Novel entanglement phases and phase transitions via spacetime duality


Khemani, V. (2021). Novel entanglement phases and phase transitions via spacetime duality. Perimeter Institute. https://pirsa.org/21030002


Khemani, Vedika. Novel entanglement phases and phase transitions via spacetime duality. Perimeter Institute, Mar. 22, 2021, https://pirsa.org/21030002


          @misc{ pirsa_21030002,
            doi = {10.48660/21030002},
            url = {https://pirsa.org/21030002},
            author = {Khemani, Vedika},
            keywords = {Condensed Matter},
            language = {en},
            title = {Novel entanglement phases and phase transitions via spacetime duality},
            publisher = {Perimeter Institute},
            year = {2021},
            month = {mar},
            note = {PIRSA:21030002 see, \url{https://pirsa.org}}

Vedika Khemani Harvard University



The extension of many-body quantum dynamics to the non-unitary domain has led to a series of exciting developments, including new out-of-equilibrium entanglement phases and phase transitions. We show how a duality transformation between space and time on one hand, and unitarity and non-unitarity on the other, can be used to realize steady state phases of non-unitary dynamics that exhibit a rich variety of behavior in their entanglement scaling with subsystem size --- from logarithmic to extensive to fractal. We show how these outcomes in non-unitary circuits (that are ``spacetime-dual" to unitary circuits) relate to the growth of entanglement in time in the corresponding unitary circuits, and how they differ, through an exact mapping to a problem of unitary evolution with boundary decoherence, in which information gets ``radiated away'' from one edge of the system. In spacetime-duals of chaotic unitary circuits, this mapping allows us to uncover a non-thermal volume-law entangled phase with a logarithmic correction to the entropy distinct from other known examples. Most notably, we also find novel steady state phases with fractal entanglement scaling, $S(\ell) \sim \ell^{\alpha}$ with tunable $0 < \alpha < 1$ for subsystems of size $\ell$ in one dimension. These fractally entangled states add a qualitatively new entry to the families of many-body quantum states that have been studied as energy eigenstates or dynamical steady states, whose entropy almost always displays either area-law, volume-law or logarithmic scaling. We also present an experimental protocol for preparing these novel steady states with only a very limited amount of postselection via a type of ``teleportation" between spacelike and timelike slices of quantum circuits.