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A large class of gapped phases of matter can be described by topological finite group gauge theories. In this paper we show how such gauge theories possess a higher-group global symmetry, which we study in detail. We derive the $d$-group…
The program of classifying symmetry protected topological (SPT) phases in 1D has been recently completed and has opened the doors to study closely the properties of systems belonging to these phases. It was recently found that being able to…
The Lieb-Schultz-Mattis (LSM) theorem and its higher-dimensional generalizations by Oshikawa and Hastings establish that a translation-invariant lattice model of spin-$1/2$'s can not have a non-degenerate ground state preserving both spin…
We introduce a two-body quantum Hamiltonian model with spins-$\half$ located on the vertices of a 2D spatial lattice. The model exhibits an exact topological degeneracy in all coupling regimes. This is a remarkable non-perturbative effect.…
We propose an exotic scenario that topological superconductivity can emerge by doping strongly interacting fermionic systems whose spin degrees of freedom form bosonic symmetry protected topological (SPT) state. Specifically, we study a…
Novel fermionic quasiparticles with integer pseudospins in some energy bands, such as pseudospin-1 triple-point fermions, recently attract increasing interest since they are beyond the conventional spin-$1/2$ Dirac and Weyl counterparts. In…
We study different quantum phases in integer spin systems with on-site D2h=D2xZ2 and translation symmetry. We find four distinct non-trivial phases in S=1 spin chains despite they all have the same symmetry. All the four phases have gapped…
We present an exactly solvable spin-3/2 model defined on a pentacoordinated three-dimensional graphite lattice, which realizes a novel quantum spin liquid with second-order topology. The exact solutions are described by Majorana fermions…
Here we study the emergence of different Symmetry-Protected Topological (SPT) phases in a spin-2 quantum chain. We consider a Heisenberg-like model with bilinear, biquadratic, bicubic, and biquartic nearest-neighbor interactions, as well as…
Solitonic symmetry has been believed to follow the homotopy-group classification of topological solitons. Here, we point out a more sophisticated algebraic structure when solitons of different dimensions coexist in the spectrum. We uncover…
The Z_2 topological order in Z_2 spin liquid and in exactly soluble Kitaev toric code model is the simplest topological order for 2+1D bosonic systems. More general 2+1D bosonic topologically ordered states can be constructed via exact…
Progress in understanding symmetry-protected topological (SPT) phases has been greatly aided by our ability to construct lattice models realizing these states. In contrast, a systematic approach to constructing models that realize quantum…
Gutzwiller projection is a way to construct many-body wave functions that could carry topological order or symmetry protected topological (SPT) order. However, an important issue is to determine whether or not a given Gutzwiller-projected…
In this work we study the possible occurrence of topological insulators for 2D fermions of high spin. They can be realized in cold fermion systems with ground-state atomic spin $F>\tfrac{1}{2}$, if the optical potential is properly…
We propose a generalization of the supersymmetric representation of spins with symplectic symmetry, generalizing the rotation group of the spin from SU(2) to SP(N). As a test application of this new representation, we consider two toy…
We review recent results on lattice models for spin-less fermions with strong repulsive interactions. A judicious tuning of kinetic and interaction terms leads to a model possessing supersymmetry. In the 1D case, this model displays…
A systematic procedure is developed for constructing fermion systems in discrete space-time which have a given outer symmetry. The construction is illustrated by simple examples. For the symmetric group, we derive constraints for the number…
Gapped phases in 2+1 dimensional quantum field theories with fusion 2-categorical symmetries were recently classified and characterized using the Symmetry Topological Field Theory (SymTFT) approach arXiv:2408.05266, arXiv:2502.20440. In…
This paper derives a large web of exact lattice dualities in one and two spatial dimensions. Some of the dualities are well-known, while others, such as two-dimensional boson-parafermion dualities, are new. The procedure is systematic,…
Symmetry protected topological (SPT) states have boundary 't Hooft anomalies that obstruct an effective boundary theory realized in its own dimension with UV completion and an on-site $G$-symmetry. In this work, yet we show that a certain…