Identifying topological order by entanglement entropy

By Hong-Chen Jiang, Zhenghan Wang, L. Balents. Nature Physics, 2012

487 citations recorded by the source corpus.

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. Topological entanglement entropy provides a robust measure for detecting the long-range entanglement that characterizes quantum ground states displaying topological order. A new method for calculating this entropy isolates minimally entangled states from the ground states of a topological phase—offering a reliable test for identifying topological spin liquids.

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

View Paper: https://www.semanticscholar.org/paper/f78d3d1baab89abfc49223f16feb1f0a8468f40a

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. Ashvin Vishwanath
2. R. Verresen
3. Xie Chen
4. X. Wen
5. K. Kanoda
6. Yi Zhou
7. T. Ng
8. Bei Zeng

In Condensed Matter Physics

1. Ashvin Vishwanath
2. Yi Zhou
3. T. Ng
4. K. Kanoda
5. Xie Chen
6. R. Verresen
7. Bei Zeng
8. Duan-Lu Zhou

Citations in the corpus

• Quantum spin liquid states (2016, methodology): “This nodal Z2 spin liquid is energetically competitive with calculations performed using the DMRG (Gong et al., 2014b; Jiang et al., 2012b) and PEPS (Wang et al., 2013) approaches.”
• The Hubbard Model (2021, methodology): “, whether it has a spin gap (134) or a gapless Dirac spinon spectrum (136).”
• Entanglement temperature and entanglement entropy of excited states (2013, methodology): “For example in [2] the interplay of DMRG and entanglement entropy on a torus has been used to identify the nature of topological degeneracy.”
• Physics of the Kitaev Model: Fractionalization, Dynamic Correlations, and Material Connections (2017, unknown): “[8] Hong-Chen Jiang, Zhenghan Wang, and Leon Balents.”
• Prediction of Toric Code Topological Order from Rydberg Blockade (2020, background): “[108] Hong-Chen Jiang, Zhenghan Wang, and Leon Ba-”
• Quantum Information Meets Quantum Matter (2015, background): “For a full reference one may turn to other classical sources such as ‘Quantum Computation and Quantum Information’ by Nielsen & Chuang and Preskill’s lecture notes for the course of ‘Quantum Computation’ at Caltech.”