Subdimensional Topological Quantum Phases of Matter

Kevin Slagle, Yong Baek Kim

The authors present a generic lattice construction for a generalized X-cube model of fracton topological order and propose a coarser definition of phase of matter for fracton orders. Similar to other fracton models, this model hosts emergent subdimensional excitations, which are topologically robust excitations that are confined to only move along certain lines or surfaces. The model is constructed from stacks of intersecting surfaces, and the subdimensional excitations are confined to move only along these (possibly curved) surfaces or their intersections. Surprisingly, for certain curved intersecting surfaces, a robust ground-state degeneracy on a manifold with trivial topology can result.

Wei-Feng Tsai, Hsin Lin, Arun Bansil

Meng-Yuan Li, Peng Ye

We introduce the subdimensional entanglement entropy (SEE), defined on subdimensional entanglement subsystems (SESs) embedded in the bulk, as an entanglement-based probe of how geometry and topology jointly shape universal properties of quantum matter. By varying the dimension, geometry, and topology of the SES, we show that the subleading term of SEE exhibits sharply distinct responses in a series of stabilizer states representing fixed points of different phases, including cluster states, Z q topological orders, and fracton orders. Treating the reduced density matrix of an SES as a many-body mixed state supported on the SES manifold, we further establish a general correspondence between bulk stabilizers and mixed-state symmetries on SESs, separating them into strong and weak classes, and use it to identify strong-to-weak spontaneous symmetry breaking within SESs. Finally, for SESs with nontrivial SEE, we show that a set of weak symmetries acts as transparent patch operators of the corresponding strong symmetries. This motivates the notion of transparent composite symmetry, which remains robust under bipartition-factorized finite-depth quantum circuits that preserve SEE, and implies that a D -dimensional SES may holographically encode a ( D + 1 ) -dimensional topological order. These results establish SEE not only as a sharp probe of geometric-topological response, but also as a route from bulk pure-state entanglement to mixed-state symmetry and holography on subdimensional manifolds.

F. D. M. Haldane

Brandon C. Rayhaun, Dominic J. Williamson

Subsystem symmetry has emerged as a powerful organizing principle for unconventional quantum phases of matter, most prominently fracton topological orders. Here, we focus on a special subclass of such symmetries, known as higher-form subsystem symmetries, which allow us to adapt tools from the study of conventional topological phases to the fracton setting. We demonstrate that certain transitions out of familiar fracton phases, including the X-cube model, can be understood in terms of the spontaneous breaking of higher-form subsystem symmetries. We find simple pictures for these seemingly complicated fracton topological phase transitions by relating them in an exact manner, via gauging, to spontaneous higher-form subsystem symmetry breaking phase transitions of decoupled stacks of lower-dimensional models. We harness this perspective to construct a sequence of unconventional subdimensional critical points in two and three spatial dimensions based on the stacking and gauging of canonical models with higher-form symmetry. Through numerous examples, we illustrate the ubiquity of coupled layer constructions in theories with higher-form subsystem symmetries.