Physics of Many-body Nonreciprocal Model: From Non-Hermitian Skin effect to Quantum Maxwell's Pressure-Demon Effect

Non-Hermitian (NH) systems may have quite different physics properties from that of Hermitian counterparts. For example, in the NH systems with nonreciprocal hopping, there exists (single-body version of) skin effect-The eigenstates are exponentially localized at the boundaries. An interesting problem is about the generalization of NH skin effect to a many-body NH system. In this paper, we studied many-body physics in the quantum systems with nonreciprocal hoppings and obtained analytical results. In these many-body NH systems, the single-body NH skin effect upgrades to quantum (Maxwell' s) pressure-demon effect, which leads to band-width renormalization and a uniform pressure gradient to the system. In particular, according to the quantum pressure-demon effect, in many-body Bosonic/Fermionic Hotano-Nelson model, there exist new physical phenomena compared with their Hermitian counterparts: Liouvillian Bose-Einstein condensation and Liouvillian Fermi-surface in real space, respectively. This discovery will open a door to learn many-body physics for NH quantum systems.