Fragility of time-reversal symmetry protected topological phases

The second law of thermodynamics points to the existence of an 'arrow of time', along which entropy only increases. This arises despite the time-reversal symmetry (TRS) of the microscopic laws of nature. Within quantum theory, TRS underpins many interesting phenomena, most notably topological insulators(1-4)and the Haldane phase of quantum magnets(5,6). Here, we demonstrate that such TRS-protected effects are fundamentally unstable against coupling to an environment. Irrespective of the microscopic symmetries, interactions between a quantum system and its surroundings facilitate processes that would be forbidden by TRS in an isolated system. This leads not only to entanglement entropy production and the emergence of macroscopic irreversibility(7-9), but also to the demise of TRS-protected phenomena, including those associated with certain symmetry-protected topological phases. Our results highlight the enigmatic nature of TRS in quantum mechanics and elucidate potential challenges in utilizing topological systems for quantum technologies. When a quantum system couples with its surroundings, macroscopic irreversibility emerges even though the microscopic Hamiltonian is itself time-reversal symmetric, causing the phenomena associated with certain symmetry-protected topological phases to be unstable.