Boundary Symmetry Breaking in CFT and the String Order Parameter

Abstract

We consider the ground state of a one-dimensional critical quantum system carrying a global symmetry in the bulk, which is explicitly broken by its boundary conditions. We probe the system via a string-order parameter, showing how it detects the symmetry breaking pattern. We give a precise characterization of the mechanism depicted above in Boundary CFT, and we find a general logarithmic scaling for the order parameter. As a first example we analyze the breaking of a $U(1)$ symmetry for complex free theories induced by a boundary pairing term. Moreover, we give predictions for the breaking of $U(N)$ in free theories, arising from a boundary mixing. We test our predictions with numerical calculations for some lattice realizations of free fermionic system with boundary symmetry breaking, finding a good agreement.

arXiv comment24 pages, 4 figures

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Cited by in corpus (4)

• Non-equilibrium entanglement asymmetry for discrete groups: the example of the XY spin chain
• A universal formula for the entanglement asymmetry of matrix product states
• Full counting statistics and symmetry resolved entanglement for free conformal theories with interface defects
• Universal time evolution of string order parameter in quantum critical systems with boundary invertible or non-invertible symmetry breaking