Related papers: Quantum Phase Transitions between Symmetry-Enriche…
In this paper, we explore the interplay between symmetry and fracton order, motivated by the analogous close relationship for topologically ordered systems. Specifically, we consider models with 3D planar subsystem symmetry, and show that…
The study of gapped quantum many-body systems in three spatial dimensions has uncovered the existence of quantum states hosting quasiparticles that are confined, not by energetics but by the structure of local operators, to move along lower…
Entanglement entropy provides a powerful characterization of two-dimensional gapped topological phases of quantum matter, intimately tied to their description by topological quantum field theories (TQFTs). Fracton topological orders are…
We examine the interplay of symmetry and topological order in $2+1$ dimensional topological phases of matter. We present a definition of the \it topological symmetry \rm group, which characterizes the symmetry of the emergent topological…
Second order quantum phase transitions, with well-known features such as long-range entanglement, symmetry breaking, and gap closing, exhibit quantum enhancement for sensing at criticality. However, it is unclear which of these features are…
We study quantum phase transitions out of the fracton ordered phase of the $\mathbb{Z}_N$ X-cube model. These phase transitions occur when various types of sub-dimensional excitations and their composites are condensed. The condensed phases…
Recently a new class of quantum phases of matter: symmetry protected topological states, such as topological insulators, attracted much attention. In presence of interactions, group cohomology provides a classification of these [X. Chen et…
Fracton models, a collection of exotic gapped lattice Hamiltonians recently discovered in three spatial dimensions, contain some 'topological' features: they support fractional bulk excitations (dubbed fractons), and a ground state…
This work reports an extensive study of three-dimensional topological ordered phases that, in one of the directions behave like usual topological order concerning mobility of excitations, but in the perpendicular plane manifest type-II…
We have performed large-scale Monte Carlo simulations on a model describing a (2+1)-dimensional array of dissipative Josephson junctions. We find three distinct stable quantum phases of the system. The most ordered state features long-range…
Fathoming interplay between symmetry and topology of many-electron wave-functions has deepened understanding of quantum many body systems, especially after the discovery of topological insulators. Topology of electron wave-functions…
We study spin systems which exhibit symmetries that act on a fractal subset of sites, with fractal structures generated by linear cellular automata. In addition to the trivial symmetric paramagnet and spontaneously symmetry broken phases,…
In a phase with fractional excitations, topological properties are enriched in the presence of global symmetry. In particular, fractional excitations can transform under symmetry in a fractionalized manner, resulting in different Symmetry…
We propose a set of constraints on the ground-state wavefunctions of fracton phases, which provide a possible generalization of the string-net equations used to characterize topological orders in two spatial dimensions. Our constraint…
The nature of phase transitions involving the questions why and how phase transitions take place has not been sufficiently touched in the literature. In contrast, the current attention to certain extent still focus on the description of…
We determine the computational power of isometric tensor network states (isoTNS), a variational ansatz originally developed to numerically find and compute properties of gapped ground states and topological states in two dimensions. By…
Changes in the entanglement structure and critical phenomena are hallmarks of quantum phase transitions. Here, we discuss how they appear in transitions between classes of states with distinct entanglement patterns beyond the paradigm of…
We have constructed a general theory describing the topological quantum phase transitions in 3D systems with broken inversion symmetry. While the consideration of the system's codimension generally predicts the appearance of a stable…
In this chapter we discuss aspects of the quantum critical behavior that occurs at a quantum phase transition separating a topological phase from a conventionally ordered one. We concentrate on a family of quantum lattice models, namely…
In topological phases in $2+1$ dimensions, anyons fall into representations of quantum group symmetries. As proposed in our work (arXiv:1308.4673), physics of a symmetry enriched phase can be extracted by the Mathematics of (hidden) quantum…