Universal Thermodynamic Signature of Self-dual Quantum Critical Points

Self-duality is an algebraic structure of certain critical theories, which is not encoded in the scaling dimensions and critical exponents. In this work, a universal thermodynamic signature of self-dual quantum critical points (QCPs) is proposed. It is shown that the Gr\"uneisen ratio at a self-dual QCP remains finite as $T\rightarrow 0$, which is in sharp contrast to its universal divergence at a generic QCP without self-duality, $\Gamma(T,g_{c})\sim T^{-1/z\nu}$. This conclusion is drawn based on the hyperscaling theory near the QCP, and has far-reaching implications for experiments and numerical simulations.