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The interpretation of the magnetic phase diagrams of strongly correlated electron systems remains controversial. In particular, the physics of quantum phase transitions, which occur at zero temperature, is still enigmatic. Heavy-fermion…
A d-wave high temperature cuprate superconductor exhibits a nematic ordering transition at zero temperature. Near the quantum critical point, the coupling between gapless nodal quasiparticles and nematic order parameter fluctuation can…
This article reviews the unconventional effects of random disorder on magnetic quantum phase transitions, focusing on a number of new experimental and theoretical developments during the last three years. On the theory side, we address…
The effects of quenched disorder on the critical properties of itinerant quantum magnets are considered. Particular attention is paid to locally ordered rare regions that are formed in the presence of quenched disorder even when the bulk…
When a metal undergoes a continuous quantum phase transition, non-Fermi liquid behaviour arises near the critical point. It is standard to assume that all low-energy degrees of freedom induced by quantum criticality are spatially extended,…
We investigate the quantum phase transition of itinerant ferromagnets. It is shown that correlation effects in the underlying itinerant electron system lead to singularities in the order parameter field theory that result in an effective…
A magnetic field applied to a three-dimensional antiferromagnetic metal can destroy the long-range order and thereby induce a quantum critical point. Such field-induced quantum critical behavior is the focus of many recent experiments. We…
We study the effects of dissipation on a disordered quantum phase transition with O$(N)$ order parameter symmetry by applying a strong-disorder renormalization group to the Landau-Ginzburg-Wilson field theory of the problem. We find that…
The effects of rare regions on the critical properties of quantum antiferromagnets with hidden degrees of freedom within the renormalization group is discussed. It is shown that for ``constrained'' systems the stability range on the phase…
Quantum criticality describes the collective fluctuations of matter undergoing a second-order phase transition at zero temperature. It is being discussed in a number of strongly correlated electron systems. A prototype case occurs in the…
The anisotropic Kondo necklace model in 2D and 3D is treated as a genuine model for magnetic to Kondo singlet quantum phase transitions in the heavy fermion (HF) compounds. The variation of the quantum critical point (QCP) with anisotropy…
We derive an order-parameter field theory for a quantum phase transition between a disordered metal and an exotic (non-s-wave) superconductor. Mode coupling effects between the order parameter and other fermionic soft modes lead to an…
Quantum phase transitions are among the most intriguing phenomena that can occur when the electronic ground state of correlated metals are tuned by external parameters such as pressure, magnetic field or chemical substitution. Such…
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…
Quantum magnets represent an ideal playground for the controlled realization of novel quantum phases and of quantum phase transitions. The Hamiltonian of the system can be indeed manipulated by applying a magnetic field or pressure on the…
The subtle interplay of randomness and quantum fluctuations at low temperatures gives rise to a plethora of unconventional phenomena in systems ranging from quantum magnets and correlated electron materials to ultracold atomic gases.…
We discuss three different scenarios recently proposed to account for the non-Fermi liquid behavior near antiferromagnetic (AFM) quantum critical points in heavy-Fermion systems: (i) scattering of Fermi liquid quasiparticles by strong spin…
We quantitatively discuss the influence of quenched disorder on the ferromagnetic quantum phase transition in metals, using a theory that describes the coupling of the magnetization to gapless fermionic excitations. In clean systems, the…
Strongly correlated electron systems at the border of magnetism are of active current interest, particularly because the accompanying quantum criticality provides a route towards both strange-metal non-Fermi liquid behavior and…
We investigate the influence of spatial disorder correlations on smeared phase transitions, taking the quantum phase transition in itinerant magnets as an example. We find that even short-range correlations can have a dramatic effect and…