Frustrated quantum spin models

We have calculated the ground-state properties of the $s=\frac{1}{2}$ $\mathrm{XY}$ and Heisenberg models on finite triangular and square lattices with competing interactions which would lead to frustrated classical spin models. The evidence favors the hypothesis that quantum spin models on infinite two-dimensional lattices experience no frustration.We have calculated the ground-state properties of the $s=\frac{1}{2}$ $\mathrm{XY}$ and Heisenberg models on finite triangular and square lattices with competing interactions which would lead to frustrated classical spin models. The evidence favors the hypothesis that quantum spin models on infinite two-dimensional lattices experience no frustration.

Physical Review LettersNov 19, 197968 citations

Strongly Frustrated Quantum Spin Systems

Kenn Kubo, Tota Nakamura

Jun 1, 19950 citations

Geometric and bond frustration in transverse field Ising clusters

Abhiraj Jalagekar

The Ising model, often seen as the paradigmatic spin model, has been heavily studied for its mathematical description of ferromagnetism in statistical mechanics. We explore a quantum version of this model, the transverse field Ising model, and investigate how the quantum property of magnetization fluctuates with geometrical frustration, a phenomenon arising from the geometry of a spin system's ground state. We introduce a general measure for frustration and then implement a computational model built in Python that translates spin lattices into adjacency matrices, solves the spectrum of the transverse field Ising model, calculates the expected magnetization of the ground state, plots the variable over randomly generated spin systems with controllable degrees of geometrical frustration, and compares the evolution of these plots over an increasing transverse field. Our finite-size studies exhibit an expected decrease in magnetization with increasing frustration and suggest the possibility of robust phases in the large N limit over finite ranges of frustration, which may be precursors to spin liquids or spin glasses.The Ising model, often seen as the paradigmatic spin model, has been heavily studied for its mathematical description of ferromagnetism in statistical mechanics. We explore a quantum version of this model, the transverse field Ising model, and investigate how the quantum property of magnetization fluctuates with geometrical frustration, a phenomenon arising from the geometry of a spin system's ground state. We introduce a general measure for frustration and then implement a computational model built in Python that translates spin lattices into adjacency matrices, solves the spectrum of the transverse field Ising model, calculates the expected magnetization of the ground state, plots the variable over randomly generated spin systems with controllable degrees of geometrical frustration, and compares the evolution of these plots over an increasing transverse field. Our finite-size studies exhibit an expected decrease in magnetization with increasing frustration and suggest the possibility of robust phases in the large N limit over finite ranges of frustration, which may be precursors to spin liquids or spin glasses.

arXiv:2311.04553Nov 8, 20230 citations

Two-dimensional spin-1 frustrated Heisenberg model with valence-bond ground states

Zi Cai, Shu Chen, Su-Peng Kou +1 more

In this paper, we propose a method to understand the nature of the quantum disorder phase of the two-dimensional (2D) high-spin frustrated model. The ground state and excitation properties of a fully frustrated 2D spin-1 model are studied based on a model whose ground state can be found exactly. By analogy to the pseudopotential approach in the fractional quantum Hall effect, we conclude that the ground states of the fully frustrated spin-1 model are doubly degenerate valence-bond solid (VBS) states along the horizontal or vertical direction of the square lattice. We also find that the ground state could be characterized by a nonzero string order, which rarely happened in the 2D case. The method that we used reveals the connection between the fractional quantum Hall effect and the frustrated 2D antiferromagnetism system. The VBS states capture the main character of the disordered phase in the 2D spin-1 frustrated system and can be verified by a numerical method.In this paper, we propose a method to understand the nature of the quantum disorder phase of the two-dimensional (2D) high-spin frustrated model. The ground state and excitation properties of a fully frustrated 2D spin-1 model are studied based on a model whose ground state can be found exactly. By analogy to the pseudopotential approach in the fractional quantum Hall effect, we conclude that the ground states of the fully frustrated spin-1 model are doubly degenerate valence-bond solid (VBS) states along the horizontal or vertical direction of the square lattice. We also find that the ground state could be characterized by a nonzero string order, which rarely happened in the 2D case. The method that we used reveals the connection between the fractional quantum Hall effect and the frustrated 2D antiferromagnetism system. The VBS states capture the main character of the disordered phase in the 2D spin-1 frustrated system and can be verified by a numerical method.

arXiv:cond-mat/0611170Physical Review BAug 24, 20076 citations

Exactly solvable 1D frustrated quantum spin models

Д. В. Дмитриев, V. Ya. Krivnov, А. А. Овчинников

Zeitschrift für Physik B Condensed MatterJun 1, 19969 citations

We have calculated the ground-state properties of the

s=\frac{1}{2}

\mathrm{XY}

and Heisenberg models on finite triangular and square lattices with competing interactions which would lead to frustrated classical spin models. The evidence favors the hypothesis that quantum spin models on infinite two-dimensional lattices experience no frustration.