Abstract
Fracton topological order (FTO) is a new classification of correlated phases in three spatial dimensions with topological ground state degeneracy (GSD) scaling up with system size, and fractional excitations which are immobile or have restricted mobility. With the topological origin of GSD, FTO is immune to local perturbations, whereas a strong enough global external perturbation is expected to break the order. The critical point of the topological transition is however very challenging to identify. In this work, we propose to characterize quantum phase transition of the type-I FTOs induced by external terms and develop a theory to study analytically the critical point of the transition. In particular, for the external perturbation term creating lineon-type excitations, we predict a generic formula for the critical point of the quantum phase transition, characterized by the breaking-down of GSD. This theory applies to a board class of FTOs, including X-cube model, and for more generic FTO models under perturbations creating two-dimensional (2D) or 3D excitations, we predict the upper and lower limits of the critical point. Our work makes a step in characterizing analytically the quantum phase transition of generic fracton orders.
Highlights
The discovery of topological quantum phases revolutionized the characterization and classification of fundamental states of quantum matter beyond the Landau symmetrybreaking paradigm
We have presented an analytic theory of the quantum phase transition in Fracton topological order (FTO) induced by external terms which create fracton excitations
We developed an effective Hamiltonian approach that is model independent to investigate the critical point of phase transition, which can be characterized by the breaking down of ground-state degeneracy (GSD)
Summary
The discovery of topological quantum phases revolutionized the characterization and classification of fundamental states of quantum matter beyond the Landau symmetrybreaking paradigm. With the protection by the topological bulk gap, the FTOs are expected to be stable against small external perturbations and may undergo quantum phase transition when the system is tuned far away from the fine-tuning point. We aim to characterize quantum phase transition in type-I FTOs induced by external perturbation terms. As the external term exceeds the critical value, the GSD either breaks down or is enhanced For the former case (second-order transition), the GSD is lifted since there are nonzero transition matrix elements between some ground states at infinite system size. The analytic theory of the critical point of phase transition is presented in Sec. IV, with a universal result being obtained by mapping the present framework to a random-walk theory and applicable to a class of FTOs, including the X-cube model.
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