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Dynamics of a Quantum Phase Transition: Exact Solution of the Quantum Ising Model
Open accessAbstract
The Quantum Ising model is an exactly solvable model of quantum phase transition. This Letter gives an exact solution when the system is driven through the critical point at a finite rate. The evolution goes through a series of Landau-Zener level anticrossings when pairs of quasiparticles with opposite pseudomomenta get excited with a probability depending on the transition rate. The average density of defects excited in this way scales like a square root of the transition rate. This scaling is the same as the scaling obtained when the standard Kibble-Zurek mechanism of thermodynamic second order phase transitions is applied to the quantum phase transition in the Ising model.
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Citations
Cites
Non-adiabatic crossing of energy levels
Zener, C. (1932) · Proceedings of the Royal Society of London Series A Containing Papers of a Mathematical and Physical Character · doi:10.1098/rspa.1932.0165 · Cited by 4,572
�ber das Paulische �quivalenzverbot
Jordan, P., & Wigner, E. (1928) · Zeitschrift f�r Physik · doi:10.1007/bf01331938 · Cited by 2,597
Cited by
Colloquium: Nonequilibrium dynamics of closed interacting quantum systems
Polkovnikov, A., Sengupta, K., Silva, A., & Vengalattore, M. (2011) · Reviews of Modern Physics · doi:10.1103/revmodphys.83.863 · Cited by 2,562
Probing topological spin liquids on a programmable quantum simulator
Semeghini, G., Levine, H., Keesling, A., Ebadi, S., Wang, T. T., Bluvstein, D., Verresen, R., Pichler, H., Kalinowski, M., Samajdar, R., et al. (2021) · Science · doi:10.1126/science.abi8794 · Cited by 781
Quantum Kibble–Zurek mechanism and critical dynamics on a programmable Rydberg simulator
Keesling, A., Omran, A., Levine, H., Bernien, H., Pichler, H., Choi, S., Samajdar, R., Schwartz, S., Silvi, P., Sachdev, S., et al. (2019) · Nature · doi:10.1038/s41586-019-1070-1 · Cited by 534
Quantum Phase Transition and Universal Dynamics in the Rabi Model
Hwang, M.-J., Puebla, R., & Plenio, M. B. (2015) · Physical Review Letters · doi:10.1103/physrevlett.115.180404 · Cited by 441
Universality of phase transition dynamics: Topological defects from symmetry breaking
del Campo, A., & Zurek, W. H. (2014) · International Journal of Modern Physics A · doi:10.1142/s0217751x1430018x · Cited by 364
Metadata
- Authors
- Dziarmaga, J.
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2005-12-09
- Volume
- 95
- Issue
- 24
- Pages
- 245701-245701
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2090911654
- Cited by
- 672
- References
- 2
- FWCI
- 9.02
- Type
- journal article
- Language
- en
- Open access
- green
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- Dziarmaga, J. (2005). Dynamics of a Quantum Phase Transition: Exact Solution of the Quantum Ising Model. Physical Review Letters. https://doi.org/10.1103/physrevlett.95.245701
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