Quantum phase transitions

Quantum phase transitions take place at 0 K, unlike normal phase transitions which occur as a function of temperature, driven by the greater entropy of the high-temperature phase. An electronic phase transition as a function of composition x or gate voltage, or a magnetic phase transition as a function of J₀/ΔJ (Fig. 1) may be examples of a quantum phase transition. Magnetic field or pressure are the easiest variables to control in the laboratory. In any case, by tuning some variable g one may enter a region where two states compete to be the ground state of the system. In quantum systems, fluctuations like those described by the uncertainty principle are always present.
An example is the compound LiHoF4, where the Ho³⁺ ion sits in a site with uniaxial anisotropy which stabilizes an M_J = ±8 doublet, giving the ion an Ising-like character. Weak coupling between the Ho³⁺ ions causes the compound to order ferromagnetically at 1.6 K. A field applied perpendicular to the axis causes tunnelling between the two states, and eventually destroys the ferromagnetic order, creating a quantum paramagnet.

Figure 1: Theoretical phase diagrams calculated in mean field theory for (a) an Ising spin glass by D. Sherrington and S. Kirkpatrick (Phys. Rev. Letters 35, 1792 (1975)) and (b) for vector spins by M. Gabay and G. Toulouse (Phys. Rev. Letters 47, 201 (1981)). There is a distribution of exchange of width Δ and average value J₀.