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A quantum tricritical point is shown to exists in coupled time-reversalsymmetry (TRS) broken Majorana chains. The tricriticality separatestopologically ordered, symmetry protected topological (SPT), and trivial phasesof the system. Here we demonstrate that the breaking of the TRS manifestsitself in an emergence of a new dimensionless scale, $g = \alpha(\xi) B\sqrt{N}$, where $N$ is the system size, $B$ is a generic TRS breaking field,and $\alpha(\xi)$, with $\alpha(0)\equiv 1$, is a model-dependent function ofthe localization length, $\xi$, of boundary Majorana zero modes at thetricriticality. This scale determines the scaling of the finite sizecorrections around the tricriticality, which are shown to be {\it universal},and independent of the nature of the breaking of the TRS. We show that thesingle variable scaling function, $f(w)$, $w\propto m N$, where $m$ is theexcitation gap, that defines finite-size corrections to the ground state energyof the system around topological phase transition at $B=0$, becomesdouble-scaling, $f=f(w,g)$, at finite $B$. We realize TRS breaking throughthree different methods with completely different lattice details and find thesame universal behavior of $f(w,g)$. In the critical regime, $m=0$, thefunction $f(0,g)$ is nonmonotonic, and reproduces the Ising conformal fieldtheory scaling only in limits $g=0$ and $g\rightarrow \infty$. The obtainedresult sets a scale of $N \gg 1/(\alpha B)^2$ for the system to reach thethermodynamic limit in the presence of the TRS breaking. We derive theeffective low-energy theory describing the tricriticality and analytically findthe asymptotic behavior of the finite-size scaling function. Our results showthat the boundary entropy around the tricriticality is also a universalfunction of $g$ at $m=0$.

Universal finite size scaling around tricriticality between topologically ordered, SPT, and trivial phases