Entanglement Entropy of Local Operators in Quantum Lifshitz Theory

We study the growth of entanglement entropy(EE) of local operator excitation in the quantum Lifshitz model which has dynamic exponent z = 2. Specifically, we act a local vertex operator on the groundstate at a distance $l$ to the entanglement cut and calculate the EE as a function of time for the state's subsequent time evolution. We find that the excess EE compared with the groundstate is a monotonically increasing function which is vanishingly small before the onset at $t \sim l^2$ and eventually saturates to a constant proportional to the scaling dimension of the vertex operator. The quasi-particle picture can interpret the final saturation as the exhaustion of the quasi-particle pairs, while the diffusive nature of the time scale $t \sim l^2$ replaces the common causality constraint in CFT calculation. To further understand this property, we compute the excess EE of a small disk probe far from the excitation point and find chromatography pattern in EE generated by quasi-particles of different propagation speeds.