Metallic spin glasses

Recent work on the zero temperature phases and phase transitions of strongly random electronic system is reviewed. The transition between the spin glass and quantum paramagnet is examined, for both metallic and insulating systems. Insight gained from the solution of infinite range models leads to a quantum field theory for the transition between a metallic quantum paramagnetic and a metallic spin glass. The finite temperature phase diagram is described and crossover functions are computed in mean field theory. A study of fluctuations about mean field leads to the formulation of scaling hypotheses.Comment: Contribution to the Proceedings of the ITP Santa Barbara conference on Non-Fermi liquids, 25 pages, requires IOP style file

Metamagnetic Quantum Criticality Revealed by 17O-NMR in the Itinerant Metamagnet Sr3Ru2O7

We have investigated the spin dynamics in the bilayered perovskite Sr3Ru2O7 as a function of magnetic field and temperature using 17O-NMR. This system sits close to a metamagnetic quantum critical point (MMQCP) for the field perpendicular to the ruthenium oxide planes. We confirm Fermi-liquid behavior at low temperatures except for a narrow field region close to the MMQCP. The nuclear spin-lattice relaxation rate divided by temperature 1/T1T is enhanced on approaching the metamagnetic critical field of 7.9 T and at the critical field 1/T1T continues to increase and does not show Fermi- liquid behavior down to 0.3 K. The temperature dependence of T1T in this region suggests the critical temperature Theta to be 0 K, which is a strong evidence that the spin dynamics possesses a quantum critical character. Comparison between uniform susceptibility and 1/T1T reveals that antiferromagnetic fluctuations instead of two-dimensional ferromagnetic fluctuations dominate the spin fluctuation spectrum at the critical field, which is unexpected for itinerant metamagnetism.Comment: 5 pages, 4 figures, Accepted by Phys. Rev. Let

Quantum rotor description of the Mott-insulator transition in the Bose-Hubbard model

We present the novel approach to the Bose-Hubbard model using the $\mathrm{U}(1)$ quantum rotor description. The effective action formalism allows us to formulate a problem in the phase only action and obtain an analytical formulas for the critical lines. We show that the nontrivial $\mathrm{U}(1)$ phase field configurations have an impact on the phase diagrams. The topological character of the quantum field is governed by terms of the integer charges - winding numbers. The comparison presented results to recently obtained quantum Monte Carlo numerical calculations suggests that the competition between quantum effects in strongly interacting boson systems is correctly captured by our model.Comment: accepted to PR

Adiabatic quantum computation and quantum phase transitions

We analyze the ground state entanglement in a quantum adiabatic evolution algorithm designed to solve the NP-complete Exact Cover problem. The entropy of entanglement seems to obey linear and universal scaling at the point where the mass gap becomes small, suggesting that the system passes near a quantum phase transition. Such a large scaling of entanglement suggests that the effective connectivity of the system diverges as the number of qubits goes to infinity and that this algorithm cannot be efficiently simulated by classical means. On the other hand, entanglement in Grover's algorithm is bounded by a constant.Comment: 5 pages, 4 figures, accepted for publication in PR

Evidence of columnar order in the fully frustrated transverse field Ising model on the square lattice

Using extensive classical and quantum Monte Carlo simulations, we investigate the ground-state phase diagram of the fully frustrated transverse field Ising model on the square lattice. We show that pure columnar order develops in the low-field phase above a surprisingly large length scale, below which an effective U(1) symmetry is present. The same conclusion applies to the Quantum Dimer Model with purely kinetic energy, to which the model reduces in the zero-field limit, as well as to the stacked classical version of the model. By contrast, the 2D classical version of the model is shown to develop plaquette order. Semiclassical arguments show that the transition from plaquette to columnar order is a consequence of quantum fluctuations.Comment: 5 pages (including Supplemental Material), 5 figure

Effect of long range connections on an infinite randomness fixed point associated with the quantum phase transitions in a transverse Ising model

We study the effect of long-range connections on the infinite-randomness fixed point associated with the quantum phase transitions in a transverse Ising model (TIM). The TIM resides on a long-range connected lattice where any two sites at a distance r are connected with a non-random ferromagnetic bond with a probability that falls algebraically with the distance between the sites as 1/r^{d+\sigma}. The interplay of the fluctuations due to dilutions together with the quantum fluctuations due to the transverse field leads to an interesting critical behaviour. The exponents at the critical fixed point (which is an infinite randomness fixed point (IRFP)) are related to the classical "long-range" percolation exponents. The most interesting observation is that the gap exponent \psi is exactly obtained for all values of \sigma and d. Exponents depend on the range parameter \sigma and show a crossover to short-range values when \sigma >= 2 -\eta_{SR} where \eta_{SR} is the anomalous dimension for the conventional percolation problem. Long-range connections are also found to tune the strength of the Griffiths phase.Comment: 5 pages, 1 figure, To appear in Phys. Rev.

