Quantum many-body scars from infinite temperature thermofield-double states in bilayer systems

Recently, a new class of quantum many-body scar (QMBS) states --called rainbow scars-- was introduced in arXiv:2107.03416. In this work, we explore a closely related construction of QMBS based on infinite-temperature thermofield-double (TFD) states, which we dub TFD scars. The construction naturally applies to bilayer systems, including both spatial bilayers (with two spatially separated layers) and ``internal'' bilayers where the two layers correspond to different internal degrees of freedom (e.g., electron spins). Like the rainbow scar states, the TFD scars exhibit extensive bipartite entanglement entropy between the two layers despite having a simple entanglement structure. We explicitly investigate several bilayer systems with different kinds of degrees of freedom, e.g. spins, bosons, fermions, and quantum dimers with constrained Hilbert spaces. Some of the examples we consider subsume previously known examples of quantum many-body scars, including the spin-1 XY model and the $\eta$-pairing states in Fermi-Hubbard-like models. Furthermore, the construction also leads to new examples of QMBS, including in Bose-Hubbard and quantum dimer models. Building on recent experimental advances, we discuss potential relations to systems that can be engineered in a laboratory setting.