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Parity Effects in the Scaling of Block Entanglement in Gapless Spin Chains
Open accessAbstract
We consider the R\'enyi $\ensuremath{\alpha}$ entropies for Luttinger liquids (LL). For large block lengths $\ensuremath{\ell}$, these are known to grow like $\mathrm{ln}\ensuremath{\ell}$. We show that there are subleading terms that oscillate with frequency $2{k}_{F}$ (the Fermi wave number of the LL) and exhibit a universal power-law decay with $\ensuremath{\ell}$. The new critical exponent is equal to $K/(2\ensuremath{\alpha})$, where $K$ is the LL parameter. We present numerical results for the anisotropic XXZ model and the full analytic solution for the free fermion (XX) point.
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Citations
Cites
Entanglement in many-body systems
Amico, L., Fazio, R., Osterloh, A., & Vedral, V. (2008) · Reviews of Modern Physics · doi:10.1103/revmodphys.80.517 · Cited by 3,745
Entanglement Entropy and Quantum Field Theory
Calabrese, P., & Cardy, J. (2004) · arXiv · doi:10.48550/arxiv.hep-th/0405152 · Cited by 3,275
Self-citationEntanglement in Quantum Critical Phenomena
Vidal, G., Latorre, J. I., Rico, E., & Kitaev, A. (2003) · Physical Review Letters · doi:10.1103/physrevlett.90.227902 · Cited by 2,793
Entanglement entropy and conformal field theory
Calabrese, P., & Cardy, J. (2009) · Journal of Physics A: Mathematical and Theoretical · doi:10.1088/1751-8113/42/50/504005 · Cited by 1,688
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Quantum entanglement in condensed matter systems
Laflorencie, N. (2016) · Physics Reports · doi:10.1016/j.physrep.2016.06.008 · Cited by 765
Metadata
- Authors
- Calabrese, P., Campostrini, M., Essler, F., & Nienhuis, B.
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2010-03-05
- Volume
- 104
- Issue
- 9
- Pages
- 095701-095701
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W1988632248
- Cited by
- 195
- References
- 4
- FWCI
- 11.03
- Type
- journal article
- Language
- en
- Open access
- bronze
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- Calabrese, P., Campostrini, M., Essler, F., & Nienhuis, B. (2010). Parity Effects in the Scaling of Block Entanglement in Gapless Spin Chains. Physical Review Letters. https://doi.org/10.1103/physrevlett.104.095701
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