Many-body topological and skin states without open boundaries

Robust boundary states have been the focus of much recent research, both as topologically protected and non-Hermitian skin states. In this work, we show that many-body effects can also induce analogs these robust in place actual physical boundaries. Particle statistics or suitably engineered interactions i.e. ultracold atomic lattices restrict accessible Hilbert space, introduce effective boundaries a spatially periodic higher-dimensional configuration space. We demonstrate emergence topological chiral modes two-fermion hopping model without open boundaries, with fermion pairs confined asymmetrically propagated by chosen fluxes. Heterogeneous non-reciprocal hoppings across different particle species result clumping translation invariant setting, reminiscent mode accumulation at an boundary. But unlike fixed correspond to locations impenetrable particles are dynamic, giving rise fundamentally vs. single-body time evolution behavior. Since is agnostic dimensionality restricted spaces, our generalize directly thermodynamic limit. The states, however, nontrivially dimension-dependent, their detailed exploration will stimulate further studies higher dimensional invariants.