Quantum criticality in SU(3) and SU(4) anti-ferromagnets

We study the quantum phase transition out of the Neel state in SU(3) and SU(4) generalizations of the Heisenberg anti-ferromagnet with a sign problem free four spin coupling (so-called JQ model), by extensive quantum Monte Carlo simulations. We present evidence that the SU(3) and SU(4) order parameters and the SU(3) and SU(4) stiffness' go to zero continuously without any evidence for a first order transition. However, we find considerable deviations from simple scaling laws for the stiffness even in the largest system sizes studied. We interpret these as arising from multiplicative scaling terms in these quantities which affect the leading behavior, i.e., they will persist in the thermodynamic limit unlike the conventional additive corrections from irrelevant operators. We conjecture that these multiplicative terms arise from dangerously irrelevant operators whose contributions to the quantities of interest are non-analytic

Frustrated quantum Ising spins simulated by spinless bosons in a tilted lattice: from a quantum liquid to antiferromagnetic order

We study spinless bosons in a decorated square lattice with a near-diagonal tilt. The resonant subspace of the tilted Mott insulator is described by an effective Hamiltonian of frustrated quantum Ising spins on a non-bipartite lattice. This generalizes an earlier proposal for the unfrustrated quantum Ising model in one dimension which was realized in a recent experiment on ultracold $^{87}$Rb atoms in an optical lattice. Very close to diagonal tilt, we find a quantum liquid state which is continuously connected to the paramagnet. Frustration can be reduced by increasing the tilt angle away from the diagonal, and the system undergoes a transition to an antiferromagnetically ordered state. Using quantum Monte Carlo simulations and exact diagonalization, we find that for realistic system sizes the antiferromagnetic order appears to be quasi-one-dimensional; however, in the thermodynamic limit the order is two-dimensional.Comment: 27 pages, 14 figure

Exotic vs. conventional scaling and universality in a disordered bilayer quantum Heisenberg antiferromagnet

We present large-scale Monte-Carlo simulations of a two-dimensional (2d) bilayer quantum Heisenberg antiferromagnet with random dimer dilution. In contrast to the exotic scaling scenarios found in many other random quantum systems, the quantum phase transition in this system is characterized by a finite-disorder fixed point with power-law scaling. After accounting for strong corrections to scaling, characterized by a leading irrelevant exponent of \omega = 0.48, we find universal, i.e., disorder-independent, critical exponents z=1.310(6) and \nu=1.16(3). We discuss the consequences of these findings and suggest new experiments.Comment: 4 pages, 5eps figures included, final version as publishe

Quantum criticality of U(1) gauge theories with fermionic and bosonic matter in two spatial dimensions

We consider relativistic U(1) gauge theories in 2+1 dimensions, with N_b species of complex bosons and N_f species of Dirac fermions at finite temperature. The quantum phase transition between the Higgs and Coulomb phases is described by a conformal field theory (CFT). At large N_b and N_f, but for arbitrary values of the ratio N_b/N_f, we present computations of various critical exponents and universal amplitudes for these CFTs. We make contact with the different spin-liquids, charge-liquids and deconfined critical points of quantum magnets that these field theories describe. We compute physical observables that may be measured in experiments or numerical simulations of insulating and doped quantum magnets.Comment: 30 pages, 8 figure

Quench dynamics across quantum critical points

We study the quantum dynamics of a number of model systems as their coupling constants are changed rapidly across a quantum critical point. The primary motivation is provided by the recent experiments of Greiner et al. (Nature 415, 39 (2002)) who studied the response of a Mott insulator of ultracold atoms in an optical lattice to a strong potential gradient. In a previous work (cond-mat/0205169), it had been argued that the resonant response observed at a critical potential gradient could be understood by proximity to an Ising quantum critical point describing the onset of density wave order. Here we obtain numerical results on the evolution of the density wave order as the potential gradient is scanned across the quantum critical point. This is supplemented by studies of the integrable quantum Ising spin chain in a transverse field, where we obtain exact results for the evolution of the Ising order correlations under a time-dependent transverse field. We also study the evolution of transverse superfluid order in the three dimensional case. In all cases, the order parameter is best enhanced in the vicinity of the quantum critical point.Comment: 10 pages, 6 figure

