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Tigran Hakobyan

Publications and source records attributed to Tigran Hakobyan.

At least 19 recordsLinked to original sources
arXiv2026

Topological edge states in two-dimensional $\mathbb{Z}_4$ Potts paramagnet protected by the $\mathbb{Z}_4^{\times 3}$ symmetry

We construct a two-dimensional bosonic symmetry-protected topological (SPT) paramagnet protected by an on-site $G=\mathbb{Z}_4^{\times 3}$ symmetry, starting from a three-component $\mathbb{Z}_4$ Potts paramagnet on a triangular lattice. Within the group-cohomology framework, $H^{3}(G,U(1))\cong \mathbb{Z}_4^{\times 7}$, we focus on a "colorless" cocycle representative obtained by antisymmetrizing the basic $\mathbb{Z}_4$ three-cocycle, and generate the corresponding SPT Hamiltonian via a cocycle-induced nonlocal unitary transformation followed by symmetry averaging. For open geometry, we derive the boundary theory explicitly: one color sector decouples, while the nontrivial edge reduces to an interacting $\mathbb{Z}_4$ chain with next-to-nearest-neighbor constraints that admits a compact dressed-Potts form. Using DMRG we show that the boundary model is gapless, with the lowest gap scaling as $1/L$ and an entanglement-entropy scaling consistent with a conformal field theory of central charge $c=2.191(4)\simeq 11/5$. The rational value $c=11/5$ matches the coset $SU(3)_3/SU(2)_3$, making it a candidate for the continuum description of the $\mathbb{Z}_4^{\times 3}$ edge; we outline spectral and symmetry-resolved diagnostics needed to test this identification at the level of conformal towers beyond the central charge.

cond-mat.str-el↗
arXiv2026

T-Fermat integers

We introduce the concept of a T-Fermat integer, which generalizes the notion of a prime number. We show that any composite T-Fermat integer, if one exists, must be a Carmichael number. We prove several properties of T-Fermat integers and conjecture that there are infinitely many composite T-Fermat integers. Together with a further structural conjecture, this suggests a possible route toward proving the infinitude of primes $p$ such that $ω(p-1)\leq 2$.

math.NT↗
arXiv2026

Dynamical symmetries of the Calogero-Coulomb model

We construct the dynamical symmetry of the quantum Calogero model with particle exchange in a confining Coulomb field. This symmetry is governed by the algebra $so(N+1,2)$, deformed by exchange (Dunkl) operators, with its invariant sector generated by the Dunkl angular momentum tensor and the modified Laplace-Runge-Lenz vector. The equidistant analogue of the Hamiltonian, with a linear spectrum, is expressed in terms of the conformal subalgebra $so(1,2)$. In addition, the wave functions of the Calogero-Coulomb Hamiltonian are classified into infinite-dimensional lowest-weight $so(1,2)$ multiplets.

hep-th↗
arXiv2025

Parafermionic representation of Potts-based cluster chain

The cluster chain with $\mathbb{Z}_p \times \mathbb{Z}_p$ symmetry-protected topological (SPT) order is decomposed into two distinct bilinear parafermionic chains, each possessing intrinsic topological order. These chains are formed by standard parafermions and time-reversal parafermions, respectively. Each subsystem retains its own $\mathbb{Z}_p$ symmetry component, which characterizes the total parity of constituent particles. Their topological orders are inherited from the two SPT orders of the cluster model. The transformations of particles under reflection, translation, and time reversal are derived. In the open chain, four zero-energy parafermionic edge modes are identified, and their structure is analyzed. For the closed system, the boundaries are twisted by the total parafermion parity. It is shown that the open chain is reflection-invariant when the number of spins is even, and $\mathcal{PT}$-invariant when the number of spins is odd. Meanwhile, the closed model exhibits a symmetry characterized by an antiunitary analog of the dihedral group.

cond-mat.str-el↗
arXiv2025

Dunkl symplectic algebra in generalized Calogero models

We study the properties of the symplectic sp(2N) algebra deformed using Dunkl operators, which describe the dynamical symmetry of the generalized N-particle quantum Calogero model. It contains a symmetry subalgebra formed by the deformed unitary generators as well as the (nondeformed) sl(2,R) conformal subalgebra. An explicit relation among the deformed symplectic generators is derived. Based on the matching between the Casimir elements of the conformal spin and Dunkl angular momentum algebras, the independent wavefunctions of the both the standard and generalized Calogero models, expressed in terms of the deformed spherical harmonics, are classified according to infinite-dimensional lowest-state sl(2,R) multiplets. Meanwhile, any polynomial integral of motion of the (generalized) Calogero-Moser model generates a finite-dimensional highest-state conformal multiplet with descendants expressed via the Weyl-ordered product in quantum field theory.

hep-th↗
arXiv2020

Lowest energy states of an $O(N)$ fermionic chain

A quite general finite-size chain of fermions with $N$ internal degrees of freedom (flavors) and $O(N)$ symmetry is considered. In the case of the free boundary condition, we prove that the ground state in the invariant sector having exactly $m$ flavors with an odd particle number is represented by a single rank-$m$ antisymmetric multiplet. For the even-length chains, its particle-hole quantum number (if it's a good one) is given by the parity of the $m$. For the odd-length chains, the particle-hole symmetry leads to the twofold degeneracy among the conjugate multiplets. Similar statements are proven for the $O(N)$ mixed-spin chains in antisymmetric representations. The results are extended to the long-range interacting fermions and (partially) to the translation invariant chains.

