The Budapest Quantum Optics Group

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Journal Club: Topological Order through Entanglement Entropy

Örs Legeza

(Department of Strongly Correlated Systems, Institute for Solid State Physics and Optics, Wigner RCP, HAS)

Time: Tue Jun 18 14:30:00 2013
Location: Building 1, Room 114, Auditorium

Hong-Chen Jiang, Zhenghan Wang, and Leon Balents
Identifying topological order by entanglement entropy
Nature Physics 8, 902–905 (2012)

Topological phases are unique states of matter that incorporate long-range quantum entanglement and host exotic excitations with fractional quantum statistics. Here we report a practical method to identify topological phases in arbitrary realistic models by accurately calculating the topological entanglement entropy using the density matrix renormalization group (DMRG). We argue that the DMRG algorithm systematically selects a minimally entangled state from the quasi-degenerate ground states in a topological phase. This tendency explains both the success of our method and the absence of ground-state degeneracy in previous DMRG studies of topological phases. We demonstrate the effectiveness of our procedure by obtaining the topological entanglement entropy for several microscopic models, with an accuracy of the order of 10−3, when the circumference of the cylinder is around ten times the correlation length. As an example, we definitively show that the ground state of the quantum S = 1/2 antiferromagnet on the kagome lattice is a topological spin liquid, and strongly constrain the conditions for identification of this phase of matter. © 2012 Nature Publishing Group, a division of Macmillan Publishers Limited. All Rights Reserved.