Thermodynamic Discovery of Tetracriticality and Emergent Multicomponent Superconductivity in UTe${}_2$

The candidate topological superconductor UTe${}_2$ exhibits a complex phase diagram with multiple superconducting states, yet the nature of their coexistence has remained a central mystery. In particular, the apparent intersection of two second-order phase boundaries at a triple point'' in the pressure-temperature phase diagram is thermodynamically forbidden, suggesting hidden phase transitions or a fundamental misunderstanding of the superconductivity in UTe$_2$. Here, we use pulse-echo ultrasound to resolve this puzzle by discovering a new phase boundary that is characterized by a unique upward jump" in the sound velocity – direct thermodynamic evidence for a re-entrant phase transition. Our results establish $(P^{\star },T^{\star })$ as a tetracrtical point, beyond which the ambient and pressure-induced superconducting order parameters form a multi-component state. We use the measured phase diagram to construct a Ginzburg-Landau theory that shows that strong competition between the two superconducting order parameters drives the re-entrance and leads to phase locking that suppress superconducting fluctuations. These findings provide the definitive magnetic field-temperature-pressure phase diagram and establish a thermodynamic foundation for multi-component – and potentially topological – superconductivity in UTe${}_2$.