Ground state entanglement and geometric entropy in the Kitaev model

By A. Hamma, R. Ionicioiu, Paolo Zanardi. 2004

206 citations recorded by the source corpus.

Abstract We study the entanglement properties of the ground state in Kitaev's model. This is a two-dimensional spin system with a torus topology and non-trivial four-body interactions between its spins. For a generic partition ( A , B ) of the lattice we calculate analytically the von Neumann entropy of the reduced density matrix ρ A in the ground state. We prove that the geometric entropy associated with a region A is linear in the length of its boundary. Moreover, we argue that entanglement can probe the topology of the system and reveal topological order. Finally, no partition has zero entanglement and we find the partition that maximizes the entanglement in the given ground state.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics

View Paper: https://www.semanticscholar.org/paper/f24cade99f6f2013db2b40986822c5a104d99bf1

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

1. A. Nahum
2. Matthew Fisher
3. Yaodong Li
4. J. Ruhman
5. R. Myers
6. S. Vijay
7. Xiao Chen
8. H. Casini

In Condensed Matter Physics

1. Matthew Fisher
2. A. Nahum
3. Yaodong Li
4. J. Ruhman
5. Xiao Chen
6. S. Vijay
7. Chris N. Self
8. R. Myers

Citations in the corpus

• Quantum Entanglement Growth Under Random Unitary Dynamics (2016, background): “This expression for the entanglement entropy has also appeared in [48, 49].”
• Quantum memories at finite temperature (2014, background): “For finite temperature systems these can be found using the topological entropy (Hamma et al., 2005a; Kitaev and Preskill, 2006; Levin and Wen, 2006), topological mutual information (Iblisdir et al., 2009) or anyonic topological entropy (Wootton, 2013).”
• Measurement-driven entanglement transition in hybrid quantum circuits (2019, background): “[34] Alioscia Hamma, Radu Ionicioiu, and Paolo Zanardi, “Ground state entanglement and geometric entropy in the Kitaev model [rapid communication],” Physics Letters A 337, 22–28 (2005), arXiv:quant-ph/0406202 [quant-ph].”
• Relative entropy and holography (2013, background): “For example, in condensed matter theory, it can be used to distinguish new topological phases or different critical points [1, 2].”
• Quantum Entanglement in Neural Network States (2017, methodology): “For calculating the exactly entanglement entropy of a finite system, we note the quotient group method, which has been used to calculate the entropy of an arbitrary bipartition of the 2D toric code states [118, 119].”