Quantum vortex lattice: Lifshitz duality, topological defects and multipole symmetries
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866917760302317568 |
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| author | Du, Yi-Hsien Lam, Ho Tat Radzihovsky, Leo |
| author_facet | Du, Yi-Hsien Lam, Ho Tat Radzihovsky, Leo |
| contents | We study an effective field theory of a vortex lattice in a two-dimensional neutral rotating superfluid. Utilizing particle-vortex dualities, we explore its formulation in terms of a $U(1)$ gauge theory coupled to elasticity, that at low energies reduces to a compact Lifshitz theory augmented with a Berry phase term encoding the vortex dynamics in the presence of a superflow. Utilizing elasticity- and Lifshitz-gauge theory dualities, we derive dual formulations of the vortex lattice in terms of a traceless symmetric scalar-charge theory and demonstrate low-energy equivalence of our dual gauge theory to its elasticity-gauge theory dual. We further discuss a multipole symmetry of the vortex lattice and its dual gauge theory's multipole one-form symmetries. We also study its topological crystalline defects, where the multipole one-form symmetry plays a prominent role. It classifies the defects, explains their restricted mobility, and characterizes descendant vortex phases, which includes a novel vortex supersolid phase. Using the dual gauge theory, we also develop a mean-field theory for the quantum melting transition from a vortex crystal to a vortex supersolid. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_13794 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Quantum vortex lattice: Lifshitz duality, topological defects and multipole symmetries Du, Yi-Hsien Lam, Ho Tat Radzihovsky, Leo Strongly Correlated Electrons Quantum Gases Statistical Mechanics High Energy Physics - Theory We study an effective field theory of a vortex lattice in a two-dimensional neutral rotating superfluid. Utilizing particle-vortex dualities, we explore its formulation in terms of a $U(1)$ gauge theory coupled to elasticity, that at low energies reduces to a compact Lifshitz theory augmented with a Berry phase term encoding the vortex dynamics in the presence of a superflow. Utilizing elasticity- and Lifshitz-gauge theory dualities, we derive dual formulations of the vortex lattice in terms of a traceless symmetric scalar-charge theory and demonstrate low-energy equivalence of our dual gauge theory to its elasticity-gauge theory dual. We further discuss a multipole symmetry of the vortex lattice and its dual gauge theory's multipole one-form symmetries. We also study its topological crystalline defects, where the multipole one-form symmetry plays a prominent role. It classifies the defects, explains their restricted mobility, and characterizes descendant vortex phases, which includes a novel vortex supersolid phase. Using the dual gauge theory, we also develop a mean-field theory for the quantum melting transition from a vortex crystal to a vortex supersolid. |
| title | Quantum vortex lattice: Lifshitz duality, topological defects and multipole symmetries |
| topic | Strongly Correlated Electrons Quantum Gases Statistical Mechanics High Energy Physics - Theory |
| url | https://arxiv.org/abs/2310.13794 |