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

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φ 2,A = φ ′ 1,A φ 2,B = φ ′ 2,B φ 1,A = φ ′ 2,A φ 1,B = φ ′ 1,B Ω A Γ Ω B 22
• The boundary terms impose continuity of the fields in the CFT because strong local fluctuations are penalized in the action. A key feature of the replicas in the numerator is that each replica on A is connected symmetrically to two different replicas on B and vice versa. The symmetry, which for N replicas is the Schoenflies group C Nv (the cyclic group plus vertical mirror plane), prevents a unique idenfitication of replicas on A with replicas on B except for N = 1, so the numerator cannot be equivalent to the denominator (N free fields on A ∪ B). Instead the fields from different replicas are forced to agree on the boundary: schematically Tr ρ n A = Z(n configurations agreeing on the boundary) Z(n independent configurations) = Trρ n B • Trρ n A can be put in a form that simplifies taking the derivative as n → 1: for an explicit realization, consider the case of a free scalar field. Then the condition that n scalar fields φ i agree with each other on the boundary can be satisfied by forming n − 1 linear combinations 1 √ 2 (φ i − φ i+1 ), which vanish at the boundary i.e., satisfy Dirichlet boundary conditions, plus one linear combination 1 √ n Pi=1,...,n φ i that has no boundary condition (i.e., is a free field on A ∪ B). 23
Page 1 and 2: Entanglement entropy at quantum cri
Page 3 and 4: Motivation • Entanglement entropy
Page 5 and 6: Quantum Phase Transitions and Quant
Page 7 and 8: Entanglement and Conformal Invarian
Page 9 and 10: Spin Liquids and Topological States
Page 11 and 12: Challenges • To develop a consist
Page 13 and 14: The Quantum Dimer Model H RK = ∑
Page 15 and 16: Scale Invariant Ground State Wave F
Page 17 and 18: Phase diagram for a quantum eight v
Page 19 and 20: Entanglement Entropy of 2D Quantum
Page 21: • 〈{φ A 1 }|ρ A |{φ A 2 }〉
Page 25 and 26: • For the QCPs we are discussing
Page 27 and 28: If the A and B share a common bound
Page 29: Conclusions • We examined the beh

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

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