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With advances in quantum computing, new opportunities arise to tackle challenging calculations in quantum field theory. We show that trotterized time-evolution operators can be related by analytic continuation to the Euclidean transfer matrix on an anisotropic lattice. In turn, trotterization entails renormalization of the temporal and spatial lattice spacings. Based on the tools of Euclidean lattice field theory, we propose two schemes to determine Minkowski lattice spacings, using Euclidean data and thereby overcoming the demands on quantum resources for scale setting. In addition, we advocate using a fixed-anisotropy approach to the continuum to reduce both circuit depth and number of independent simulations. We demonstrate these methods with Qiskit noiseless simulators for a $2+1$D discrete non-Abelian $D_4$ gauge theory with two spatial plaquettes.
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Quantum technologies offer the prospect to efficiently simulate sign-problem afflicted regimes in lattice field theory, such as the presence of topological terms, chemical potentials, and out-of-equilibrium dynamics. In this work, we derive the 3+1D topological $theta$-term for Abelian and non-Abelian lattice gauge theories in the Hamiltonian formulation, paving the way towards Hamiltonian-based simulations of such terms on quantum and classical computers. We further study numerically the zero-temperature phase structure of a 3+1D U(1) lattice gauge theory with the $theta$-term via exact diagonalization for a single periodic cube. In the strong coupling regime, our results suggest the occurrence of a phase transition at constant values of $theta$, as indicated by an avoided level-crossing and abrupt changes in the plaquette expectation value, the electric energy density, and the topological charge density. These results could in principle be cross-checked by the recently developed 3+1D tensor network methods and quantum simulations, once sufficient resources become available.
Recent developments in non-perturbative renormalization for lattice QCD are reviewed with a particular emphasis on RI/MOM scheme and its variants, RI/SMOM schemes. Summary of recent developments in Schroedinger functional scheme, as well as the summary of related topics are presented. Comparison of strong coupling constant and the strange quark mass from various methods are made.
Many non-Hermitian but PT-symmetric theories are known to have a real positive spectrum. Since the action is complex for there theories, Monte Carlo methods do not apply. In this paper the first field-theoretic method for numerical simulations of PT-symmetric Hamiltonians is presented. The method is the complex Langevin equation, which has been used previously to study complex Hamiltonians in statistical physics and in Minkowski space. We compute the equal-time one-point and two-point Greens functions in zero and one dimension, where comparisons to known results can be made. The method should also be applicable in four-dimensional space-time. Our approach may also give insight into how to formulate a probabilistic interpretation of PT-symmetric theories.
The Fermilab Lattice and MILC collaborations have shown in one-loop lattice QCD perturbation theory that the renormalization constants of vector and axial-vector mixed clover-asqtad currents are closely related to the product of those for clover-clover and asqtad-asqtad (local) vector currents. To be useful for future higher precision calculations this relationship must be valid beyond one-loop and very general. We test its validity nonperturbatively using clover and Highly Improved Staggered (HISQ) strange quarks, utilising the absolute normalization of the HISQ temporal axial current. We find that the renormalization of the mixed current differs from the square root of the product of the pure HISQ and pure clover currents by $2-3%$. We also compare discretization errors between the clover and HISQ formalisms.
We have technically improved the non-perturbative renormalization method, proposed by Martinelli et al., by using quark momentum sources and sinks. Composite two-fermion operators up to three derivatives have been measured for Wilson fermions and Sheikholeslami-Wohlert improved fermions in the quenched approximation. The calculations are performed in the Landau gauge on 16^3x32 lattices at beta = 6.0 for 3 kappa values in each case. The improved sources greatly decrease the statistical noise. We extract and discuss here renormalization factors for local operators and moments of the structure functions for Wilson fermions.
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