PhD Seminar - Complexity of Steady States of Open Quantum Systems

Understanding the structure and physical properties of open many-body quantum systems is a significant challenge in condensed matter physics. Specifically, we explore entanglement, correlations, and the representability of states that arise in the long-term dynamics of open systems, namely, their steady states. These properties are essential for understanding non equilibrium phases and phase transitions. Unlike closed systems, the non-hermitian generators for the dynamics, do not allow for straightforward spectral methods.

In this talk, I will present the general problem and relevant questions under study. I will discuss my main project which focuses on steady states of local Lindbladians. We demonstrate area laws and a tensor network construction for the purification of steady states in detailed-balance systems. This is achieved by mapping the Lindbladian to a local Hamiltonian on an extended lattice, for which the purification is a ground state. Moreover, we purpose an extension to generally non-detailed-balance systems. Finally, we discuss potential leads for applying this mapping to classify non-equilibrium phases of open systems.