arXiv subjects

Hrachya Babujian

Publications and source records attributed to Hrachya Babujian.

6 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

Bethe Ansatz without Nesting

We develop a non-nested Bethe ansatz description of rational $\mathfrak{gl}_\ell$ spin chains in the vector representation. Starting from the quantum spectral curve and the separation-of-variables framework, we derive closed systems of Bethe equations involving only the momentum-carrying Bethe roots. The construction is worked out explicitly for the $\mathfrak{gl}_3$ and $\mathfrak{gl}_4$ spin chains and then generalized to arbitrary rank. A central result of this work is the identification of a recursive hierarchy associated with the fundamental transfer matrices. The hierarchy is generated by regularity conditions of the lower transfer matrices and closes through a universal rank-$\ell$ equation $\mathcal{R}_{\ell}=0$. This equation replaces the final level of the conventional nested Bethe ansatz and eliminates all auxiliary Bethe roots. Consequently, the complete spectral data of an eigenstate are encoded solely in the first Baxter polynomial $Q_{1}(u)$. We further obtain explicit expressions for the eigenvalues of all fundamental transfer matrices in terms of the momentum-carrying roots alone. The resulting formulation provides a compact characterization of the spectrum of rational $\mathfrak{gl}_\ell$ spin chains and reveals a direct connection between the quantum spectral curve, transfer-matrix fusion relations, and a truncated $Q$-system underlying the non-nested description. Finally, we investigate the quasi-classical (Gaudin) limit of the non-nested Bethe equations. For the $\mathfrak{gl}_3$ spin chain, we show that the leading non-trivial contribution gives rise to Gaudin equations whose pole-free form naturally defines a scalar third-order $\mathfrak{gl}_3$ oper.

hep-th↗

arXiv2019

Correlation Functions of Classical and Quantum Artin System defined on Lobachevsky Plane and Scrambling Time

We consider the quantisation of the Artin dynamical system defined on the fundamental region of the modular group. In classical regime the geodesic flow in the fundamental region represents one of the most chaotic dynamical systems, it has mixing of all orders, Lebesgue spectrum and non-zero Kolmogorov entropy. As a result, the classical correlation functions decay exponentially. In order to investigate the influence of the classical chaotic behaviour on the quantum-mechanical properties of the Artin system we calculated the corresponding thermal quantum-mechanical correlation functions. It was conjectured by Maldacena, Shenker and Stanford that the classical chaos can be diagnosed in thermal quantum systems by using an out-of-time-order correlation function as well as the square of the commutator of operators separated in time. We demonstrated that the two- and four-point correlation functions of the Louiville-like operators decay exponentially with a temperature dependent exponent. As conjectured the square of the commutator of the Louiville-like operators separated in time grows exponentially, similar to the exponential divergency of trajectories in the classical regime. The corresponding exponent does not saturate the maximal growth condition.

hep-th↗

arXiv2018

Artin Billiard Exponential Decay of Correlation Functions

The hyperbolic Anosov C-systems have exponential instability of their trajectories and as such represent the most natural chaotic dynamical systems. Of special interest are C-systems which are defined on compact surfaces of the Lobachevsky plane of constant negative curvature. An example of such system has been introduced in a brilliant article published in 1924 by the mathematician Emil Artin. The dynamical system is defined on the fundamental region of the Lobachevsky plane which is obtained by the identification of points congruent with respect to the modular group, a discrete subgroup of the Lobachevsky plane isometries. The fundamental region in this case is a hyperbolic triangle. The geodesic trajectories of the non-Euclidean billiard are bounded to propagate on the fundamental hyperbolic triangle. In this article we shall expose his results, will calculate the correlation functions/observables which are defined on the phase space of the Artin billiard and demonstrate the exponential decay of the correlation functions with time. We use Artin symbolic dynamics, the differential geometry and group theoretical methods of Gelfand and Fomin.

nlin.CD↗

arXiv2015

Thermodynamics of the Topological Kondo Model

Using the thermodynamic Bethe ansatz, we investigate the topological Kondo model, which describes a set of one-dimensional external wires, pertinently coupled to a central region hosting a set of Majorana bound states. After a short review of the Bethe ansatz solution, we study the system at finite temperature and derive its free energy for arbitrary (even and odd) number of external wires. We then analyse the ground state energy as a function of the number of external wires and of their couplings to the Majorana bound states. Then, we compute, both for small and large temperatures, the entropy of the Majorana degrees of freedom localized within the central region and connected to the external wires. Our exact computation of the impurity entropy provides evidence of the importance of fermion parity symmetry in the realization of the topological Kondo model. Finally, we also obtain the low-temperature behaviour of the specific heat of the Majorana bound states, which provides a signature of the non-Fermi-liquid nature of the strongly coupled fixed point.

cond-mat.str-el↗

arXiv2009

Exact form factors of the SU(N) Gross-Neveu model and 1/N expansion

The general SU(N) form factor formula is constructed. Exact form factors for the field, the energy momentum and the current operators are derived and compared with the 1/N-expansion of the chiral Gross-Neveu model and full agreement is found. As an application of the form factor approach the equal time commutation rules of arbitrary local fields are derived and in general anyonic behavior is found.

hep-th↗