Bipartite Fidelity and Loschmidt Echo of Bosonic Conformal Interface

Abstract

We study the quantum quench problem for a class of bosonic conformal interfaces by computing the Loschmidt echo and the bipartite fidelity. The quench can be viewed as a sudden change of boundary conditions parameterized by $θ$ when connecting two one-dimensional critical systems. They are classified by $S(θ)$ matrices associated with the current scattering processes on the interface. The resulting Loschmidt echo of the quench has long time algebraic decay $t^{-α}$, whose exponent also appears in the finite size bipartite fidelity as $L^{-\fracα{2}}$. We perform analytic and numerical calculations of the exponent $α$, and find that it has a quadratic dependence on the change of $θ$ if the prior and post quench boundary conditions are of the same type of $S$, while remaining $\frac{1}{4}$ otherwise. Possible physical realizations of these interfaces include, for instance, connecting different quantum wires (Luttinger liquids), quench of the topological phase edge states, etc. and the exponent can be detected in a X-ray edge singularity type experiment.