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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2504.19310 |
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| _version_ | 1866911684628578304 |
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| author | Kalagov, Georgii |
| author_facet | Kalagov, Georgii |
| contents | We investigate the superfluid phase transition in an $\mathrm{SU}(N)$-symmetric Fermi gas with $N$ distinct spin states using the functional renormalization group. To capture pairing phenomena beyond mean-field theory, we introduce an auxiliary bosonic field and employ the leading order of the derivative expansion of the partially bosonized effective average action. By discretizing the effective potential on a grid and numerically integrating the flow equations, we resolve the thermodynamic behavior near the transition. Our results reveal a fluctuation-induced first-order phase transition for $N \geq 4$, which is absent at the mean-field level. In the unitary regime, we provide quantitative predictions for the critical temperature, as well as for the discontinuities in the superfluid gap and entropy density as functions of $N$. With increasing $N$, the critical temperature decreases, while the discontinuities become more pronounced, indicating a stronger first-order transition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_19310 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fluctuation-induced first-order superfluid transition in unitary $\mathrm{SU}(N)$ Fermi gases Kalagov, Georgii Quantum Gases Statistical Mechanics We investigate the superfluid phase transition in an $\mathrm{SU}(N)$-symmetric Fermi gas with $N$ distinct spin states using the functional renormalization group. To capture pairing phenomena beyond mean-field theory, we introduce an auxiliary bosonic field and employ the leading order of the derivative expansion of the partially bosonized effective average action. By discretizing the effective potential on a grid and numerically integrating the flow equations, we resolve the thermodynamic behavior near the transition. Our results reveal a fluctuation-induced first-order phase transition for $N \geq 4$, which is absent at the mean-field level. In the unitary regime, we provide quantitative predictions for the critical temperature, as well as for the discontinuities in the superfluid gap and entropy density as functions of $N$. With increasing $N$, the critical temperature decreases, while the discontinuities become more pronounced, indicating a stronger first-order transition. |
| title | Fluctuation-induced first-order superfluid transition in unitary $\mathrm{SU}(N)$ Fermi gases |
| topic | Quantum Gases Statistical Mechanics |
| url | https://arxiv.org/abs/2504.19310 |