Entanglement in non-unitary quantum critical spin chains

Abstract

Entanglement entropy has proven invaluable to our understanding of quantum criticality. It is natural to try to extend the concept to non-unitary quantum mechanics, which has seen growing interest from areas as diverse as open quantum systems, non-interacting electronic disordered systems, or non-unitary conformal field theory (CFT). We propose and investigate such an extension here, by focussing on the case of one-dimensional quantum group symmetric or supergroup symmetric spin chains. We show that the consideration of left and right eigenstates combined with appropriate definitions of the trace leads to a natural definition of Rényi entropies in a large variety of models. We interpret this definition geometrically in terms of related loop models and calculate the corresponding scaling in the conformal case. This allows us to distinguish the role of the central charge and effective central charge in rational minimal models of CFT, and to define an effective central charge in other, less well understood cases. The example of the $sl(2|1)$ alternating spin chain for percolation is discussed in detail.

11 pages, 3 figures

References in corpus (6)

• Entanglement spectrum in one-dimensional systems
• Interacting anyons in topological quantum liquids: The golden chain
• Entanglement of low-energy excitations in Conformal Field Theory
• Entanglement Entropy of Non Unitary Conformal Field Theory
• Branch Point Twist Field Correlators in the Massive Free Boson Theory
• Entanglement Entropy in Extended Quantum Systems

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