Nonlinear Lifshitz Photon Theory in Condensed Matter Systems
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866929217054179328 |
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| author | Du, Yi-Hsien Xu, Cenke Son, Dam Thanh |
| author_facet | Du, Yi-Hsien Xu, Cenke Son, Dam Thanh |
| contents | We present an interacting theory of a $U(1)$ gauge boson with a quadratic dispersion relation, which we call the "nonlinear Lifshitz photon theory.'' The Lifshitz photon is a three-dimensional generalization of the Tkachenko mode in rotating superfluids. Starting from the Wigner crystal of charged particles coupled to a dynamical $U(1)$ gauge field, after integrating out gapped degrees of freedom, we arrive at the Lagrangian for the nonlinear Lifshitz photon. The symmetries of the theory include a global $U(1)$ 1-form symmetry and nonlinearly realized "magnetic" translation and rotation symmetries. The interaction terms in the theory lead to the decay of the Lifshitz photon, the rate of which we estimate. We show that the Wilson loop, which plays the role of the order parameter of the spontaneous breaking of the 1-form global symmetry, deviates from the perimeter law by an additional logarithmic factor. We explore potential connections to other condensed matter systems, with a particular focus on quantum spin ice and ferromagnets. Finally, we generalize our theory to higher dimensions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_03946 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Nonlinear Lifshitz Photon Theory in Condensed Matter Systems Du, Yi-Hsien Xu, Cenke Son, Dam Thanh Strongly Correlated Electrons High Energy Physics - Theory We present an interacting theory of a $U(1)$ gauge boson with a quadratic dispersion relation, which we call the "nonlinear Lifshitz photon theory.'' The Lifshitz photon is a three-dimensional generalization of the Tkachenko mode in rotating superfluids. Starting from the Wigner crystal of charged particles coupled to a dynamical $U(1)$ gauge field, after integrating out gapped degrees of freedom, we arrive at the Lagrangian for the nonlinear Lifshitz photon. The symmetries of the theory include a global $U(1)$ 1-form symmetry and nonlinearly realized "magnetic" translation and rotation symmetries. The interaction terms in the theory lead to the decay of the Lifshitz photon, the rate of which we estimate. We show that the Wilson loop, which plays the role of the order parameter of the spontaneous breaking of the 1-form global symmetry, deviates from the perimeter law by an additional logarithmic factor. We explore potential connections to other condensed matter systems, with a particular focus on quantum spin ice and ferromagnets. Finally, we generalize our theory to higher dimensions. |
| title | Nonlinear Lifshitz Photon Theory in Condensed Matter Systems |
| topic | Strongly Correlated Electrons High Energy Physics - Theory |
| url | https://arxiv.org/abs/2309.03946 |