Quasi-Phases of Quantum Matter

Within quantum many-body phase diagrams, continuous transition lines can appear and then terminate. However, it has remained unclear whether the neighboring regimes can be meaningfully described as distinct phases, akin to water and vapour, since any sharp characterization would have to go beyond the usual notion of phases of matter. We answer this in the affirmative by introducing quasi-phases: gapped regimes near a critical point that are connected in the broader phase diagram, but not by any gapped path accessible from small perturbations of the critical theory. The physical consequences include interface modes between regimes in the same phase of matter. More striking still, describing both the extended critical line and the gapped path connecting the regimes requires a bigger multicritical parent theory. In spin-chain examples with continuous terminating lines with central charge $c=1$, we find multicritical $c=3/2$ and $c=9/5$ orbifolds describing so-called 'quotient symmetry protected' and 'representation symmetry protected' topological phenomena. While one-dimensional symmetry-protected topological phases are labeled by projective representation classes, these quasi-phases can have interface modes carrying higher-dimensional linear representations. We turn this into a constructive principle through a weakening of the Lieb-Schultz-Mattis anomaly. Supporting distinct quasi-phases makes an unnecessary critical point infrared-necessary, even if it is unnecessary at the ultraviolet scale. This condition is more restrictive than simply having a codimension-one critical line, revealing richer structure within phases of matter than their conventional classification suggests.