Magnetochiral eigenstate of the Heisenberg chain with spontaneous symmetry breaking

We propose a protocol to construct atypical high-energy eigenstates in quantum systems by using ground states of Hamiltonians deformed by conserved charges. For the spin-1/2 Heisenberg XXX chain we study a chiral Hamiltonian built from the scalar-chirality charge and total magnetization and solve it exactly by Bethe ansatz. Its ground state is a magnetized, current-carrying XXX eigenstate that breaks SU(2), time-reversal, and parity yet stays critical. This zero-entropy macrostate shows ballistic spin and chirality transport and admits realistic cold-atom and Rydberg platforms.