Phase diagrams of SO($N$) Majorana-Hubbard models: Dimerization, internal symmetry breaking, and fluctuation-induced first-order transitions

Abstract

We study the zero-temperature phase diagrams of Majorana-Hubbard models with SO($N$) symmetry on two-dimensional honeycomb and $\pi$-flux square lattices, using mean-field and renormalization group approaches. The models can be understood as real counterparts of the SU($N$) Hubbard-Heisenberg models, and may be realized in Abrikosov vortex phases of topological superconductors, or in fractionalized phases of strongly-frustrated spin-orbital magnets. In the weakly-interacting limit, the models feature stable and fully symmetric Majorana semimetal phases. Increasing the interaction strength beyond a finite threshold for large $N$, we find a direct transition towards dimerized phases, which can be understood as staggered valence bond solid orders, in which part of the lattice symmetry is spontaneously broken and the Majorana fermions acquire a mass gap. For small to intermediate $N$, on the other hand, phases with spontaneously broken SO($N$) symmetry, which can be understood as generalized Néel antiferromagnets, may be stabilized. These antiferromagnetic phases feature fully gapped fermion spectra for even $N$, but gapless Majorana modes for odd $N$. While the transitions between Majorana semimetal and dimerized phases are strongly first order, the transitions between Majorana semimetal and antiferromagnetic phases are continuous for small $N\le 3$ and weakly first order for intermediate $N\ge 4$. The weakly-first-order nature of the latter transitions arises from fixed-point annihilation in the corresponding effective field theory, which contains a real symmetric tensorial order parameter coupled to the gapless Majorana degrees of freedom, realizing interesting examples of fluctuation-induced first-order transitions.

14 pages, 4 figures

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Cited by in corpus (8)

• Gross-Neveu-Heisenberg criticality from $2+\mathbf{\epsilon }$ expansion
• Emergence of Competing Orders and Possible Quantum Spin Liquid in SU(N) Fermions
• Gross-Neveu-Yukawa theory of $\text{SO}(2N)\to \text{SO}(N)\times \text{SO}(N)$ spontaneous symmetry breaking
• Chiral bosonic quantum spin liquid in the integer-spin Heisenberg-Kitaev model
• Beyond one-loop calculation: Higher-order effects on Gross-Neveu-Yukawa tensorial criticality
• Superconductivity in Luttinger semimetals near the SU(4) limit
• Continuous order-to-order quantum phase transitions from fixed-point annihilation
• Functional renormalization group equations for antisymmetric tensor field models at finite temperature