Iranian Journal of Physics Research

Time-dependent variational principle treatment of quantum phase transition

Document Type : Original Article

Authors

Azar Vafafard 1
Alireza Nourmandipour 2
Roberto Franzosi 3

1 -Faculty of Physics, University of Tabriz, Tabriz, Iran -Quantum Technology Center, University of Tabriz, Iran

2 Department of Physics, Sirjan University of Technology, Sirjan, Iran

3 DSFTA, University of Siena, Siena, Italy

https://doi.org/10.47176/ijpr.25.3.22022
Abstract
Phase transitions are fundamental phenomena in physics, characterized by abrupt changes in the properties of a system. While classical phase transitions occur due to thermal fluctuations, quantum phase transitions (QPTs) are driven by quantum fluctuations at zero temperature. In this work, we explore the presence of QPTs in cavity quantum electrodynamics systems using the Time-Dependent Variational Principle (TDVP), a semi-classical approach for analyzing complex quantum systems. Beginning with the Rabi model, where a single qubit interacts with a single-mode cavity field, we examine the influence of counter-rotating terms on the system's ground state properties. Subsequently, we extend our analysis to the Jaynes-Cummings model, where rotating-wave approximation applies, and finally, to the Dicke model, which considers the collective interaction of multiple qubits with a bosonic mode. For each model, we derive analytical expressions for the ground state properties and identify critical coupling strengths indicative of phase transitions. Our findings reveal second-order quantum phase transitions, including superradiant phases with distinct ground state behaviors, emphasizing the utility of TDVP in understanding QPTs across a variety of systems.

Keywords

time-dependent variation principle
Hamiltonian
quantum phase transition
qubit
Subjects
1. H Nishimori and G Ortiz, Elements of Phase Transitions and Critical Phenomena (Oxford University Press, 2010).
2. A Carollo, D Valenti, and B Spagnolo, Phys. Rep. 838 (2020) 1.
3. K A Takeuchi, M Kuroda, H Chaté, and M Sano, Phys. Rev. E 80 (2009) 051116.
4. E Michon et al., New J. Phys. 20 (2018).
5. A Pippard, Physica 22 (1956) 99.
6. N Goldenfeld, Lectures On Phase Transitions And The Renormalization Group (Frontiers in Physics, Westview Press, 1992).
7. H E Stanley, Phase Transitions and Critical Phenomena (Clarendon Press, Oxford, 1971).
8. M Vojta, Rep. Prog. Phys. 66 (2003) 2069.
9. M J Hwang and M. B. Plenio, Phys. Rev. Lett. 117 (2016) 123602.
10. N Lambert, C Emary, and T Brandes, Phys. Rev. Lett. 92 (2004) 073602.
11. B Dietz et al., Phys. Rev. B 88 (2013) 104101.
12. C Emary and T Brandes, Phys. Rev. E 67 (2003) 066203.
13. H Lipkin, N Meshkov, and A Glick, Nucl. Phys. 62 (1965) 188.
14. M J Hwang, R Puebla, and M B Plenio, Phys. Rev. Lett. 115 (2015) 180404.
15. M L Cai et al., Nat. Commun. 12 (2021) 1126.
16. R Puebla et al., Phys. Rev. Lett. 118 (2017) 073001.
17. R Puebla, M J Hwang, and M. B. Plenio, Phys. Rev. A 94 (2016) 023835.
18. M J Hwang, P Rabl, and M B Plenio, Phys. Rev. A 97 (2018) 013825.
19. P Kramer, J. Phys. Conf. Ser. 99 (2008) 012009.
20. C V Kraus and T J Osborne, Phys. Rev. A 86 (2012) 062115.
21. M Reh, M Schmitt, and M Garttner, Phys. Rev. Lett. 127 (2021) 230501.

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