cond-mat.str-el↗
arXiv2019

Algebra of Dunkl Laplace-Runge-Lenz vector

We consider Dunkl version of Laplace-Runge-Lenz vector associated with a finite Coxeter group $W$ acting geometrically in $\mathbb R^N$ with multiplicity function $g$. This vector generalizes the usual Laplace-Runge-Lenz vector and its components commute with Dunkl-Coulomb Hamiltonian given as Dunkl Laplacian with additional Coulomb potential $γ/r$. We study resulting symmetry algebra $R_{g, γ}(W)$ and show that it has Poincaré-Birkhoff-Witt property. In the absence of Coulomb potential this symmetry algebra $R_{g,0}(W)$ is a subalgebra of the rational Cherednik algebra $H_g(W)$. We show that a central quotient of the algebra $R_{g, γ}(W)$ is a quadratic algebras isomorphic to a central quotient of the corresponding Dunkl angular momenta algebra $H_g^{so(N+1)}(W)$. This gives interpretation of the algebra $H_g^{so(N+1)}(W)$ as the hidden symmetry algebra of Dunkl-Coulomb problem in $\mathbb R^N$. By specialising $R_{g, γ}(W)$ to $g=0$ we recover a quotient of the universal enveloping algebra $U(so(N+1))$ as the hidden symmetry algebra of Coulomb problem in $\mathbb R^N$. We also apply Dunkl Laplace-Runge-Lenz vector to establish maximal superintegrability of generalised Calogero-Moser systems.

math-ph↗
arXiv2018

Honda formal group as Galois module in unramified extensions of local fields

For given rational prime number $p$ consider the tower of finite extensions of fields $K_0/\mathbb{Q}_p,$ $K/K_0, L/K, M/L$, where $K/K_0$ is unramified and $M/L$ is a Galois extension with Galois group $G$. Suppose one dimensional Honda formal group over the ring $\mathcal{O}_K$, relative to the extension $K/K_0$ and uniformizer $π\in K_0$ is given. The operation $x\underset{F}+y=F(x,y)$ sets a new structure of abelian group on the maximal ideal $\mathfrak{p}_M$ of the ring $\mathcal{O}_M$ which we will denote by $F(\mathfrak{p}_M)$. In this paper the structure of $F(\mathfrak{p}_M)$ as $\mathcal{O}_{K_0}[G]$-module is studied for specific unramified $p$-extensions $M/L$.

math.NT↗
arXiv2018

Definability in differential-henselian monotone fields

This paper is a sequel to [1] and considers definability in differential-henselian monotone fields with c-map and angular component map. We prove an Equivalence Theorem among whose consequences are a relative quantifier reduction and an NIP result.

math.LO↗
arXiv2017

Near horizon extremal Myers-Perry black holes and integrability of associated conformal mechanics

We investigate dynamics of probe particles moving in the near-horizon limit of (2N+1)-dimensional extremal Myers-Perry black hole with arbitrary rotation parameters. We observe that in the most general case with nonequal nonvanishing rotational parameters the system admits separation of variables in N-dimensional ellipsoidal coordinates. This allows us to find solution of the corresponding Hamilton-Jacobi equation and write down the explicit expressions of Liouville constants of motion.

hep-th↗
arXiv2017

Algebraically Closed Fields with a Generic Multiplicative Character

We study the model theory of the $2$-sorted structure $(\mathbb{F}, \mathbb{C};χ)$, where $\mathbb{F}$ is an algebraic closure of a finite field of characteristic $p$, $\mathbb{C}$ is the field of complex numbers and $χ: \mathbb{F} \to \mathbb{C}$ is an injective, multiplication preserving map. We obtain an axiomatization $\mathrm{ACFC}_p$ of $\mathrm{Th}(\mathbb{F},\mathbb{C};χ)$ in a suitable language $L$, classify the models of $\mathrm{ACFC}_p$ up to isomorphism, prove a modified model companion result, give various descriptions of definable sets inside a model of $\mathrm{ACFC}_p$, and deduce that $\mathrm{ACFC}_p$ is $ω$-stable and has definability of Morley rank in families.

math.LO↗
arXiv2016

Spherical Calogero model with oscillator/Coulomb potential: classical case

We construct the Hamiltonians and symmetry generators of Calogero-oscillator and Calogero-Coulomb models on the N-dimensional sphere within the matrix-model reduction approach. Our method also produces the integrable Calogero-Coulomb-Stark model on the sphere and proves the integrability of the spin extensions of all these systems.

hep-th↗
arXiv2016

Spherical Calogero model with oscillator/Coulomb potential: quantum case

We consider the quantum mechanics of Calogero models in an oscillator or Coulomb potential on the N-dimensional sphere. Their Hamiltonians are obtained by an appropriate Dunkl deformation of the oscillator/Coulomb system on the sphere and its restriction to (Coxeter reflection) symmetric wave functions. By the same method we also find the symmetry generators and compute their algebras.

hep-th↗
arXiv2016

Integrability and separation of variables in Calogero-Coulomb-Stark and two-center Calogero-Coulomb systems

We propose the integrable N-dimensional Calogero-Coulomb-Stark and two-center Calogero-Coulomb systems and construct their constants of motion via the Dunkl operators. Their Schrödinger equations decouple in parabolic and elliptic coordinates into the set of three differential equations like for the Coulomb-Stark and two-center Coulomb problems. The Calogero term preserves the energy levels, but changes their degrees of degeneracy.

math-ph↗
arXiv2016

Lobachevsky geometry in TTW and PW systems

We review the classical properties of Tremblay-Turbiner-Winternitz and Post-Wintenitz systems and their relation with N-dimensional rational Calogero model with oscillator and Coulomb potentials, paying special attention to their hidden symmetries. Then we show that combining the radial coordinate and momentum in a single complex coordinate in proper way, we get an elegant description for the hidden and dynamical symmetries in these systems related with action-angle variables.

math-ph↗