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We devise a generic and experimentally accessible recipe to prepare boundary states of topological or nontopological quantum systems through an interplay between coherent Hamiltonian dynamics and local dissipation. Intuitively, our recipe harnesses the spatial structure of boundary states which vanish on sublattices where losses are suitably engineered. This yields unique nontrivial steady states that populate the targeted boundary states with infinite lifetimes while all other states are exponentially damped in time. Remarkably, applying loss only at one boundary can yield a unique steady state localized at the very same boundary. We detail our construction and rigorously derive full Liouvillian spectra and dissipative gaps in the presence of a spectral mirror symmetry for a one-dimensional Su-Schrieffer-Heeger model and a two-dimensional Chern insulator. We outline how our recipe extends to generic noninteracting systems.

We explore anomalous skin effects at non-Hermitian impurities by studying their interplay with potential disorder and by exactly solving a minimal lattice model. A striking feature of the solvable single-impurity model is that the presence of anisotropic hopping terms can induce a scale-free accumulation of all eigenstates opposite to the bulk hopping direction, although the nonmonotonic behavior is fine tuned and further increasing such hopping weakens and eventually reverses the effect. The interplay with bulk potential disorder, however, qualitatively enriches this phenomenology leading to a robust nonmonotonic localization behavior as directional hopping strengths are tuned. Nonmonotonicity persists even in the limit of an entirely Hermitian bulk with a single non-Hermitian impurity.

The ground states of noninteracting fermions in one-dimension with chiral symmetry form a class of topological band insulators, described by a topological invariant that can be related to the Zak phase. Recently, a generalization of this quantity to open systems—known as the ensemble geometric phase (EGP)—has emerged as a robust way to describe topology at nonzero temperature. By using this quantity, we explore the nature of topology allowed for dissipation beyond a Lindblad description, to allow for coupling to external baths at finite temperatures. We introduce two main aspects to the theory of open-system topology. First, we discover topological phase transitions as a function of the temperature T, manifesting as changes in differences of the EGP accumulated over a closed loop in parameter space. We characterize the nature of these transitions and reveal that the corresponding nonequilibrium steady state can exhibit a nontrivial structure—contrary to previous studies where it was found to be in a fully mixed state. Second, we demonstrate that the EGP itself becomes quantized when key symmetries are present, allowing it to be viewed as a topological marker which can undergo equilibrium topological transitions at nonzero temperatures.

With rapid progress in control and manipulation of ultracold magnetic atoms and dipolar molecules, the quantum simulation of lattice models with strongly interacting dipole-dipole interactions (DDIs) and high densities is now within experimental reach. This rapid development raises the issue about the validity of quantum simulation in such regimes. In this study, we address this question by performing a full quantitative comparison between the continuum description of a one-dimensional gas of dipolar bosons in an optical lattice and the single-band Bose-Hubbard lattice model that it quantum simulates. By comparing energies and density distributions and calculating direct overlaps between the continuum and lattice many-body wave functions, we demonstrate that in regimes of strong DDIs and high densities the continuum system fails to recreate the desired lattice model. Two-band Hubbard models become necessary to reduce the discrepancy observed between continuum and lattice descriptions, but appreciable deviations in the density profile still remain. Our study elucidates the role of strong DDIs in generating physics beyond lowest-band descriptions and should offer a guideline for the calibration of near-term dipolar quantum simulators.