Symmetry Resolved Entanglement in Interacting Models

Over the last two decades, entanglement measures have been employed in probing quantum phases of matter and quantum phase transitions, in addition to being undisputably detected experimentally and efficiently calculated using quantum stochastic methods. More recently, there has been an accelerated interest in utilizing the presence of conservation laws to gain a deeper understanding of the entanglement structure in different quantum scenarios. In the presence of conservation laws in a quantum state, such as the conservation of the total charge Q, the resulting entanglement spectrum obtained from a mode-bipartite reduced density matrix can be resolved based on the local charge q and thus identify the contribution from each charge q sector to the total entanglement. From the point of view of quantum information, a quantum state of conserved charge Q contains less accessible entanglement as the unaccessible contribution to the entanglement is due to the fluctuations of the local charge q, and thus preparing a state with a large amount of accessible entanglement is an obvious goal. Motivated by this vigorous interplay between condensed matter and quantum information, we investigate the symmetry-resolved entanglement in bosonic and fermionic lattice models, namely the Bose-Hubbard model and spinless lattice fermions. We show that accessible entanglement peaks around continuous phase transitions singling a distinct scaling, suggesting that quantum states near quantum phase transitions are more resourceful in terms of quantum information. We also extend our investigation to include particle-bipartite symmetry-resolved entanglement in a translationally invariant system, where the entanglement resolution is due to the conservation of the total quasi-momentum of the lattice model. We show that the resulting symmetry-resolved particle entanglement entropy demonstrates a comparable behavior across phase transitions.