Solid state and molecular theory group Semiannual progress report

Use of scattered wave method to compute molecular wave functions, augmented plane wave method for energy band calculations, and Casimir invariants as invariant operators in Lie group

Domain wall QCD with physical quark masses

We present results for several light hadronic quantities ($f_\pi$, $f_K$, $B_K$, $m_{ud}$, $m_s$, $t_0^{1/2}$, $w_0$) obtained from simulations of 2+1 flavor domain wall lattice QCD with large physical volumes and nearly-physical pion masses at two lattice spacings. We perform a short, O(3)%, extrapolation in pion mass to the physical values by combining our new data in a simultaneous chiral/continuum `global fit' with a number of other ensembles with heavier pion masses. We use the physical values of $m_\pi$, $m_K$ and $m_\Omega$ to determine the two quark masses and the scale - all other quantities are outputs from our simulations. We obtain results with sub-percent statistical errors and negligible chiral and finite-volume systematics for these light hadronic quantities, including: $f_\pi$ = 130.2(9) MeV; $f_K$ = 155.5(8) MeV; the average up/down quark mass and strange quark mass in the $\bar {\rm MS}$ scheme at 3 GeV, 2.997(49) and 81.64(1.17) MeV respectively; and the neutral kaon mixing parameter, $B_K$, in the RGI scheme, 0.750(15) and the $\bar{\rm MS}$ scheme at 3 GeV, 0.530(11).Comment: 131 pages, 30 figures. Updated to match published versio

Domain wall QCD with near-physical pions

We present physical results for a variety of light hadronic quantities obtained via a combined analysis of three 2+1 flavour domain wall fermion ensemble sets. For two of our ensemble sets we used the Iwasaki gauge action with β=2.13 (a-1=1.75(4) GeV) and β=2.25 (a -1=2.31(4) GeV) and lattice sizes of 243×64 and 323×64 respectively, with unitary pion masses in the range 293(5)-417(10) MeV. The extent Ls for the 5th dimension of the domain wall fermion formulation is Ls=16 in these ensembles. In this analysis we include a third ensemble set that makes use of the novel Iwasaki+DSDR (dislocation suppressing determinant ratio) gauge action at β=1.75 (a -1=1.37(1) GeV) with a lattice size of 323×64 and L s=32 to reach down to partially-quenched pion masses as low as 143(1) MeV and a unitary pion mass of 171(1) MeV, while retaining good chiral symmetry and topological tunneling. We demonstrate a significant improvement in our control over the chiral extrapolation, resulting in much improved continuum predictions for the above quantities. The main results of this analysis include the pion and kaon decay constants, fπ=127(3)stat(3) sys MeV and fK=152(3)stat(2)sys MeV respectively (fK/fπ=1.199(12)stat(14) sys); the average up/down quark mass and the strange-quark mass in the MS̄-scheme at 3 GeV, mud(MS̄,3 GeV)=3.05(8) stat(6)sys MeV and ms(MS̄,3 GeV)=83.5(1.7)stat(1.1)sys; the neutral kaon mixing parameter in the MS̄-scheme at 3 GeV, BK(MS̄,3 GeV)=0.535(8)stat(13)sys, and in the RGI scheme, B ^K=0.758(11)stat(19)sys; and the Sommer scales r1=0.323(8)stat(4)sys fm and r 0=0.480(10)stat(4)sys (r1/r 0=0.673(11)stat(3)sys). We also obtain values for the SU(2) chiral perturbation theory effective couplings, l 3̄=2.91(23)stat(7)sys and l 4̄=3.99(16)stat(9)sys. © 2013 American Physical Society.R. Arthur, T. Blum, P. A. Boyle, N. H. Christ, N. Garron, R. J. Hudspith, T. Izubuchi, C. Jung, C. Kelly, A. T. Lytle, R. D. Mawhinney, D. Murphy, S. Ohta (太田滋生), C. T. Sachrajda, A. Soni, J. Yu, and J. M. Zanotti (RBC and UKQCD Collaborations

Perturbative Approach to Flat Chern Bands in the Hofstadter Model

We present a perturbative approach to the study of the Hofstadter model for when the amount of flux per plaquette is close to a rational fraction. Within this approximation certain eigenstates of the system are shown to be multi-component wavefunctions that connect smoothly to the Landau levels of the continuum. The perturbative corrections to these are higher Landau level contributions that break rotational invariance and allow the perturbed states to adopt the symmetry of the lattice. In the presence of interactions, this approach allows for the calculation of generalised Haldane pseudopotentials, and in turn, the many-body properties of the system. The method is sufficiently general that it can apply to a wide variety of lattices, interactions and magnetic field strengths.Comment: 40 pages, 15 figures; v2 includes minor changes, additional references and an expanded background sectio

Monitoring quantum Otto engines

Unlike classical systems, a measurement performed on a quantum system always alters its state. In this work, the impacts of two diagnostic schemes to determine the performance of quantum Otto heat engines are compared: In one scheme, the energy of the engine's working substance is measured after each stroke (repeated measurements), and in the other one, the energies after each stroke are recorded in one or two pointer states and measured only after the completion of a prescribed number of cycles (repeated contacts). A single pointer state suffices if one is only interested in either work or heat. For joint work and heat diagnostics, two pointers are needed. These schemes are applied to Otto engines, whose working substance consists of a two-level system. Depending on the engine protocol, the duration of a single cycle may be infinite or finite. Because in the repeated contact scheme, the number of measurements is drastically reduced compared to the repeated measurement scheme, the quantum coherence after and during the contact diagnostics is much better maintained than repeated measurements that destroy any coherence at the end of each stroke. We demonstrate that maximum power, reliability, and efficiency of the engine in the presence of repeated contacts typically outperform these figures of merit of repeated measurements. Due to the improved coherence persistence, heat engines with a finite cycle duration require a larger number of cycles to reach a periodically asymptotic state. Overall, our results document the importance of taking into account the particular nature of diagnostic tools for monitoring and testing purposes but also for feedback control, both in theory and experiment.Comment: 21 pages and 6 figures. Comments are welcom

Nucleation of Ergodicity by a Single Mobile Impurity in Supercooled Insulators

We consider a disordered Hubbard model and show that, at sufficiently weak disorder, a single spin-down mobile impurity can thermalize an extensive initially localized system of spin-up particles. Thermalization is enabled by resonant processes that involve correlated hops of the impurity and localized particles. This effect indicates that Anderson localized insulators behave as “supercooled” systems, with mobile impurities acting as ergodic seeds. We provide analytical estimates, supported by numerical exact diagonalization, showing how the critical disorder strength for such mechanism depends on the particle density of the localized system. In the U→∞ limit, doublons are stable excitations, and they can thermalize mesoscopic systems by a similar mechanism. The emergence of an additional conservation law leads to an eventual localization of doublons. Our predictions apply to fermionic and bosonic systems and are readily accessible in ongoing experiments simulating synthetic quantum lattices with tunable disorder

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