Entanglement entropy at quantum critical points: Can you ... - INFN

The Quantum Dimer Model
H RK = ∑ i
(vV i − tF i ), Rokhsar and Kivelson (1988)
V i = ∣ ∣
〉〈 ∣ ∣ + ∣ ∣
〉〈 ∣ ∣ F i = ∣ ∣
〉〈 ∣ ∣ + ∣ ∣
〉〈 ∣ ∣
Here each bar represents a spin singlet bond.
For t = v ⇒ H RK = P i Q† i Q i , with Q i = ` 1 −1
−1 1
´.
• The ground state wave function |Ψ 0 〉 has E = 0
|Ψ 0 〉 = 1 √
Zcl
X
where Z cl is the sum over all dimer configurations
C
|C〉 ,
• Equal-time correlators in the quantum dimer model at the RK point are given by
correlators of the classical dimer model.
• This is actually a loop model: loops are the dimer moves from a reference state. This
is the simplest loop model: the SU(2) 1 fully packed loop model.
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