Comment on "Spin Transport properties of the quantum one-dimensional non-linear sigma model"

In a recent preprint (cond-mat/9905415), Fujimoto has used the Bethe ansatz to compute the finite temperature, zero frequency Drude weight of spin transport in the quantum O(3) non-linear sigma model in a magnetic field $H \neq 0$. We show here that, contrary to his claims, the results are in accord with earlier semiclassical results (Sachdev and Damle, cond-mat/9610115). We also comment on his 1/N expansion, and show that it does not properly describe the long-time correlations.Comment: 4 page

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

Putting competing orders in their place near the Mott transition

We describe the localization transition of superfluids on two-dimensional lattices into commensurate Mott insulators with average particle density p/q (p, q relatively prime integers) per lattice site. For bosons on the square lattice, we argue that the superfluid has at least q degenerate species of vortices which transform under a projective representation of the square lattice space group (a PSG). The formation of a single vortex condensate produces the Mott insulator, which is required by the PSG to have density wave order at wavelengths of q/n lattice sites (n integer) along the principle axes; such a second-order transition is forbidden in the Landau-Ginzburg-Wilson framework. We also discuss the superfluid-insulator transition in the direct boson representation, and find that an interpretation of the quantum criticality in terms of deconfined fractionalized bosons is only permitted at special values of q for which a permutative representation of the PSG exists. We argue (and demonstrate in detail in a companion paper: L. Balents et al., cond-mat/0409470) that our results apply essentially unchanged to electronic systems with short-range pairing, with the PSG determined by the particle density of Cooper pairs. We also describe the effect of static impurities in the superfluid: the impurities locally break the degeneracy between the q vortex species, and this induces density wave order near each vortex. We suggest that such a theory offers an appealing rationale for the local density of states modulations observed by Hoffman et al. (cond-mat/0201348) in STM studies of the vortex lattice of BSCCO, and allows a unified description of the nucleation of density wave order in zero and finite magnetic fields. We note signatures of our theory that may be tested by future STM experiments.Comment: 35 pages, 16 figures; (v2) part II is cond-mat/0409470; (v3) added new appendix and clarifying remarks; (v4) corrected typo

Scaling in the Fan of an Unconventional Quantum Critical Point

We present results of extensive finite-temperature Quantum Monte Carlo simulations on a SU(2) symmetric S=1/2 quantum antiferromagnet with a four-spin interaction [Sandvik, Phys. Rev. Lett. 98, 227202 (2007)]. Our simulations, which are free of the sign-problem and carried out on lattices containing in excess of 1.6 X 10^4 spins, indicate that the four-spin interaction destroys the N\'eel order at an unconventional z=1 quantum critical point, producing a valence-bond solid paramagnet. Our results are consistent with the `deconfined quantum criticality' scenario.Comment: published version, minor change

Ising and Spin orders in Iron-based Superconductors

Motivated by recent neutron scattering experiments, we study the ordering of spins in the iron-based superconductors La(O_{1-x}F_x)FeAs, assuming them in proximity to a Mott insulator in the phase diagram. The ground state of the parent system with x = 0 is a spin density wave with ordering wave vector Q = (0, \pi) or (\pi, 0). Upon raising the temperature, we find the system to restore SU(2) symmetry, while an Ising symmetry remains broken, explaining the experimentally observed lattice distortion to a monoclinic crystal structure. Upon further temperature increase, the spins finally disorder at a second transition. The phase transition driven by doping with charge carriers similarly splits into an O(3) transition, and an Ising transition with z = 3 at larger doping.Comment: 4.5 pages, 2 figure