arXiv subjects

Grigor Adamyan

Publications and source records attributed to Grigor Adamyan.

5 recordsLinked to original sources

arXiv2026

Geometric Spin Rotation in Triangular Antiferromagnets

We describe a geometric phenomenon in which a traveling wave made of degenerate Goldstone modes leaves behind a transformed ground state. In a triangular Heisenberg antiferromagnet, a pulse of circularly polarized spin waves rotates the spins within their plane. An exact solution of the nonlinear equations of motion demonstrates that the accumulated rotation is a geometric phase related to parallel transport of the order parameter. We point out a curious analogy between the motion of the magnetic order parameter and that of a wobbling coin. This phenomenon opens a new route for controlling antiferromagnetic order by spin waves and may extend to other frustrated magnets as well as other physical systems with noncommuting broken-symmetry generators.

cond-mat.str-el↗

arXiv2025

Spontaneous symmetry breaking in the Heisenberg antiferromagnet on a triangular lattice

We present a detailed investigation of an overlooked symmetry structure in non-collinear antiferromagnets that gives rise to an emergent quantum number for magnons. Focusing on the triangular-lattice Heisenberg antiferromagnet, we show that its spin order parameter transforms under an enlarged symmetry group, $\mathrm{SO(3)_L \times SO(2)_R}$, rather than the conventional spin-rotation group $\mathrm{SO(3)}$. Although this larger symmetry is spontaneously broken by the ground state, a residual subgroup survives, leading to conserved Noether charges that, upon quantization, endow magnons with an additional quantum number -- \emph{isospin} -- beyond their energy and momentum. Our results provide a comprehensive framework for understanding symmetry, degeneracy, and quantum numbers in non-collinear magnetic systems, and bridge an unexpected connection between the paradigms of symmetry breaking in non-collinear antiferromagnets and chiral symmetry breaking in particle physics.

cond-mat.str-el↗

arXiv2024

Conformal maps and edge mode attenuation on imperfect boundaries

We developed a conformal map technique to analyze the attenuation of edge modes propagating along imperfect boundaries. In systems where the potential energy exhibits conformal invariance, the conformal transformation can straighten the boundary, simplifying the boundary conditions. Using the example of edge modes in a simple field-theoretical model, we examined scattering into the bulk and identified conditions that ensure the robustness of edge modes against damping. This technique has the potential to be applied to other edge-mode problems in 2+1 dimensions.

cond-mat.str-el↗

arXiv2024

Helical edge modes in a triangular Heisenberg antiferromagnet

We investigate the emergence of helical edge modes in a Heisenberg antiferromagnet on a triangular lattice, driven by a topological mechanism similar to that proposed by Dong et al. [Phys. Rev. Lett. 130, 206701 (2023)] for chiral spin waves in ferromagnets. The spin-frame field theory of a three-sublattice antiferromagnet allows for a topological term in the energy that modifies the boundary conditions for certain polarizations of spin waves and gives rise to edge modes. These edge modes are helical: modes with left and right circular polarizations propagate in opposite directions along the boundary in a way reminiscent of the electron edge modes in two-dimensional topological insulators. The field-theoretic arguments are verified in a realistic lattice model of a Heisenberg antiferromagnet with superexchange interactions that exhibits helical edge modes. The strength of the topological term is proportional to the disparity between two inequivalent superexchange paths. These findings suggest potential avenues for realizing magnonic edge states in frustrated antiferromagnets without requiring Dzyaloshinskii-Moriya interactions or nontrivial magnon band topology.

cond-mat.str-el↗

arXiv2023

Hofstadter quasicrystals, hidden symmetries and irrational quantum oscillations

Landau levels perturbed by a periodic potential is a prime setting to design quantum systems with exotic fractal spectra. Motivated by recent advances in twistronics, we introduce `Hofstadter quasicrystal' problem describing Landau levels perturbed by a set of incommensurate cosine waves. We illustrate the underlying physics for moir\'{e} quasicrystals with octagonal and dodecagonal symmetries, finding spectra that are vastly more complex than the Hofstadter spectrum. Surprisingly, due to the high spatial symmetry, the quasicrystal problem exhibits hidden `inner' symmetry arising at special `magic' values of the magnetic field. The $1/B$-periodic pattern of magic field values explains striking wide-range oscillations in the observed spectra that have irrational periodicity incommensurate with the Aharonov-Bohm and Brown-Zak periodicities. The prominent character of these oscillations makes them readily accessible in state-of-the-art moir\'{e} graphene systems.

cond-mat.mes-hall↗