# Boundary critical exponents of the 1D quantum XY model

Critical properties of the two-dimensional Ising model in the bulk and at the boundary are characterized by different critical exponent, see Ising model: exact results and McCoy: The boundary Ising model for example.
Are there boundary critical exponents known for the quantum 1D spin-1/2 anisotropic XY model in a field?
Hamiltonian of the model with open boundary conditions has a form $$\hat{H} = -\sum_{j=1}^{L-1}\left(J_x\hat{S}^x_j\hat{S}^x_{j+1}+J_y\hat{S}^y_j\hat{S}^y_{j+1}\right) - h\sum_{j=1}^L\hat{S}^z_j,$$ where $\hat{S}^\alpha_j$ are spin-1/2 operators.

• You may find some useful insights from the fact that the 1D XY model maps to two disjoint critical Ising models. Then you may find the scaling of many properties from Boundary operators of Ising CFTs. See for instance supplementary section of journals.aps.org/prl/abstract/10.1103/PhysRevLett.118.260602 – symanzik138 May 15 at 14:20
• @symanzik138 Thank you! – Gec May 15 at 16:39