[d+1]$ dimensions: combined local equations and commutativity of the transfer matrices

We propose new inhomogeneous local integrability equations - combined equations, for statistical vertex models of general dimensions in the framework of the Algebraic Bethe Ansatz (ABA). For the low dimensional cases the efficiency of the step by step consideration of the transfer matrices' commutation is demonstrated. We construct some simple 3D solutions with the three-state $R$-matrices of certain 20-vertex structure; the connection with the quantum three-qubit gates is discussed. New, restricted versions of 3D local integrability equations with four-state $R$-matrices are defined, too. Then we construct a new 3D analogue of the two-dimensional star-triangle equations.

nlin.SI↗