Speaker
Alberto Ruiz-de-Alarcón, CUNEF Universidad
Abstract
In recent decades, exotic phases of matter have emerged as a central theme in condensed matter physics. One particularly interesting case is that of one-dimensional open systems: while gapped quantum phases are relatively well understood and characterized for pure states by virtue of renormalization techniques, extending this framework to mixed states presents certain challenges. The focus of this talk will be on matrix product density operators that are fixed points under renormalization. In essence, these capture the structure of mixed-state phases in one dimension. In this context, two mixed states are said to be in the same phase if they can be transformed into each other via a shallow circuit of local quantum channels. First, I will present a systematic construction of families of renormalization fixed-point matrix product density operators derived from representations of C*-weak Hopf algebras—which encompass unitary multifusion categories. I will further prove that these mixed states arise as boundary states of two-dimensional tensor network pure states via a rigorous bulk-boundary correspondence. Moreover, I will construct explicit local fine- and coarse-graining quantum channels, and prove that a subclass corresponds to the trivial phase. Finally, I will show that they emerge as steady states of minimal, local, frustration-free Lindbladians. This talk is based on arXiv:2204.05940, 2204.06295, and 2501.10552.