Chaos in hyperscaling violating Lifshitz theories

We holographically study quantum chaos in hyperscaling-violating Lifshitz (HVL) theories (with charge). Specifically, we present a detailed computation of the out-of-time ordered correlator (OTOC) via shockwave analysis in the bulk HVL geometry with a planar horizon topology. We also compute the butterfly velocity $v_B$ using the entanglement wedge reconstruction and find that it matches the result obtained from the shockwave analysis. Using a recently developed thermodynamic dictionary for HVL theories, we express v_B purely in terms of boundary thermodynamic variables. Furthermore, we analyze in detail the behavior of v_B with respect to the dynamical critical exponent (z), hyperscaling-violating parameter (θ), entropy more precisely, the ratio of entropy to the central charge, ${S}$, and charge more precisely, the ratio of charge to the central charge, ${Q}$. Interestingly, v_B varies non-monotonically with z for {S} < 1, whereas it increases monotonically with z for {S} geq 1. Additionally, v_B varies non-monotonically with θ for non-zero charge. Moreover, v_B monotonically increases with {S} and decreases with {Q} for all allowed values of z and θ. All these features are reported for combinations /{z, θ, {S}, {Q}/} for which the temperature is positive, the null energy condition is satisfied, and v_B is not superluminal. Unpacking the non-monotonicities in v_B can offer interesting insights into these theories.