Laboratoire de Physique Théorique
Toulouse - UMR 5152

A spin gap system in an applied magnetic field undergoes a quantum phase transition at zero temperature, when the gap is closed by the applied field. If the system is one dimensional, the quantum critical point is described by a free fermion effective theory, while the gapless phase above the critical field can be regarded as a Tomonaga-Luttinger liquid. The quantum critical phenomena associated to this field-induced transition may be among the simplest yet nontrivial examples of quantum phase transition. However, several of its physical consequences have been apparently overlooked. In this talk, I will discuss our recent findings on this topic.

1) Universal magnetization minimum [1] In the gapless Tomonaga-Luttinger liquid phase above the critical field, the magnetization as a function of temperature exhibits a minimum. This is similar in appearance to the magnetization cusp observed in a Bose-Einstein Condensation of magnons in higher dimensions. However, in the one-dimensional case, the minimum represents a crossover, as there is no phase transition at finite temperature.

2) Susceptibility and phase diagram of quasi one-dimensional systems [2] The transverse staggered susceptibility around the quantum critical point also exhibits a crossover between the Tomonaga-Luttinger liquid and the "quantum critical" behavior. Using this result, we can further predict field-temperature phase diagram for quasi one-dimensional systems in which one-dimensional spin gap systems are coupled weakly.

[1] Y. Maeda, C. Hotta, and M. Oshikawa, Phys. Rev. Lett. 99, 057205 (2007). [2] T. Ono and M. Oshikawa, in preparation