Motivated by the remarkable properties of superfluid edge dislocations in ${}^4\mathrm{He}$, we discuss a broad class of quantum systems—boundaries in phase-separated lattice states, magnetic domain walls, and ensembles of Luttinger liquids—that can be classified as transverse quantum fluids (TQFs). After introducing the general idea of a TQF, we focus on a coupled array of Luttinger liquids forming an incoherent TQF. This state is a long-range ordered quasi-one-dimensional superfluid, topologically protected against quantum phase slips by the tight binding of instanton dipoles, that has no coherent quasiparticle excitations at low energies. An incoherent TQF is a striking example of the irrelevance of the Landau quasiparticle criterion for superfluidity in systems that lack Galilean invariance. We detail its phenomenology, to motivate a number of experimental studies in condensed matter and cold atomic systems.

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• Magnetism
• Superfluidity
• Surface & interfacial phenomena