Würzburg Seminar on Quantum Field Theory and Gravity

Symmetry breaking is a mechanism at the core of many intriguing physical phenomena, ranging from superfluidity, superconductivity, ferromagnetism, to the Higgs mechanism. Its characterization usually proceeds through the lens of local order parameters, such as magnetization. A recent entanglement-based probe has been introduced in the context of U(1) symmetry restoration; it aims to detect whether a subregion of the system can be considered symmetric or not. In our work, we extend this concept to generic compact (finite or Lie) groups, and we compute the entanglement asymmetry for translational invariant Matrix Product States (MPS). We derive a universal formula in the limit of large subregions, which depends only on the symmetry-breaking pattern associated with the state. In particular, we characterize the exponential decay or saturation of certain charged moments. The scenario described above is expected to be the general mechanism underlying the asymmetry of pure states with short-ranged correlations.
This seminar is based on Ref. arXiv:2310.01962, a joint work with Vittorio Vitale.