Wave function and strange correlator of short-range entangled states

Area of Science:

• Condensed Matter Physics
• Quantum Information Theory

Background:

• Short-range entangled (SRE) states are fundamental in understanding quantum matter.
• Distinguishing SRE states from trivial disordered states is challenging.
• Topological order and entanglement properties are key to classifying quantum phases.

Purpose of the Study:

• To introduce a novel diagnostic tool for identifying nontrivial short-range entangled states.
• To analyze the behavior of a "strange correlator" between entangled and trivial states.
• To provide a method applicable to both one-dimensional (1D) and two-dimensional (2D) systems.

Main Methods:

• Field theory analysis was employed to derive general properties of the strange correlator.
• Explicit computation of the strange correlator for specific quantum models.
• Investigated four distinct physical systems exhibiting short-range entanglement.

Main Results:

• The strange correlator C(r,r ecursive)=⟨Ω|ϕ(r)ϕ(r ecursive)|Ψ⟩/⟨Ω|Ψ⟩ exhibits either constant saturation or power-law decay at large distances.
• This behavior is observed even when comparing nontrivial SRE states |Ψ⟩ with trivial disordered states |Ω⟩.
• The diagnostic is robust against short-range correlations present in both states.

Conclusions:

• The strange correlator serves as a reliable indicator for nontrivial short-range entanglement in 1D and 2D.
• This finding offers a new perspective on characterizing quantum phases of matter.
• The method provides a practical tool for experimental and theoretical investigations of entanglement.