Quantum dynamics in a spin-1/2 square lattice $J_{1}$ - $J_{2}$ - $δ$ altermagnetQuantum dynamics in a spin-1/2 square lattice $J_{1}$-$J_{2}$-$δ$ altermagnet

Yang Liu, Shiqi Shao, Saisai He +4 more

A key feature of the newly discovered altermagnet is that its spin degeneracy is lifted, although it has an antiferromagnetic order and zero net magnetization. In this work, we investigate a frustrated spin-1/2 $J_1$ - $J_2$ - $δ$ Heisenberg model on the square lattice by the tensor network methodin combination with the linear spin-wave theory, with our focus on both the magnon excitations and longitudinal excitations.For a small $J_2$ and a finite range of $δ$ we demonstrate that such a model hosts an altermagnetic ground state. Its magnon spectrum is split into two branches and the largest splitting occurs at $\left(\pmπ/2, \pmπ/2\right)$ in the Brillouin zone. The magnitudes of splitting in the two magnon modes are equal with respect to the case of $δ=0$ . Dynamical spin structure factors show that the low-energy peak in the longitudinal spectral weight around $(π/2, π/2)$ is also split, and thus the relative positions of the magnon modes and longitudinal modes in energy may change in the presence of a finite $δ$ . These findings demonstrate that the altermagnets harbor more complex quantum dynamics than the conventional collinear antiferromagnets.A key feature of the newly discovered altermagnet is that its spin degeneracy is lifted, although it has an antiferromagnetic order and zero net magnetization. In this work, we investigate a frustrated spin-1/2 $J_1$-$J_2$-$δ$ Heisenberg model on the square lattice by the tensor network methodin combination with the linear spin-wave theory, with our focus on both the magnon excitations and longitudinal excitations.For a small $J_2$ and a finite range of $δ$ we demonstrate that such a model hosts an altermagnetic ground state. Its magnon spectrum is split into two branches and the largest splitting occurs at $\left(\pmπ/2, \pmπ/2\right)$ in the Brillouin zone. The magnitudes of splitting in the two magnon modes are equal with respect to the case of $δ=0$. Dynamical spin structure factors show that the low-energy peak in the longitudinal spectral weight around $(π/2, π/2)$ is also split, and thus the relative positions of the magnon modes and longitudinal modes in energy may change in the presence of a finite $δ$. These findings demonstrate that the altermagnets harbor more complex quantum dynamics than the conventional collinear antiferromagnets.

arXiv:2410.06955Oct 9, 20240 citations

Towards the Dynamic Properties of Square-Lattice Quantum Spin Models

Oleg Derzhko, Taras Krokhmalskii

Acta Physica Polonica BOct 1, 20011 citation

Altermagnetism and bond-nematicity in the spin- $1/2$ square lattice $J_1-J_2-δ$ modelAltermagnetism and bond-nematicity in the spin-$1/2$ square lattice $J_1-J_2-δ$ model

