We investigate the zero-temperature superfluid to insulator transitions in a diluted twodimensional 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 largescale 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), β/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.
We rederive the semiconductor Bloch equations emphasizing the close link to the Berry connection. Our rigorous derivation reveals the existence of a third contribution to the (longitudinal) current in addition to the traditional intraband and polarization-related interband terms. The novel term becomes sizable in situations where the dipole-matrix elements are strongly wave-number dependent. We apply the formalism to high-harmonic generation for a Dirac metal. The novel term adds to the frequency-dependent emission intensity (high-harmonic spectrum) significantly at certain frequencies reaching up to 90% of the total signal.
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