A numerical study of the 2-flavour Schwinger model with dynamical overlap hypercube fermions

Abstract

We present numerical results for the 2-flavour Schwinger model with dynamical chiral lattice fermions. We insert an approximately chiral hypercube Dirac operator into the overlap formula to construct the overlap hypercube operator. This is an exact solution to the Ginsparg-Wilson relation, with an excellent level of locality and scaling. Due to its similarity with the hypercubic kernel, a low polynomial in this kernel provides a numerically efficient Hybrid Monte Carlo force. We measure the microscopic Dirac spectrum and discuss the corresponding scale-invariant parameter, which takes a surprising form. This is an interesting case, since Random Matrix Theory is unexplored for this setting, where the chiral condensate Σ vanishes in the chiral limit. We also measure Σ and the "pion" mass, in distinct topological sectors. In this context we discuss and probe the topological summation of observables by various methods, as well as the evaluation of the topological susceptibility. The feasibility of this summation is essential for the prospects of dynamical overlap fermions in QCD.1

Berezinskii–Kosterlitz–Thouless transition with a constraint lattice action

“…This property was confirmed explicitly on the lattice for QCD [39] and for the Schwinger model [40].…”

Bosonic partition functions at nonzero (imaginary) chemical potential

“…At the mean field level, the free energy of the phase-quenched partition function only depends on N f through an overal multiplicative factor. So we have that 4) and the mean field result for the one-flavor bosonic partition function factorizes as 5) where Z N f =1+1 * (µ) (also denoted by Z 1+1 * /0 (µ)) is the phase quenched partition function, or equivalently, the product of the same one flavor partition function and the bosonic phase quenched partition function (see eq. (3.17)).…”

“…Because this agreement is based on the spontaneous breaking of the flavor symmetry, one would expect that, as a consequence of the Coleman-Mermin-Wagner theorem, the agreement with Random Matrix Theory in two dimensions is structurally different from the agreement found in four dimensions. Yet this is not the case [4][5][6][7][8]. The picture that emerges from the two-flavor massless Schwinger model [4][5][6]9], is that the low-lying eigenvalues are correlated according to chiral Random Matrix Theory while the chiral condensate defined in the usual way vanishes.…”

Topological susceptibility from slabs

“…However, even at |Q| ≤ 1 the finite size effects are highly persistent. In fact, other methods and formulae show that these effects are only suppressed by a power series in 1/V for topologically fixed measurements [6][7][8][9][10][11][12].…”

“…Recently, several indirect methods to measure χ t nevertheless have been suggested and tested [6][7][8][9][10][11][12]. Here we address a different approach for this purpose, which was first sketched in ref.…”