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Register a new userPade - Z$_2$ Estimator of Determinants
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We introduce the Pade--Z$_2$ (PZ) stochastic estimator for calculating determinants and determinant ratios. The estimator is applied to the calculation of fermion determinants from the two ends of the Hybrid Monte Carlo trajectories with pseudofermions. Our results on the $8^3 times 12$ lattice with Wilson action show that the statistical errors from the stochastic estimator can be reduced by more than an order of magnitude by employing an unbiased variational subtraction scheme which utilizes the off-diagonal matrices from the hopping expansion. Having been able to reduce the error of the determinant ratios to about 20 % with a relatively small number of noise vectors, this may become a feasible algorithm for simulating dynamical fermions in full QCD. We also discuss the application to the density of states in Hamiltonian systems.
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We perform a digital pseudoquantum simulation of $mathbb{Z}_2$ gauge Higgs model on a $3times 3$ lattice. First we propose the quantum algorithm for the digital quantum simulation, based on Trotter decomposition, quantum adiabatic algorithm and its circuit realization. Then we classically demonstrate it in a GPU simulator, obtaining useful results, which indicate the topological properties of deconfined phase and clarify the phase diagram. Especially, our work suggests that the tricitical point, where the two critical lines of second-order transitions meet, lies on the critical line of the first-order transition rather than its end.
Using a dimensional reduction formula for the lattice fermion determinant we study canonical determinants on quenched SU(3) gauge configurations. The canonical determinants decribe a fixed quark number and we analyze their properties below and above the transition temperature. We find that above $T_c$ the signatures of center symmetry breaking are very strongly manifest in the distribution of the canonical determinants in the complex plane, and we discuss possible physical implications of this finding. We furthermore analyze the relative weight of the different quark sectors below and above the transition temperature.
We propose a novel Bayesian method to analytically continue observables to real baryochemical potential $mu_B$ in finite density QCD. Taylor coefficients at $mu_B=0$ and data at imaginary chemical potential $mu_B^I$ are treated on equal footing. We consider two different constructions for the Pade approximants, the classical multipoint Pade approximation and a mixed approximation that is a slight generalization of a recent idea in Pade approximation theory. Approximants with spurious poles are excluded from the analysis. As an application, we perform a joint analysis of the available continuum extrapolated lattice data for both pseudocritical temperature $T_c$ at $mu_B^I$ from the Wuppertal-Budapest Collaboration and Taylor coefficients $kappa_2$ and $kappa_4$ from the HotQCD Collaboration. An apparent convergence of $[p/p]$ and $[p/p+1]$ sequences of rational functions is observed with increasing $p.$ We present our extrapolation up to $mu_Bapprox 600$ MeV.
In this paper we study thermodynamic properties of dense cold $SU(2)$ QCD within lattice simulation with dynamical rooted staggered quarks which in the continuum limit correspond to $N_f=2$ quark flavours. We calculate baryon density, renormalized chiral and diquark condensates for various baryon chemical potentials in the region $mu in (0,,2000)$ MeV. It is found, that in the region $mu in (0,,540)$ MeV the system is well described by the ChPT predictions. In the region $mu > 540$ MeV the system becomes sufficiently dense and ChPT is no longer applicable to describe lattice data. For chemical potentials $mu > 900$ MeV we observe formation of the Fermi sphere, and the system is similar to the one described by the Bardeen-Cooper-Schrieffer theory where the the diquarks play a role of Cooper pairs. In order to study how nonzero baryon density influences the gluon background we calculate chromoelectric and chromomagnetic fields, as well as the topological susceptibility. We find that the chromoelectric field and the topological susceptibility decrease, whereas the chromomagnetic field increases with rising of baryon chemical potential. Finally we study the equation of state of dense two-color quark matter.
A large class of two dimensional quantum gravity theories of Jackiw-Teitelboim form have a description in terms of random matrix models. Such models, treated fully non-perturbatively, can give an explicit and tractable description of the underlying ``microstate degrees of freedom. They play a prominent role in regimes where the smooth geometrical picture of the physics is inadequate. This is shown using a natural tool for extracting the detailed microstate physics, a Fredholm determinant ${rm det}(mathbf{1}{-}mathbf{ K})$. Its associated kernel $K(E,E^prime)$ can be defined explicitly for a wide variety of JT gravity theories. To illustrate the methods, the statistics of the first several energy levels of a non-perturbative definition of JT gravity are constructed explicitly using numerical methods, and the full quenched free energy $F_Q(T)$ of the system is computed for the first time. These results are also of relevance to quantum properties of black holes in higher dimensions.
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