Geometrically Frustrated Quadrupoles on the Pyrochlore Lattice and Generalized Spin Liquids
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| Format: | Preprint |
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2025
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| _version_ | 1866913911464263680 |
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| author | Chung, Kristian Tyn Kai Petit, Sylvain Robert, Julien McClarty, Paul |
| author_facet | Chung, Kristian Tyn Kai Petit, Sylvain Robert, Julien McClarty, Paul |
| contents | As an instance of geometrical frustration with non-magnetic degrees of freedom, we explore the physics of local spin $S\geq 1$ moments on the pyrochlore lattice that interact via pure quadrupolar couplings. In the presence of spin-orbit coupling, there are nine allowed couplings between nearest neighbor quadrupoles. We determine the semi-classical phases and survey the phase diagram of the model. One may view the Hamiltonian as being composed of two copies of the well-studied dipolar model with couplings between the copies, and we find that each easy-plane dipolar phase has two quadrupolar counterparts. As geometrical frustration is important over broad swathes of the parameter space, there are many classical quadrupolar liquids and regions with order-by-disorder selection of discrete states. Order-by-disorder with quadrupoles admits cubic terms in the Landau theory whose effects appear in Monte Carlo simulations and flavor wave calculations for fixed spin $S$. We showcase a number of examples of quadrupolar spin liquids, including one realizing a rank-3 symmetric tensor gauge theory exhibiting 6-fold pinch point singularities. We discuss remarkable differences between the quadrupolar physics of different spin quantum number. We also discuss connections to the non-Kramers rare earth pyrochlore materials. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_19908 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Geometrically Frustrated Quadrupoles on the Pyrochlore Lattice and Generalized Spin Liquids Chung, Kristian Tyn Kai Petit, Sylvain Robert, Julien McClarty, Paul Strongly Correlated Electrons As an instance of geometrical frustration with non-magnetic degrees of freedom, we explore the physics of local spin $S\geq 1$ moments on the pyrochlore lattice that interact via pure quadrupolar couplings. In the presence of spin-orbit coupling, there are nine allowed couplings between nearest neighbor quadrupoles. We determine the semi-classical phases and survey the phase diagram of the model. One may view the Hamiltonian as being composed of two copies of the well-studied dipolar model with couplings between the copies, and we find that each easy-plane dipolar phase has two quadrupolar counterparts. As geometrical frustration is important over broad swathes of the parameter space, there are many classical quadrupolar liquids and regions with order-by-disorder selection of discrete states. Order-by-disorder with quadrupoles admits cubic terms in the Landau theory whose effects appear in Monte Carlo simulations and flavor wave calculations for fixed spin $S$. We showcase a number of examples of quadrupolar spin liquids, including one realizing a rank-3 symmetric tensor gauge theory exhibiting 6-fold pinch point singularities. We discuss remarkable differences between the quadrupolar physics of different spin quantum number. We also discuss connections to the non-Kramers rare earth pyrochlore materials. |
| title | Geometrically Frustrated Quadrupoles on the Pyrochlore Lattice and Generalized Spin Liquids |
| topic | Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2506.19908 |