Quantum Memory: Exact Emergent Hamiltonians in 1D and 2D Lattice Systems

With the advent of exquisite quantum emulators, storing highly entangled many-body states becomes essential. While entanglement typically builds over time after initializing a quantum system with a product state, freezing that information at any given instant requires quenching to a Hamiltonian with the time-evolved state as an eigenstate, which we achieve via the Emergent Hamiltonian framework introduced by Vidmar et al., Phys. Rev. X7, 021012 (2017) in a quantum system of hard-core bosons. While the Emergent Hamiltonian is generically non-local and may lack a closed form, in our case it is exact and capable of pausing dynamics indefinitely with perfect precision, thus opening a new frontier in quantum memory applications. Unlike other phenomena such as many-body localization, our method preserves both local and global properties of the quantum state. In particular, we demonstrate that this formalism is exact for 1D hardcore bosons at any filling and for single-particles in any dimension. A complete spectral characterization of the original and emergent Hamiltonians at various times is carried out . Additionally, we explore the duality between the many-body dynamics of spin-½ particles on a 2D lattice and the dynamics of two interacting large spins within this framework.