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- W3208127624 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 N'eel 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 $N leq 3$ and weakly first order for intermediate $N geq 4$. 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." @default.
- W3208127624 created "2021-11-08" @default.
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- W3208127624 date "2022-01-14" @default.
- W3208127624 modified "2023-10-14" @default.
- W3208127624 title "Phase diagrams of SO( <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mi>N</mml:mi></mml:math> ) Majorana-Hubbard models: Dimerization, internal symmetry breaking, and fluctuation-induced first-order transitions" @default.
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- W3208127624 doi "https://doi.org/10.1103/physrevb.105.045120" @default.
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