General two-order-parameter Ginzburg-Landau model with quadratic and quartic interactions

Abstract

Ginzburg-Landau model with two order parameters appears in many condensed-matter problems. However, even for scalar order parameters, the most general U(1)-symmetric Landau potential with all quadratic and quartic terms contains 13 independent coefficients and cannot be minimized with straightforward algebra. Here, we develop a geometric approach that circumvents this computational difficulty and allows one to study properties of the model without knowing the exact position of the minimum. In particular, we find the number of minima of the potential, classify explicit symmetries possible in this model, establish conditions when and how these symmetries are spontaneously broken, and explicitly describe the phase diagram.

36 pages, 7 figures; v2: added additional clarifications and a discussion on how this method differs from the MIB-approach

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Cited by in corpus (14)

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• Tree-level metastability bounds for the most general two Higgs doublet model
• Discrete symmetries in the three-Higgs-doublet model
• Properties of the general NHDM. I. The orbit space
• Competition/Enhancement of Two Probe Order Parameters in the Unbalanced Holographic Superconductor
• Coexistence of two vector order parameters: a holographic model for ferromagnetic superconductivity
• CDF $W$ boson mass and muon $g-2$ in type-X two-Higgs-doublet model with a Higgs-phobic light pseudoscalar
• High scale impact in alignment and decoupling in two-Higgs doublet models
• Higgs masses of the general 2HDM in the Minkowski-space formalism
• Fermiophobic light Higgs boson in the type-I two-Higgs-doublet model
• Pseudoscalar decays to gauge bosons at the LHC and at a future 100 TeV collider
• Disentangling the high and low cutoff scales via the trilinear Higgs couplings in the type-I two-Higgs-doublet model
• Phase diagram of interacting pion matter and isospin charge fluctuations
• First-order phase transition between superconductivity and charge/spin-density wave as the reason of their coexistence in organic metals