A universal formula for the entanglement asymmetry of matrix product states

Symmetry breaking is a fundamental concept in understanding quantum phases of matter, studied so far mostly through the lens of local order parameters. Recently, a new entanglement-based probe of symmetry breaking has been introduced under the name of $\mathit{\text{entanglement}}\mathit{\text{asymmetry}}$, which has been employed to investigate the mechanism of dynamical symmetry restoration. Here, we provide a universal formula for the entanglement asymmetry of matrix product states with finite bond dimension, valid in the large volume limit. We show that the entanglement asymmetry of any compact – discrete or continuous – group depends only on the symmetry breaking pattern, and is not related to any other microscopic features.