Nature of the Quantum Phase Transition in Clean, Itinerant Heisenberg Ferromagnets

These are notes for lectures delivered at the NATO ASI on Dynamics in Leiden, The Netherlands, in July 1998. The main concepts relating to quantum phase transitions are explained, using the paramagnet-to-ferromagnet transition of itinerant electrons as the primary example. Some aspects of metal-insulator transitions are also briefly discussed. The exposition is strictly pedagogical in nature, with no ambitions with respect to completeness or going into technical details. The ...

The quantum critical behavior of disordered itinerant ferromagnets is determined exactly by solving a recently developed effective field theory. It is shown that there are logarithmic corrections to a previous calculation of the critical behavior, and that the exact critical behavior coincides with that found earlier for a phase transition of undetermined nature in disordered interacting electron systems. This confirms a previous suggestion that the unspecified transition sho...

To illustrate a simple mean-field-like approach for examining quantum phase transitions we consider the $J-J^\prime$ quantum Heisenberg antiferromagnet on a square lattice. The exchange couplings $J$ and $J^\prime$ are competing with each other. The ratio $J^\prime/J$ is the control parameter and its change drives the transition. We adopt a variational ansatz, calculate the ground-state energy as well as the order parameter and describe the quantum phase transition inherent i...

We present results of extensive quantum Monte Carlo simulations of the three-dimensional (3D) S=1/2 Heisenberg antiferromagnet. Finite-size scaling of the spin stiffness and the sublattice magnetization gives the critical temperature Tc/J = 0.946 +/- 0.001. The critical behavior is consistent with the classical 3D Heisenberg universality class, as expected. We discuss the general nature of the transition from quantum mechanical to classical (thermal) order parameter fluctuati...

Quantum phase transitions occur at zero temperature when some non-thermal control-parameter like pressure or chemical composition is changed. They are driven by quantum rather than thermal fluctuations. In this review we first give a pedagogical introduction to quantum phase transitions and quantum critical behavior emphasizing similarities with and differences to classical thermal phase transitions. We then illustrate the general concepts by discussing a few examples of quan...

It is shown that the phase transition in low-T_c clean itinerant ferromagnets is generically of first order, due to correlation effects that lead to a nonanalytic term in the free energy. A tricritical point separates the line of first order transitions from Heisenberg critical behavior at higher temperatures. Sufficiently strong quenched disorder suppresses the first order transition via the appearance of a critical endpoint. A semi-quantitative discussion is given in terms ...

Using a combination of unbiased quantum Monte Carlo simulations and a decoupled dimer mean-field theory, we investigate the thermal and quantum phase transitions of the spin-1/2 Heisenberg model on the dimerized diamond lattice. We find that at sufficiently strong dimerization the system exhibits a quantum disordered ground state, in contrast to the antiferromagnetic phase stabilized at weak dimerization. We determine the quantum critical point and examine the thermodynamic r...

The quantum ferromagnetic transition at zero temperature in disordered itinerant electron systems is considered. Nonmagnetic quenched disorder leads to diffusive electron dynamics that induces an effective long-range interaction between the spin or order parameter fluctuations of the form r^{2-2d}, with d the spatial dimension. This leads to unusual scaling behavior at the quantum critical point, which is determined exactly. In three-dimensional systems the quantum critical e...

An effective field theory is derived for the ferromagnetic transition of diffusive electrons at T=0. The static disorder which leads to diffusive electron dynamics induces an effective long-range interaction between the spins of the form 1/r^(2d-2). This leads to unusual scaling behavior at the quantum critical point, which is determined exactly. The crossover from this quantum fixed point to the classical Heisenberg fixed point should be observable in ferromagnetic materials...

This paper discusses why the usual notion that quantum phase transitions can be mapped onto classical phase transitions in a higher dimension, and that this makes the former uninteresting from a fundamental theoretical point of view, is in general misleading. It is shown that quantum phase transitions are often qualitatively different from their classical counterparts due to (1) long-ranged effective interactions that are induced by soft modes, and (2) in the presence of quen...