Hidden quantum critical points: spontaneous symmetry breaking without long-range order

Topological phase transitions go beyond Ginzburg and Landau’s paradigm of spontaneous symmetry breaking (SSB) in the presence of long-range order and occur without a corresponding local order parameter. Often, such transitions can instead be characterized by non-local order parameters that capture the underlying hidden order.

We investigate an instance of a hidden quantum critical point which features SSB without the presence of long-range order in a paradigmatic 1d model. This state has previously been described as an intrinsically gapless topological state [1]. We explore this phenomenon using the example of a doped transverse field Ising model and compute the dynamical structure factor. Hole doping effects the long wavelength features and causes the formation of two doping-dependent gapless points in the ordered phase while the short range features are preserved. Our numerical results are supported by analytic considerations in squeezed space.

Upon introducing next-nearest-neighbor hopping, we show a transition from the hidden order phase to a true antiferromagnetic phase at zero field which is accompanied by the confinement of holes. Leveraging the intrinsic connections between the squeezed space construction and bosonization, we are able to analytically identify this phase transition.

Our work marks a first step towards establishing a framework for detecting hidden quantum critical points in mixD and 2d.

[1] Intrinsically gapless topological phases. Thorngren, R. et al. Phys. Rev. B 104, 075132 (2021).