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Quantum many-body systems with fracton constraints are widely conjectured to exhibit unconventional low-energy phases of matter. In this work, we demonstrate the existence of a variety of such exotic quantum phases in the ground states of a…
We present a three-dimensional cubic lattice spin model, anisotropic in the $\hat{z}$ direction, that exhibits fracton topological order. The latter is a novel type of topological order characterized by the presence of immobile pointlike…
We present a scheme to explicitly construct and classify general topological states jointly protected by an onsite symmetry group and a spatial symmetry group. We show that all these symmetry protected topological states can be…
Topological phase transition is accompanied with a change of topological numbers. It has been believed that the gap closing and the breakdown of the adiabaticity at the transition point is necessary in general. However, the gap closing is…
Fracton topological order describes a remarkable phase of matter which can be characterized by fracton excitations with constrained dynamics and a ground state degeneracy that increases exponentially with the length of the system on a…
Fractons are a new type of quasiparticle which are immobile in isolation, but can often move by forming bound states. Fractons are found in a variety of physical settings, such as spin liquids and elasticity theory, and exhibit unusual…
Topological phases of matter have been extensively investigated in solid state materials and classical wave systems with integer dimensions. However, topological states in non-integer dimensions remain largely unexplored. Fractals, being…
Fracton order describes novel quantum phases of matter that host quasiparticles with restricted mobility, and thus lies beyond the existing paradigm of topological order. In particular, excitations that cannot move without creating multiple…
We propose a route toward realizing fractionalized topological phases of matter (i.e. with intrinsic topological order) by literally building on un-fractionalized phases. Our approach employs a Kondo lattice model in which a gapped…
Topological insulators exhibit boundary states protected by bulk band topology, a principle first established in quantum systems and later extended to classical waves, including phononics. Conventionally, an $n$-dimensional bulk with…
Spurred by recent development of fracton topological phases, unusual topological phases possessing fractionalized quasi-particles with mobility constraints, the concept of symmetries has been renewed. In particular, in accordance with the…
Topological order in strongly correlated systems, including quantum spin liquids, quantum Hall states in lattices and topological superconductivity is treated. Various metallic non-Fermi-liquid states are discussed, including fractionalized…
Introduction of controllable deformations into periodic materials that lead to disclinations in their structure opens novel routes for construction of higher-order topological insulators hosting topological states at disclinations.…
Fractons are gapped point-like excitations in $d=3$ topological ordered phases whose motion is constrained. They have been discovered in several gapped models but a unifying physical mechanism for generating them is still missing. It has…
We study in-gap electronic states induced by a nonmagnetic defect with short-range potential in two-dimensional topological insulators and trace their evolution as the distance between the defect and the boundary changes. The defect located…
We construct an exactly solvable Hamiltonian acting on a 3-dimensional lattice of spin-$\frac 1 2$ systems that exhibits topological quantum order. The ground state is a string-net and a membrane-net condensate. Excitations appear in the…
We present a large class of three-dimensional spin models that possess topological order with stability against local perturbations, but are beyond description of topological quantum field theory. Conventional topological spin liquids, on a…
Deconfined criticality and gapless topological states have recently attracted growing attention, as both phenomena go beyond the traditional Landau paradigm. However, the deep connection between these two critical states, particularly in…
Topological crystalline states are short-range entangled states jointly protected by onsite and crystalline symmetries. While the non-interacting limit of these states, e.g., the topological crystalline insulators, have been intensively…
Topological phases of matter are defined by their nontrivial patterns of ground-state quantum entanglement, which is irremovable so long as the excitation gap and the protecting symmetries, if any, are maintained. Recent studies on…