Emergent PT-symmetry breaking of collective modes with topological critical phenomena
Abstract The spontaneous breaking of parity-time ( PT PT ) symmetry yields rich critical behavior in non-Hermitian systems, and has stimulated much interest, albeit most previous studies were performed within the single-particle or mean-field framework. Here, by studying the collective excitations of a Fermi superfluid with PT PT -symmetric spin-orbit coupling, we uncover an emergent PT PT -symmetry breaking in the Anderson-Bogoliubov (AB) collective modes, even as the superfluid ground state retains an unbroken PT PT symmetry. The critical point of the transition is marked by a non-analytic kink in the speed of sound, which derives from the coalescence and annihilation of the AB mode and its hole partner, reminiscent of the particle-antiparticle annihilation. The system consequently becomes immune to low-frequency external perturbations at the critical point, a phenomenon associated with the spectral topology of the complex quasiparticle dispersion. This critical phenomenon offers a fascinating route toward perturbation-free quantum states.
In this letter, we propose and study a ladder triangular cluster model which possesses a Z2 symmetry and an anti-unitary Z2T symmetry generated by the spin-flip and complex conjugation, respectively. The phase diagram of the model hosts a critical line between a spontaneous symmetry breaking phase and a symmetry protected topological phase. Along the critical line, one endpoint exhibits symmetry-enriched Ashkin-Teller universality (SEATU), while other critical points fall into the symmetry-enriched Ising universality (SEIU). Both universality classes accommodate symmetry protected degenerate edge modes under open boundary conditions. This degeneracy can be lifted with a gap opening when proper perturbation is applied to the boundary. With system size (L) increasing, at the point of SEATU, the gap closes following L−1. In contrast, for the critical points of SEIU apart from a point with the known gap closing as L−14, other points surprisingly show exponentially gap closing. The coexistence of different gap closing behaviors for critical points of the same symmetry-enriched universality goes beyond the the usual understanding of symmetry-enriched universality class, implying a fine and rich structure of phase transition and universality class.
Nonstabilizerness is a critical resource for quantum advantage, but evaluating it, especially for mixed states, requires superexponentially many samples in system size, making the problem NP-hard. While symmetries are known to reduce this complexity, it is unclear whether they also restrict the amount of magic. In this work, we provide an explicit example of such a symmetry by proving that the Robustness of Magic (RoM) for N-qubit X-states is at most 3. Leveraging this symmetry constraint, we introduce a computationally efficient method to lower-bound the RoM of arbitrary many-body states, demonstrating its utility on the ground states of a spin-1/2 Hamiltonian with system sizes well beyond the reach of exact evaluation. Furthermore, for Hamiltonians whose equilibrium states are X-states, we analytically derive the critical temperature at which magic emerges. Our work shows why certain symmetries constrain magic while others do not, provides a scalable lower-bounding method, and identifies a nontrivial regime where many-body nonstabilizerness is analytically solvable.