Quantum phase transitions

Quantum phase transitions arise in many-body systems due to competing interactions that promote rivaling ground states. Recent years have seen the identification of continuous quantum phase transitions, or quantum critical points, in a host of antiferromagnetic heavy-fermion compounds. Studies of the interplay between the various effects have revealed new classes of quantum critical points, and are uncovering a plethora of new quantum phases. At the same time, quantum critica...

Magnetic insulators have proved to be fertile ground for studying new types of quantum many body states, and I survey recent experimental and theoretical examples. The insights and methods transfer also to novel superconducting and metallic states. Of particular interest are critical quantum states, sometimes found at quantum phase transitions, which have gapless excitations with no particle- or wave-like interpretation, and control a significant portion of the finite tempera...

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...

The gas-liquid transition is a first-order transition terminating at a finite-temperature critical point with diverging density fluctuations. Mott transition, a metal-insulator transition driven by Coulomb repulsion between electrons, has been identified with this textbook transition. However, the critical temperature of the Mott transition can be suppressed, resulting in unusual quantum criticality. It accounts for non-Fermi-liquid-like properties, and strongly momentum depe...

This review article describes theoretical and experimental advances in using quantum dots as a system for studying impurity quantum phase transitions and the non-Fermi liquid behavior at the quantum critical point.

This review gives an overview of the quantum phase transition (QPT) problem in metallic ferromagnets, discussing both experimental and theoretical aspects. These QPTs can be classified with respect to the presence and strength of quenched disorder: Clean systems generically show a discontinuous, or first-order, QPT from the ferromagnetic state to a paramagnetic one as a function of some control parameter, as predicted by theory. Disordered systems are much more complicated, d...

This conference summary and outlook provides a personal overview of the topics and themes of the August 2009 Dresden meeting on quantum criticality and novel phases. The dichotomy between the local moment and the itinerant views of magnetism is revisited and refreshed in new materials, new probes and new theoretical ideas. New universality and apparent zero temperature phases of matter move us beyond the old ideas of quantum criticality. This is accompanied by alternative pai...

We give a general introduction to quantum phase transitions in strongly-correlated electron systems. These transitions which occur at zero temperature when a non-thermal parameter $g$ like pressure, chemical composition or magnetic field is tuned to a critical value are characterized by a dynamic exponent $z$ related to the energy and length scales $\Delta$ and $\xi$. Simple arguments based on an expansion to first order in the effective interaction allow to define an upper-c...

Quantum phase transitions in metals are often accompanied by violations of Fermi liquid behavior in the quantum critical regime. Particularly fascinating are transitions beyond the Landau-Ginzburg-Wilson concept of a local order parameter. The breakdown of the Kondo effect in heavy-fermion metals constitutes a prime example of such a transition. Here, the strongly correlated f electrons become localized and disappear from the Fermi surface, implying that the transition is equ...

Quantum critical behavior of many-body phase transitions is one of the most fascinating yet challenging questions in quantum physics. Here, we improved the band-mapping method to investigate the quantum phase transition from superfluid to Mott insulators, and we observed the critical behaviors of quantum phase transitions in both dynamical steady-state-relaxation region and phase-oscillation region. Based on various observables, two different values for the same quantum criti...