Localization of the Higgs mode at the superfluid-Mott glass transition

The amplitude (Higgs) mode near the two-dimensional superfluid-Mott glass quantum phase transition is studied. We map the Bose-Hubbard Hamiltonian of disordered interacting bosons onto an equivalent classical XY model in (2+1) dimensions and compute the scalar susceptibility of the order parameter amplitude via Monte Carlo simulation. Analytic continuation of the scalar susceptibilities from imaginary to real frequency to obtain the spectral densities is performed by a modified maximum entropy technique. Our results show that the introduction of disorder into the system leads to unconventional dynamical behavior of the Higgs mode that violates naive scaling,despite the underlying thermodynamics of the transition being of conventional power-law type. The computed spectral densities exhibit a broad, non-critical response for all energies, and a momentum-independent dispersion for long-wavelengths, indicating strong evidence for the localization of the Higgs mode for all dilutions.Comment: 11 pages, 8 figure

Quantum critical behavior of a three-dimensional superfluid-Mott glass transition

The superfluid to insulator quantum phase transition of a three-dimensional particle-hole symmetric system of disordered bosons is studied. To this end, a site-diluted quantum rotor Hamiltonian is mapped onto a classical (3+1)-dimensional XY model with columnar disorder and analyzed by means of large-scale Monte Carlo simulations. The superfluid-Mott insulator transition of the clean, undiluted system is in the 4D XY universality class and shows mean-field critical behavior with logarithmic corrections. The clean correlation length exponent $\nu = 1/2$ violates the Harris criterion, indicating that disorder must be a relevant perturbation. For nonzero dilutions below the lattice percolation threshold of $p_c = 0.688392$, our simulations yield conventional power-law critical behavior with dilution-independent critical exponents $z=1.67(6)$, $\nu = 0.90(5)$, $\beta/\nu = 1.09(3)$, and $\gamma/\nu = 2.50(3)$. The critical behavior of the transition across the lattice percolation threshold is controlled by the classical percolation exponents. Our results are discussed in the context of a classification of disordered quantum phase transitions, as well as experiments in superfluids, superconductors and magnetic systems.Comment: 10 pages, 12 figures, published versio

Quantum critical behavior of the superfluid-Mott glass transition

We investigate the zero-temperature superfluid to insulator transitions in a diluted two-dimensional quantum rotor model with particle-hole symmetry. We map the Hamiltonian onto a classical $(2+1)$-dimensional XY model with columnar disorder which we analyze by means of large-scale Monte Carlo simulations. For dilutions below the lattice percolation threshold, the system undergoes a generic superfluid-Mott glass transition. In contrast to other quantum phase transitions in disordered systems, its critical behavior is of conventional power-law type with universal (dilution-independent) critical exponents $z=1.52(3)$, $\nu=1.16(5)$, $\beta/\nu= 0.48(2)$, $\gamma/\nu=2.52(4)$, and $\eta=-0.52(4)$. These values agree with and improve upon earlier Monte-Carlo results [Phys. Rev. Lett. 92, 015703 (2004)] while (partially) excluding other findings in the literature. As a further test of universality, we also consider a soft-spin version of the classical Hamiltonian. In addition, we study the percolation quantum phase transition across the lattice percolation threshold; its critical behavior is governed by the lattice percolation exponents in agreement with recent theoretical predictions. We relate our results to a general classification of phase transitions in disordered systems, and we briefly discuss experiments.Comment: 10 pages, 12 figures, final version as publishe

Collective modes at a disordered quantum phase transition

We study the collective excitations, i.e., the Goldstone (phase) mode and the Higgs (amplitude) mode, near the superfluid--Mott glass quantum phase transition in a two-dimensional system of disordered bosons. Using Monte Carlo simulations as well as an inhomogeneous quantum mean-field theory with Gaussian fluctuations, we show that the Higgs mode is strongly localized for all energies, leading to a noncritical scalar response. In contrast, the lowest-energy Goldstone mode undergoes a striking delocalization transition as the system enters the superfluid phase. We discuss the generality of these findings and experimental consequences, and we point out potential relations to many-body localization.Comment: 5 pages + 7 pages supplement, 10 figures included. Final version as publishe

Quantum Critical Behavior of the Superfluid-Mott Glass Transition

We investigate the zero-temperature superfluid to insulator transitions in a diluted two-dimensional quantum rotor model with particle-hole symmetry. We map the Hamiltonian onto a classical (2+1)-dimensional XY model with columnar disorder which we analyze by means of large-scale Monte Carlo simulations. For dilutions below the lattice percolation threshold, the system undergoes a generic superfluid-Mott glass transition. In contrast to other quantum phase transitions in disordered systems, its critical behavior is of conventional power-law type with universal (dilution-independent) critical exponents z=1.52(3), ν =1.16(5), ß/ν =0.48(2), γ/ν=2.52(4), and η = -0.52(4). These values agree with and improve upon earlier Monte Carlo results [Phys. Rev. Lett. 92, 015703 (2004)] while (partially) excluding other findings in the literature. As a further test of universality, we also consider a soft-spin version of the classical Hamiltonian. In addition, we study the percolation quantum phase transition across the lattice percolation threshold; its critical behavior is governed by the lattice percolation exponents in agreement with recent theoretical predictions. We relate our results to a general classification of phase transitions in disordered systems, and we briefly discuss experiments

Semiconductor Bloch-equations formalism: Derivation and application to high-harmonic generation from Dirac fermions

We rederive the semiconductor Bloch equations emphasizing the close link to the Berry connection. Our rigorous derivation reveals the existence of two further contributions to the current, in addition to the frequently considered intraband and polarization-related interband terms. The extra contributions become sizable in situations with strong dephasing or when the dipole-matrix elements are strongly wave-number dependent. We apply the formalism to high-harmonic generation for a Dirac metal. The extra terms add to the frequency-dependent emission intensity (high-harmonic spectrum) significantly at certain frequencies changing the total signal up to a factor of 10

Chromium Doping of the Topological Insulator Antimony Telluride

Topological insulators (TI’s) are recently discovered quantum states of matter characterized by an insulating bulk paired with conducting surface states such that electronic conduction occurs only across edges and surfaces. In these experiments we investigate the effect of chromium doping on the TI antimony telluride. The interesting applications involved with TI’s rely on the presence of the anomalous quantum hall effect (AQHE) in the sample. Previous experiments demonstrate that chromium-doping of antimony telluride can produce this effect in thin film samples. Here, we expand on the previous experiments to a.) determine if the effect can be produced in bulk samples and b.) more precisely determine the effects of the doping on the host material. Results indicated that the AQHE could likely be observed with further tuning of doping ratios; our samples exhibiting an anomalous hall effect that is “nearly quantized”

Chaotic Behavior in a Damped Driven Pendulum

Chaotic behavior of a physical system is characterized by its unpredictability and extreme sensitivity to initial conditions. This type of behavior is prevalent throughout the universe, yet we likely don\u27t expect it of simple systems like a pendulum. We show here that solutions to the theoretical model of a damped driven pendulum produce transcendental functions that are easily understood in small angle approximations, yet provide chaotic solutions if the angle is allowed to take all values. We then recreated this system physically to show that a system as simple as the damped driven pendulum would indeed produce unpredictable behavior, strongly dependent on initial conditions