Quantum Phase Transitions

Recently, quantum phase transitions (QPT) have been object of renewed interest and study due to recent experiments with superconducting cuprate, heavy fermions materials, organic conductors and other related compounds [1]. Although the QPT have been studied since the 70's, specially in spin models, as the Ising model with transverse field, the new interest has emerged from the Anderson model for non-interacting electrons, where the transition appears with the electronic states's localization in the presence of a random potential. The first results obtained built the bases for a better understanding of quantum systems behaviour near the critical point. Although many questions are still open and strong electronic interactions play a fundamental role yet not totally understood in these transitions, the QPT opened a new perspective for Physics.

Quantum phase transitions differ fundamentally from the classical phase transitions for not being exclusively related to temperature changes, which is counter intuitive for the concept of phase transitions. In fact QPT occur at absolute zero temperature due to quantum fluctuations of the ground state as we vary a external parameter [1,2,3]. There are different techniques to identify the QPT and the critical values for the parameters where these transitions can happen. One very common way to identify a QPT is using the energy gap between the ground state and the first excited state. The parameter's value for which the gap goes to zero or presents a minimum points the value for the transition [1]. Another important tool that can be used for characterize QPT is quantum fidelity, which had its development tied to quantum computer theory. Basically, fidelity consists of the inner product between near states differing on a small change in the external parameter. The value of the parameter that minimizes the fidelity signs the critical point for the transition [4,5].

This approach can be used for the better understanding and description of quantum systems opening new possibilities and discoveries. These analyses have possible impact in different areas as metrology, quantum computing, quantum information and still can help in revealing new fundamental physical concepts.

Researcher: Eduardo Cerutti Mattei



[1] SACHDEV, S. Quantum phase transitions. New York: Cambridge University Press, 2001.
[2] OSTERLOH, A. et al. Scalling of entanglement close to a quantum phase transition. Nature, London, v. 416, n. 4, p. 608-610, Apr. 2002.
[3] SONDHI, S. L. et al. Continuous quantum phase transition. Review of Modern Physics, Woodbury, v. 69, n. 1, p. 315-333, Jan. 1997.
[4] OELKERS, N.; LINKS, J. Ground-state properties of the attractive one-dimensional Bose-Hubbard model. Physical Review B, Melville, 75, n. 3, 115119 15p., Mar. 2007.
[5] BUONSANTE, P.; VEZZANI, A. Ground-state fidelity and bipartite entanglement in the Bose-Hubbard model. Physical Review Letters, Melville, 98, n. 3, 110601 4p., Mar. 2007.