Lieb-Robinson bounds and the exponential clustering theorem
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Publication:863132
DOI10.1007/s00220-006-1556-1zbMath1104.82013arXivmath-ph/0506030OpenAlexW1978774199MaRDI QIDQ863132
Robert Sims, Bruno Nachtergaele
Publication date: 25 January 2007
Published in: Communications in Mathematical Physics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/math-ph/0506030
Quantum equilibrium statistical mechanics (general) (82B10) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20)
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Cites Work
- Spectral gap and exponential decay of correlations
- A remark on the cluster theorem
- The spectral gap for some spin chains with discrete symmetry breaking
- Two soluble models of an antiferromagnetic chain
- Statistical mechanics of complex networks
- Spectral gap and decay of correlations in U(1)-symmetric lattice systems in dimensions D<2
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