Unbiased large-$N$ approach to competing vestigial orders of density-wave and superconducting instabilities
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| Format: | Preprint |
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2026
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| _version_ | 1866917482170679296 |
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| author | Palle, Grgur Fernandes, Rafael M. |
| author_facet | Palle, Grgur Fernandes, Rafael M. |
| contents | When a primary order breaks multiple symmetries, partially ordered phases that only break a subset of those symmetries, known as vestigial phases, may onset at a higher temperature. This concept has been applied to a wide range of systems, including iron pnictides, cuprates, van der Waals antiferromagnets, doped topological insulators, and twisted bilayer graphene. In general, a multi-component primary order parameter (OP) supports multiple vestigial channels, each described by a quadratic (or higher-order) composite OP. However, the standard large-$N$ approach to the Ginzburg-Landau action of the primary OP has an intrinsic ambiguity in how one decouples the composite OPs, leading to situations in which one can seemingly enhance or eliminate altogether any vestigial instability. Here, we show that this ambiguity is a direct consequence of redundancy relations, such as Fierz identities, that relate different composite OPs, reflecting the fact that different vestigial channels interfere with each other and thus cannot be treated separately. To resolve this ambiguity, we propose an unbiased large-$N$ approach that respects both the redundancy relations and the underlying symmetry-group structure, and that gives unique values for the effective interactions of all vestigial channels. Our analysis reveals the generic existence of regions in the parameter space of quartic Landau coefficients where no vestigial order is stable, in contrast to the standard large-$N$ approach, but in agreement with weak-coupling and variational approaches. We illustrate our results by analyzing the vestigial orders of charge-density waves, spin-density waves, and multi-component superconductors in tetragonal, hexagonal, and cubic systems, respectively, revealing the presence of exotic vestigial phases describing spin-quadrupolar, charge-$4e$ superconducting, and altermagnetic orders. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_11281 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Unbiased large-$N$ approach to competing vestigial orders of density-wave and superconducting instabilities Palle, Grgur Fernandes, Rafael M. Strongly Correlated Electrons Statistical Mechanics Superconductivity When a primary order breaks multiple symmetries, partially ordered phases that only break a subset of those symmetries, known as vestigial phases, may onset at a higher temperature. This concept has been applied to a wide range of systems, including iron pnictides, cuprates, van der Waals antiferromagnets, doped topological insulators, and twisted bilayer graphene. In general, a multi-component primary order parameter (OP) supports multiple vestigial channels, each described by a quadratic (or higher-order) composite OP. However, the standard large-$N$ approach to the Ginzburg-Landau action of the primary OP has an intrinsic ambiguity in how one decouples the composite OPs, leading to situations in which one can seemingly enhance or eliminate altogether any vestigial instability. Here, we show that this ambiguity is a direct consequence of redundancy relations, such as Fierz identities, that relate different composite OPs, reflecting the fact that different vestigial channels interfere with each other and thus cannot be treated separately. To resolve this ambiguity, we propose an unbiased large-$N$ approach that respects both the redundancy relations and the underlying symmetry-group structure, and that gives unique values for the effective interactions of all vestigial channels. Our analysis reveals the generic existence of regions in the parameter space of quartic Landau coefficients where no vestigial order is stable, in contrast to the standard large-$N$ approach, but in agreement with weak-coupling and variational approaches. We illustrate our results by analyzing the vestigial orders of charge-density waves, spin-density waves, and multi-component superconductors in tetragonal, hexagonal, and cubic systems, respectively, revealing the presence of exotic vestigial phases describing spin-quadrupolar, charge-$4e$ superconducting, and altermagnetic orders. |
| title | Unbiased large-$N$ approach to competing vestigial orders of density-wave and superconducting instabilities |
| topic | Strongly Correlated Electrons Statistical Mechanics Superconductivity |
| url | https://arxiv.org/abs/2605.11281 |