Tanja Đurić, Shenlong Yu, Pinaki Sengupta

We study appearance of bond-nematicity in insulating altermagnetic materials induced by increased frustration and quantum-fluctuations driven melting of the altermagnetic order. Using novel machine learning approach that combines symmetry enhanced neural network architectures and variational Monte Carlo we consider the spin- $1/2$ square lattice $J_1-J_2-δ$ model known to have altermagnetic ordering in the regime of small geometric frustration and a gapless spin liquid phase in the regime of strong frustration and small exchange interaction modulation parameter $δ$ . In the regime where exchange modulation is relatively large, resulting in the significant splitting of the magnon modes with different chiralities in the altermagnetic regime, we find that melting of the altermagnetic order by increased frustration leads to an intriguing phase that hosts coexisting symmetry protected topological valence bond solid and bond-nematic orders. The phase is characterized by condensation of magnon pairs that results in bond-nematicity, breaking of U(1) spin rotation and $\mathbb{Z}_2$ spin inversion symmetries and chiral splitting of the triplon-like energy levels in the excitation spectrum. Whilst numerous recent studies address non-trivial impact of altermagnetic moments on various properties in altermagnetic materials, like electronic band structure and superconductivity, influence of strong quantum fluctuations and phases that can result from melting of the altermagnetic order are much less explored. Our study therefore presents an important step in identifying exotic phases of matter that can emerge in vicinity of the altermagnetic order.We study appearance of bond-nematicity in insulating altermagnetic materials induced by increased frustration and quantum-fluctuations driven melting of the altermagnetic order. Using novel machine learning approach that combines symmetry enhanced neural network architectures and variational Monte Carlo we consider the spin-$1/2$ square lattice $J_1-J_2-δ$ model known to have altermagnetic ordering in the regime of small geometric frustration and a gapless spin liquid phase in the regime of strong frustration and small exchange interaction modulation parameter $δ$. In the regime where exchange modulation is relatively large, resulting in the significant splitting of the magnon modes with different chiralities in the altermagnetic regime, we find that melting of the altermagnetic order by increased frustration leads to an intriguing phase that hosts coexisting symmetry protected topological valence bond solid and bond-nematic orders. The phase is characterized by condensation of magnon pairs that results in bond-nematicity, breaking of U(1) spin rotation and $\mathbb{Z}_2$ spin inversion symmetries and chiral splitting of the triplon-like energy levels in the excitation spectrum. Whilst numerous recent studies address non-trivial impact of altermagnetic moments on various properties in altermagnetic materials, like electronic band structure and superconductivity, influence of strong quantum fluctuations and phases that can result from melting of the altermagnetic order are much less explored. Our study therefore presents an important step in identifying exotic phases of matter that can emerge in vicinity of the altermagnetic order.

arXiv:2606.14101Jun 12, 20260 citations

Quantum dynamics in a spin-1/2 square lattice

J_{1}

J_{2}

δ

altermagnet

J_1

J_2

δ

Heisenberg model on the square lattice by the tensor network methodin combination with the linear spin-wave theory, with our focus on both the magnon excitations and longitudinal excitations.For a small

J_2

and a finite range of

δ

we demonstrate that such a model hosts an altermagnetic ground state. Its magnon spectrum is split into two branches and the largest splitting occurs at

\left(\pmπ/2, \pmπ/2\right)

in the Brillouin zone. The magnitudes of splitting in the two magnon modes are equal with respect to the case of

δ=0

. Dynamical spin structure factors show that the low-energy peak in the longitudinal spectral weight around

(π/2, π/2)

is also split, and thus the relative positions of the magnon modes and longitudinal modes in energy may change in the presence of a finite

δ

. These findings demonstrate that the altermagnets harbor more complex quantum dynamics than the conventional collinear antiferromagnets.

Altermagnetism and bond-nematicity in the spin-

1/2

square lattice

J_1-J_2-δ

model

1/2

square lattice

J_1-J_2-δ

model known to have altermagnetic ordering in the regime of small geometric frustration and a gapless spin liquid phase in the regime of strong frustration and small exchange interaction modulation parameter

δ

. In the regime where exchange modulation is relatively large, resulting in the significant splitting of the magnon modes with different chiralities in the altermagnetic regime, we find that melting of the altermagnetic order by increased frustration leads to an intriguing phase that hosts coexisting symmetry protected topological valence bond solid and bond-nematic orders. The phase is characterized by condensation of magnon pairs that results in bond-nematicity, breaking of U(1) spin rotation and

\mathbb{Z}_2

spin inversion symmetries and chiral splitting of the triplon-like energy levels in the excitation spectrum. Whilst numerous recent studies address non-trivial impact of altermagnetic moments on various properties in altermagnetic materials, like electronic band structure and superconductivity, influence of strong quantum fluctuations and phases that can result from melting of the altermagnetic order are much less explored. Our study therefore presents an important step in identifying exotic phases of matter that can emerge in vicinity of the altermagnetic order.