Order in Boson Systems

正人 大矢

Tian Lan, Liang Kong, Xiao-Gang Wen

Topological orders are new phases of matter beyond Landau symmetry breaking. They correspond to patterns of long-range entanglement. In recent years, it was shown that in 1+1D bosonic systems there is no nontrivial topological order, while in 2+1D bosonic systems the topological orders are classified by a pair: a modular tensor category and a chiral central charge. In this paper, we propose a partial classification of topological orders for 3+1D bosonic systems: If all the point-like excitations are bosons, then such topological orders are classified by unitary pointed fusion 2-categories, which are one-to-one labeled by a finite group $G$ and its group 4-cocycle $ω_4 \in \mathcal H^4[G;U(1)]$ up to group automorphisms. Furthermore, all such 3+1D topological orders can be realized by Dijkgraaf-Witten gauge theories.

Alan Coleman, Vyacheslav I. Yukalov

Liang Kong, Tian Lan, Xiao-Gang Wen

Topological orders are new phases of matter beyond Landau symmetry breaking. They correspond to patterns of long-range entanglement. In recent years, it was shown that in 1+1D bosonic systems, there is no nontrivial topological order, while in 2+1D bosonic systems, the topological orders are classified by the following pair: a modular tensor category and a chiral central charge. In this paper, following a new line of thinking, we find that in 3+1D the classification is much simpler than it was thought to be; we propose a partial classification of topological orders for 3+1D bosonic systems: If all the pointlike excitations are bosons, then such topological orders are classified by a simpler pair (G,ω_{4}): a finite group G and its group 4-cocycle ω_{4}∈H^{4}[G;U(1)] (up to group automorphisms). Furthermore, all such 3+1D topological orders can be realized by Dijkgraaf-Witten gauge theories.

I. V. Drozdov, B. Drozdov

The ergodic second-order approach of entropy gradient maximization, applied on the problem of a quantum bosonic system, does not provide dynamic equations for pure fermionic system. The first-order dynamic equation results for a system of bosonic and fermionic \dofs interacting by a conservation of a common sum of quantum occupation numbers.

Lucas Platter, Daniel R. Phillips