Phase-ordering dynamics in itinerant quantum ferromagnets

The phase-ordering dynamics that result from domain coarsening are considered for itinerant quantum ferromagnets. The fluctuation effects that invalidate the Hertz theory of the quantum phase transition also affect the phase ordering. For a quench into the ordered phase a transient regime appears, where the domain growth follows a different power law than in the classical case, and for asymptotically long times the prefactor of the t^{1/2} growth law has an anomalous magnetization dependence. A quench to the quantum critical point results in a growth law that is not a power-law function of time. Both phenomenological scaling arguments and renormalization-group arguments are given to derive these results, and estimates of experimentally relevant length and time scales are presented.Comment: 6pp., 1 eps fig, slightly expanded versio

Critical properties of the Fermi-Bose Kondo and pseudogap Kondo models: Renormalized perturbation theory

Magnetic impurities coupled to both fermionic and bosonic baths or to a fermionic bath with pseudogap density of states, described by the Fermi-Bose Kondo and pseudogap Kondo models, display non-trivial intermediate coupling fixed points associated with critical local-moment fluctuations and local non-Fermi liquid behavior. Based on renormalization group together with a renormalized perturbation expansion around the free-impurity limit, we calculate various impurity properties in the vicinity of those intermediate-coupling fixed points. In particular, we compute the conduction electron T matrix, the impurity susceptibility, and the residual impurity entropy, and relate our findings to certain scenarios of local quantum criticality in strongly correlated lattice models.Comment: 16 pages, 5 figs; (v2) large-N results for entropy of Bose-Kondo model added; (v3) final version as publishe

Interaction effects and quantum phase transitions in topological insulators

We study strong correlation effects in topological insulators via the Lanczos algorithm, which we utilize to calculate the exact many-particle ground-state wave function and its topological properties. We analyze the simple, noninteracting Haldane model on a honeycomb lattice with known topological properties and demonstrate that these properties are already evident in small clusters. Next, we consider interacting fermions by introducing repulsive nearest-neighbor interactions. A first-order quantum phase transition was discovered at finite interaction strength between the topological band insulator and a topologically trivial Mott insulating phase by use of the fidelity metric and the charge-density-wave structure factor. We construct the phase diagram at $T = 0$ as a function of the interaction strength and the complex phase for the next-nearest-neighbor hoppings. Finally, we consider the Haldane model with interacting hard-core bosons, where no evidence for a topological phase is observed. An important general conclusion of our work is that despite the intrinsic nonlocality of topological phases their key topological properties manifest themselves already in small systems and therefore can be studied numerically via exact diagonalization and observed experimentally, e.g., with trapped ions and cold atoms in optical lattices.Comment: 13 pages, 12 figures. Published versio

Magnetic phase diagram of spatially anisotropic, frustrated spin-1/2 Heisenberg antiferromagnet on a stacked square lattice

Magnetic phase diagram of a spatially anisotropic, frustrated spin-1/2 Heisenberg antiferromagnet on a stacked square lattice is investigated using second-order spin-wave expansion. The effects of interlayer coupling and the spatial anisotropy on the magnetic ordering of two ordered ground states are explicitly studied. It is shown that with increase in next nearest neighbor frustration the second-order corrections play a significant role in stabilizing the magnetization. We obtain two ordered magnetic phases (Neel and stripe) separated by a paramagnetic disordered phase. Within second-order spin-wave expansion we find that the width of the disordered phase diminishes with increase in the interlayer coupling or with decrease in spatial anisotropy but it does not disappear. Our obtained phase diagram differs significantly from the phase diagram obtained using linear spin-wave theory.Comment: 22 pages, 6 figures, minor changes from previous versio