title: Wave function and strange correlator of short-range entangled states.
abstract: We demonstrate the following conclusion: If |Ψ⟩ is a one-dimensional (1D) or two-dimensional (2D) nontrivial short-range entangled state and |Ω⟩ is a trivial disordered state defined on the same Hilbert space, then the following quantity (so-called "strange correlator") C(r,r('))=⟨Ω|ϕ(r)ϕ(r('))|Ψ⟩/⟨Ω|Ψ⟩ either saturates to a constant or decays as a power law in the limit |r-r(')|→+∞, even though both |Ω⟩ and |Ψ⟩ are quantum disordered states with short-range correlation; ϕ(r) is some local operator in the Hilbert space. This result is obtained based on both field theory analysis and an explicit computation of C(r,r(')) for four different examples: 1D Haldane phase of spin-1 chain, 2D quantum spin Hall insulator with a strong Rashba spin-orbit coupling, 2D spin-2 Affleck-Kennedy-Lieb-Tasaki state on the square lattice, and the 2D bosonic symmetry-protected topological phase with Z(2) symmetry. This result can be used as a diagnosis for short-range entangled states in 1D and 2D.
authors.affiliation: Department of Physics, University of California, Santa Barbara, California 93106, USA.
authors.forename: Yi-Zhuang
authors.initials: YZ
authors.lastname: You
authors.affiliation: Department of Physics, University of California, Santa Barbara, California 93106, USA.
authors.forename: Zhen
authors.initials: Z
authors.lastname: Bi
authors.affiliation: Department of Physics, University of California, Santa Barbara, California 93106, USA.
authors.forename: Alex
authors.initials: A
authors.lastname: Rasmussen
authors.affiliation: Department of Physics, University of California, Santa Barbara, California 93106, USA.
authors.forename: Kevin
authors.initials: K
authors.lastname: Slagle
authors.affiliation: Department of Physics, University of California, Santa Barbara, California 93106, USA.
authors.forename: Cenke
authors.initials: C
authors.lastname: Xu