Real-time lattice gauge theory actions: unitarity, convergence, and path integral contour deformations

Abstract

The Wilson action for Euclidean lattice gauge theory defines a positive-definite transfer matrix that corresponds to a unitary lattice gauge theory time-evolution operator if analytically continued to real time. Hoshina, Fujii, and Kikukawa (HFK) recently pointed out that applying the Wilson action discretization to continuum real-time gauge theory does not lead to this, or any other, unitary theory and proposed an alternate real-time lattice gauge theory action that does result in a unitary real-time transfer matrix. The character expansion defining the HFK action is divergent, and in this work we apply a path integral contour deformation to obtain a convergent representation for U (1) HFK path integrals suitable for numerical Monte Carlo calculations. We also introduce a class of real-time lattice gauge theory actions based on analytic continuation of the Euclidean heatkernel action. Similar divergent sums are involved in defining these actions, but for one action in this class this divergence takes a particularly simple form, allowing construction of a path integral contour deformation that provides absolutely convergent representations for U (1) and SU (N ) realtime lattice gauge theory path integrals. We perform proof-of-principle Monte Carlo calculations of real-time U (1) and SU (3) lattice gauge theory and verify that exact results for unitary time evolution of static quark-antiquark pairs in (1 + 1)D are reproduced.

Quantum algorithms for transport coefficients in gauge theories

“…( 19) flipped. This section can be formulated in metric with no difference provided the Hamiltonian limit is taken [94]; we have chosen Minkowski to preserve a more straightforward correspondence with the quantum simulation.…”

Lattice Renormalization of Quantum Simulations

“…( 1) leads to a non-trivial dependence on δ τ . This causes a non-Hermitian Hamiltonian upon analytic continuation [172] although this behavior may prove manageable [130]. In contrast, using an action with a heat-kernel kinetic term (the Laplace-Beltrami operator) [173] with a Wilson single plaquette potential term, the higher order ω terms vanish and the mapping is exact.…”

Towards sampling complex actions

“…In many physical theories, the measure exp(−S(φ)) turns out to be complex. Besides real-time dynamics [6][7][8][9], this is, for example, the case for the Hubbard model [10][11][12][13][14][15], for spin-or mass-imbalanced systems [16][17][18][19][20] and graphene [21][22][23] or for quantum chromo-dynamics at finite density [24][25][26][27][28][29][30][31][32][33][34][35]. In these theories, the fermionic part of the system contributes a multiplicative fermion determinant to the path integral measure in Eq.…”