Universal shift of the fidelity susceptibility peak away from the critical point of the Berezinskii-Kosterlitz-Thouless quantum phase transition

We show that the peak which can be observed in fidelity susceptibility around the Berezinskii-Kosterlitz-Thouless transition is shifted from the quantum critical point (QCP) at Jc to J* in the gapped phase by a value |J*-Jc|=B2/36, where B2 is a transition width controlling the asymptotic form of the correlation length ξ∼exp(-B/|J-Jc|) in that phase. This is in contrast to the conventional continuous QCP where the maximum is an indicator of the position of the critical point. The shape of the peak is universal, emphasizing the close connection between fidelity susceptibility and the correlation length. We support those arguments with numerical matrix product state simulations of the one-dimensional Bose-Hubbard model in the thermodynamic limit, where the broad peak is located at J*=0.212 that is significantly different from Jc=0.3048(3). In the spin-3/2 XXZ model the shift from Jc=1 to J*=1.0021 is small but the narrow universal peak is much more pronounced over the nonuniversal background.