Topological quantum phase transitions and multicritical caloric effects in the AI symmetry class

Topological insulators (TIs), topological semimetals (TSMs) and topological metals (TMs) have attracted broad attention. A key challenge lies in realizing and controllably tuning these diverse topological states and transitions within a single, coherent system. Here, we propose a double coupled Su-Schrieffer-Heeger chain with time-reversal symmetry (AI class) to achieve this, wherein intrachain hopping drives topological quantum phase transitions with changing Zak phase and showing different types of critical TSMs, while interchain hopping drives a Wilson insulator-metal transition without altering the underlying topology. We obtain a rich phase diagram segmented by topological and Wilson critical lines intersecting at a multicritical point, consisting of two TIs (TI1, TI2) and two TMs (TM1, TM2). TI1 and TM1 share the same topology, as do TI2 and TM2. Meanwhile, thermal Drude weight used as a diagnostic tool at low temperatures, shows sharp peaks or dips at phase boundaries, successfully mapping the entire phase diagram and characterizing the low-lying excitations. Furthermore, an optimal cooling path is found: by tuning interchain hopping along the topological critical line, one can obtain a significant inverse caloric effect near the multicritical point at low temperatures with large entropy and temperature change as well as high efficiency factor. It offers a promising solid-state cooling mechanism for achieving ultra-low temperatures in quantum technologies.