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We consider a system of interacting spinless fermions on a two-leg triangularladder with $\pi/2$ magnetic flux per triangular plaquette. Microscopically,the system exhibits a U(1) symmetry corresponding to the conservation of totalfermionic charge, and a discrete $\mathbb{Z}_2$ symmetry -- a product of paritytransformation and chain permutation. Using bosonization, we show that, in thelow-energy limit, the system is described by the quantum double-frequencysine-Gordon model. On the basis of this correspondence, a rich phase diagram ofthe system is obtained. It includes trivial and topological band insulators forweak interactions, separated by a Gaussian critical line, whereas at largerinteractions a strongly correlated phase with spontaneously broken$\mathbb{Z}_2$ symmetry sets in, exhibiting a net charge imbalance and non-zerototal current. At the intersection of the three phases, the system features acritical point with an emergent SU(2) symmetry. This non-Abelian symmetry,absent in the microscopic description, is realized at low-energies as acombined effect of the magnetic flux, frustration, and many-body correlations.The criticality belongs to the SU(2)$_1$ Wess-Zumino-Novikov-Wittenuniversality class. The critical point bifurcates into two Ising critical linesthat separate the band insulators from the strong-coupling symmetry brokenphase. We establish an analytical connection between the low-energy descriptionof our model around the critical bifurcation point on one hand, and theAshkin-Teller model and a weakly dimerized XXZ spin-1/2 chain on the other. Wecomplement our field-theory understanding via tensor network simulations,providing compelling quantitative evidences of all bosonization predictions.Our findings are of interest to up-to-date cold atom experiments utilizingRydberg dressing, that have already demonstrated correlated ladder dynamics.

Emergence of non-Abelian SU(2) invariance in Abelian frustrated fermionic ladders