A numerical study of partially twisted boundary conditions

Abstract

We investigate the use of partially twisted boundary conditions in a lattice simulation with two degenerate flavours of improved Wilson sea quarks. The use of twisted boundary conditions on a cubic volume (L 3 ) gives access to components of hadronic momenta other than integer multiples of 2π/L. Partial twisting avoids the need for new gluon configurations for every choice of momentum, while, as recently demonstrated, keeping the finite-volume errors exponentially small for the physical quantities investigated in this letter. In this study we focus on the spectrum of pseudo scalar and vector mesons, on their leptonic decay constants and on Z P , the matrix element of the pseudo scalar density between the pseudo scalar meson and the vacuum. The results confirm the momentum shift imposed by these boundary conditions and in addition demonstrate that they do not introduce any appreciable noise. We therefore advocate the use of partially twisted boundary conditions in applications where good momentum resolution is necessary.

Quark disconnected diagrams in chiral perturbation theory

“…While having applications to lattice QCD in mind, reference to this regularisation is only made where we think that it helps the better understanding of our arguments. We will discuss however the finite volume case in order to show how this technique allows for using partial twisting [9][10][11][12][13][14] also for form-factors and polarisations involving flavour-diagonal operators.…”

“…Partially twisted boundary conditions for the VP: Partially twisted boundary conditions [9][10][11][12][13][14] by now have become a standard tool in lattice hadron phenomenology. For the boundary condition q i (x k + L) = e iθ k,i q i (x) for the valence quark-flavours q 1 and q 2 of a pseudo-scalar meson of mass m in a finite lattice of spatial extent L, the dispersion relation takes the form [9,12,14], which shows how the periodicity of the fermionic fields can be modified in order to induce spacial momentum to hadrons.…”

“…For the boundary condition q i (x k + L) = e iθ k,i q i (x) for the valence quark-flavours q 1 and q 2 of a pseudo-scalar meson of mass m in a finite lattice of spatial extent L, the dispersion relation takes the form [9,12,14], which shows how the periodicity of the fermionic fields can be modified in order to induce spacial momentum to hadrons. Besides an exponentially suppressed and computable finite size effect the choice of quark-field boundary conditions for processes with only one initial and/or final hadron state introduces no further systematics [9].…”

Strong interaction effects at a Fermi surface in a model for voltage-biased bilayer graphene

“…Naively this would entail making at least one of the spatial dimensions of the lattice as large as possible [13]. It is much more efficient, however, to employ partially twisted boundary conditions [14] in which the constraint ψ(L x ) = e iθ x ψ(0), with the angle θ x adjustable, is implemented in the calculation of the propagator (11) so that accessible modes have…”

“…The same trends with both k and j are observed at larger μ. Figure 2 shows results from fits to the dispersion E(k) for various μ at jã = 0.01 from (14) and (15) feature is that E(k) is nonmonotonic with a minimum in the neighborhood where the amplitude ratio A/B ≈ 1, which we have identified as the Fermi momentum k F . For k < k F quasiparticle excitations are holelike, and the energy needed to excite them from the ground state decreases as k k F .…”