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 Gruneisen ratio at a self-dual QCP remains finite as T -> 0, which is in sharp contrast to its universal divergence at a generic QCP without self-duality, Gamma(T,g(c)) similar to T-1/zv. This conclusion is drawn based on the hyperscaling theory near the QCP, and has farreaching implications for experiments and numerical simulations.