# Universal Thermodynamic Signature of Self-dual Quantum Critical Points

## TL;DR

This paper proposes a universal thermodynamic signature for self-dual quantum critical points, showing that the Grüneisen ratio remains finite at zero temperature, unlike at generic critical points where it diverges.

## Contribution

It introduces a universal thermodynamic criterion based on the Grüneisen ratio to identify self-dual quantum critical points, which was not previously understood.

## Key findings

- Grüneisen ratio remains finite at self-dual QCPs as T→0
- Divergence of Grüneisen ratio at non-self-dual QCPs
- Implications for experimental and numerical detection of self-duality

## Abstract

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.