Fingerprints of quantum phase transitions
Abstract
Phase transitions that occur at the absolute zero of temperature are driven entirely by quantum fluctuations. When such a transition is continuous, the characteristic length scale for these fluctuations diverges at a quantum critical point (QCP). Although QCPs exist only at zero temperature, they can leave fingerprints on, the finite-temperature properties of a system---effects known as quantum critical scaling. For this reason, QCPs have become prime suspects in the ongoing experimental investigation of strongly correlated systems like heavy fermions and cuprate superconductors. Before considering experimental results, it is important to identify the range in temperature over which quantum criticality can be observed. We have addressed this question by calculating the free energy exactly for two models of QCPs. In both cases we find that quantum critical scaling can persist up to a temperature on the order of the microscopic energy scale of the model; however, when we include irrelevant operators in the Hamiltonian, it is possible for the scaling regime to shrink drastically. We have also used quantum criticality to make specific predictions for the hole-doped copper oxide superconductors. If we assume that both sides of the superconducting dome terminate in a QCP, then the transition temperature Tc and the zero-temperature superfluid density rhos(0) should be related by Tc ∝ rhos(0) y in the vicinity of each QCP. We predict different values of y on the underdoped and overdoped sides of the phase diagram. The value y = 1/2 agrees with recent experiments on underdoped YBa2Cu3O6+delta; existing data on overdoped materials appear to support our conjecture that y > 1/2. The current understanding of quantum phase transitions relies almost entirely on analogies with classical critical phenomena. While these analogies are adequate in many cases, there are other models for which they certainly do not apply. For instance, Anderson localization in three dimensions features a metal-insulator transition accompanied by a diverging localization length, yet the ground state energy density is analytic at the QCP. We propose that the concept of quantum entanglement is very useful in studying QCPs that have no classical analog. In particular, we show that the von Neumann entropy (which measures ground state entanglement) is non-analytic at the QCP in a number of different models, including Anderson localization in three dimensions.
- Publication:
-
Ph.D. Thesis
- Pub Date:
- 2006
- Bibcode:
- 2006PhDT.......130K