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

Recently it was argued that quantum phase transitions can be radically different from classical phase transitions with as a highlight the 'deconfined critical points' exhibiting fractionalization of quantum numbers due to Berry phase effects. Such transitions are supposed to occur in frustrated ('$J_1$-$J_2$') quantum magnets. We have developed a novel renormalization approach for such systems which is fully respecting the underlying lattice structure. According to our findin...

We study the stability of the Quantum Critical Point (QCP) for itinerant ferromagnets commonly described by the Hertz-Millis-Moriya (HMM) theory. We argue that in $D \leq 3$, long-range spatial correlations associated with the Landau damping of the order parameter field generate a universal {\it negative}, non-analytic $|q|^{(D+1)/2}$ contribution to the static magnetic susceptibility $\chi_s (q, 0)$, which makes HMM theory unstable. We argue that the actual transition is eit...

The Mermin-Wagner theorem states that spontaneous continuous symmetry breaking is prohibited in systems with short-range interactions at spatial dimension $D\le 2$. For long-range interactions with a power-law form ($1/r^{\alpha}$), the theorem further forbids ferromagnetic or antiferromagnetic order at finite temperature when $\alpha\ge 2D$. However, the situation for $\alpha \in (2,4)$ at $D=2$ is not covered by the theorem. To address this, we conduct large-scale quantum M...

The signature for a non-Fermi liquid behavior near a quantum phase transition has been observed in thermal and transport properties of many metallic systems at low temperatures. In the present work we consider specific examples of itinerant ferromagnet as well as antiferromagnet in the limit of vanishing transition temperature. The temperature variation of spin susceptibility, electrical resistivity, specific heat, and NMR relaxation rates at low temperatures is calculated in...

In this work we extend the notion of what is meant by a meanfield. Meanfields are approximately maps - through some self consistency relation - of a complex, usually manybody, problem to a simpler more readily solvable problem. This mapping can then be solved to represent properties of the complex many body problem using some self consistency relations. Prototypical examples of simpler meanfield problems (meanfield systems) are the single site and free particle problems. Here...

An earlier theory of the quantum phase transition in metallic ferromagnets is revisited and generalized in three ways. It is shown that the mechanism that leads to a fluctuation-induced first-order transition in metallic ferromagnets with a low Curie temperature is valid, (1) irrespective of whether the magnetic moments are supplied by the conduction electrons or by electrons in another band, (2) for ferromagnets in the XY and Ising universality classes as well as for Heisenb...

We consider a $\phi^4$-theory with a position-dependent distance from the critical point. One realization of this model is a classical ferromagnet subject to non-uniform mechanical stress. We find a sharp phase transition where the envelope of the local magnetization vanishes uniformly. The first-order transition in a quantum ferromagnet also remains sharp. The universal mechanism leading to a tricritical point in an itinerant quantum ferromagnet is suppressed, and in princip...

We overview some recent work and present new results on the ground state properties and the spectrum of excitations of the two-dimensional frustrated Heisenberg antiferromagnet. Spontaneous dimer order is present in the quantum disordered phase of this model. We study the stability and analyze the structure of the spectrum, including the two-particle singlet excitation branch throughout the disordered phase, as well as in the vicinity of the Neel critical point. The variation...

It is shown that the quantum phase transition in metallic non-s-wave ferromagnets, or spin nematics, is generically of first order. This is due to a coupling of the order parameter to soft electronic modes that play a role analogous to that of the electromagnetic vector potential in a superconductor, which leads to a fluctuation-induced first-order transition. A generalized mean-field theory for the p-wave case is constructed that explicitly shows this effect. Tricritical win...

We study the influence of quenched disorder on quantum phase transitions in itinerant magnets with Heisenberg spin symmetry, paying particular attention to rare disorder fluctuations. In contrast to the Ising case where the overdamping suppresses the tunneling of the rare regions, the Heisenberg system displays strong power-law quantum Griffiths singularities in the vicinity of the quantum critical point. We discuss these phenomena based on general scaling arguments, and we i...