Propagation of Correlations in Quantum Lattice Systems
Rent the article at a discountRent now
* Final gross prices may vary according to local VAT.Get Access
We provide a simple proof of the Lieb-Robinson bound and use it to prove the existence of the dynamics for interactions with polynomial decay. We then use our results to demonstrate that there is an upper bound on the rate at which correlations between observables with separated support can accumulate as a consequence of the dynamics.
- O. Bratteli and D.W. Robinson, Operator Algebras and Quantum Statistical Mechanics. Volume 2., 2nd Edn. (Springer Verlag, 1997).
- S. Bravyi, M.B. Hastings and F. Verstraete, Lieb-Robinson bounds and the generation of correlations and toplogical quantum order, arXiv:quant-ph/0603121.
- M. Cramer and J. Eisert, Correlations and spectral gap in harmonic quantum systems on generic lattices. New J. Phys. 871, (2006), arXiv:quant-ph/0509167.
- J. Eisert and T. J. Osborne, General entanglement scaling laws from time evolution, arXiv:quant-phys/0603114.
- M. B. Hastings, Locality in Quantum and Markov Dynamics on Lattices and Networks. Phys. Rev. Lett. 93, 140402 (2004). CrossRef
- M. B. Hastings and T. Koma, Spectral Gap and Exponential Decay of Correlations, to appear in Commun. Math. Phys., arXiv:math-ph/0507008.
- T. Matsui, Markov semigroups on UHF algebras. Rev. Math. Phys. 5, 587–600 (1993). CrossRef
- E. H. Lieb and D. W. Robinson, The Finite Group Velocity of Quantum Spin Systems. Commun. Math. Phys. 28, 251–257 (1972). CrossRef
- B. Nachtergaele and R. Sims, Lieb-Robinson Bounds and the Exponential Clustering Theorem. Commun. Math. Phys. 265, 119–130 (2006), arXiv:math-ph/0506030
- N. Schuch, J. I. Cirac and M. M. Wolf, Quantum states on harmonic lattices, arXiv:quant-ph/0509166.
- B. Simon, The Statistical Mechanics of Lattice Gases, Volume I, (Princeton University Press, 1993).
- Propagation of Correlations in Quantum Lattice Systems
Journal of Statistical Physics
Volume 124, Issue 1 , pp 1-13
- Cover Date
- Print ISSN
- Online ISSN
- Springer US
- Additional Links
- Lieb-Robinson bounds
- quantum spin systems
- Industry Sectors