Related papers: Minimalist approach to the classification of symme…
In recent years, great success has been achieved on the classification of symmetry-protected topological (SPT) phases for interacting fermion systems by using generalized cohomology theory. However, the explicit calculation of generalized…
We develop a mathematical theory of symmetry protected trivial (SPT) orders and anomaly-free symmetry enriched topological (SET) orders in all dimensions via two different approaches with an emphasis on the second approach. The first…
We consider the classification problem of symmetry protected topological (SPT) phases on quantum spin systems. SPT phases are gapped short-range-entangled quantum phases with a symmetry $G$. We explain that in one and two-dimensional…
We propose and prove a family of generalized Lieb-Schultz-Mattis (LSM) theorems for symmetry protected topological (SPT) phases on boson/spin models in any dimensions. The "conventional" LSM theorem, applicable to e.g. any translation…
It has been shown that the symmetry-protected topological (SPT) phases with finite Abelian symmetries can be described by Chern-Simons field theory. We propose a topological response theory to uniquely identify the SPT orders, which allows…
We study the classification of interacting fermionic and bosonic symmetry protected topological (SPT) states. We define a SPT state as whether or not it is separated from the trivial state through a bulk phase transition, which is a general…
We present systematic constructions of tensor-network wavefunctions for bosonic symmetry protected topological (SPT) phases respecting both onsite and spatial symmetries. From the classification point of view, our results show that in…
We consider symmetry-protected topological (SPT) phases in 2D protected by linear subsystem symmetries, i.e. those that act along rigid lines. There is a distinction between a "strong" subsystem SPT phase, and a "weak" one, which is…
Symmetry-protected topological (SPT) states are short-range entangled states with a symmetry G. They belong to a new class of quantum states of matter which are classified by the group cohomology $H^{d+1}(G,\mathbb{R}/\mathbb{Z})$ in…
We study bosonic symmetry protected topological (SPT) phases with $C_{2}$ rotational symmetry in four spatial dimensions which is not captured by the group cohomology classification. By using the topological crystal approach, we show that…
Symmetry-protected topological $\left(SPT\right)$ phases are gapped short-range entangled states with symmetry $G$, which can be systematically described by group cohomology theory. $SU(3)$ and $SU(2)\times{U(1)}$ are considered as the…
We put the theory of interacting topological crystalline phases on a systematic footing. These are topological phases protected by space-group symmetries. Our central tool is an elucidation of what it means to "gauge" such symmetries. We…
We consider topological phases in periodically driven (Floquet) systems exhibiting many-body localization, protected by a symmetry $G$. We argue for a general correspondence between such phases and topological phases of undriven systems…
The construction and classification of symmetry-protected topological (SPT) phases in interacting bosonic and fermionic systems have been intensively studied in the past few years. Very recently, a complete classification and construction…
Symmetry-protected topological (SPT) phases are short-range entangled phases of matter with a non-local order parameter which are preserved under a local symmetry group. Here, by using unsupervised learning algorithm, namely the diffusion…
Symmetry protected states (SPT's) of quantum spin systems were studied by several authors. For one-dimensional systems (spin chains), there is an essentially complete and rigorous understanding: SPT's corresponding to finite on-site…
Symmetry Protected Topological (SPT) phases describe trivially-acting symmetries. We argue that a symmetry-based description of SPT phases ought to include the topological twist fields associated to the symmetry. Doing so allows us to…
We propose a simple theoretical construction of certain short-range entangled phases of interacting fermions, by putting the bound states of three fermions (which we refer to as clustons) into topological bands. We give examples in two and…
Recently, it was realized that quantum states of matter can be classified as long-range entangled (LRE) states (i.e. with non-trivial topological order) and short-range entangled (SRE) states (\ie with trivial topological order). We can use…
We study several aspects of the realization of global symmetries in highly entangled phases of quantum matter. Examples include gapped topological ordered phases, gapless quantum spin liquids and non-fermi liquid phases. An insightful…