High Energy Physics - Lattice

We compute the matrix elements of the energy-momentum tensor of the nucleon using four ensembles of twisted mass clover-improved fermions with the up, down, strange and charm quark masses tuned to approximately their physical values. The four ensembles have similar physical volume and lattice spacings $a=0.080$~fm, $0.068$~fm, $0.057$~fm, and $0.049$ fm, allowing us to take the continuum limit directly at the physical pion mass point. We compute both connected and disconnected quark contributions as well as gluon contributions. All renormalization functions, including the mixing of the quark singlet with the gluon, are determined non-perturbatively. We extract the gravitational form factors in the continuum limit at $Q^2=0$ and evaluate the contribution of quarks and gluons to the momentum and angular momentum of the proton. Using the values of the intrinsic quark spin computed using the same gauge ensembles we also determine the orbital angular momentum for each quark flavor.

We analyze confinement and screening in single-flavor quantum electrodynamics (QED$_2$) on two-dimensional anti-de Sitter space (AdS$_2$), with and without a Schwarzschild black hole, both in the continuum and on the lattice. The theory is formulated in two frames adapted to distinct choices of a preferred time coordinate: the Schwarzschild frame, associated with the Boulware vacuum, and the global AdS$_2$ frame, associated with the $\mathrm{SL}(2,\mathbb{R})$-invariant vacuum. In the massless limit, the static potential between an external charge-anticharge pair is obtained in closed form by bosonization, at both zero and finite temperature. After subtraction of the position-dependent probe self-energies, which, unlike in flat space, are not constant, the potential remains finite as the geodesic separation is taken to infinity, establishing that the theory is screened. This is consistent with the explicit breaking of the $\mathrm{U}(1)$ electric one-form symmetry by the dynamical fermions, and resolves a confining/screening ambiguity in earlier treatments that identify the static potential with the unsubtracted ground-state energy. To validate the continuum analysis, we propose a covariant discretization scheme for placing fermions in curved spacetime on the lattice while ensuring that the continuum properties of the spin and gauge connections are restored in the continuum limit. This construction resolves ambiguities in the existing literature on lattice fermions in curved backgrounds and provides the foundation for our tensor-network simulations. Using a matrix product state ansatz, we confirm our analytical predictions for the phase diagram in AdS$_2$. We perform extensive numerical simulations of the static potential and the electric flux-tube profile for varying fermion masses, which we match to the continuum prediction.

We study dynamics of an interacting theory of a real singlet scalar and an $SU(2)$ symmetry preserving complex doublet scalar fields using lattice simulations over a broad region of the parameter space. The model contains all $SU(2)$-preserving quartic and a real singlet-$SU(2)$ invariant doublet field Yukawa interactions. The field propagators and the Yukawa vertex are the central structures for the study. We complement the study by implementing machine learning routines to the correlation functions in order to probe the underlying physics. The model reveals the role of nonperturbative effects in terms of infrared enhanced field propagators with a stable amputated Yukawa vertex, and a continuum-like scaling window in the parameter space with large regulator. The ultraviolet effects are visible in terms of an scaling structure appearing in a composite operator of mixed scalar interactions and the singlet expectation value.

In this paper, we apply the deterministic quantum imaginary time evolution (QITE) algorithm to obtain the ground state of a $2+1$-dimensional pure $\mathbb{Z}_2$ lattice gauge theory. We first construct the set of Pauli operators commuting with Gauss's law constraints, generalizing a previous result. This makes the deterministic QITE gauge-invariant and reduces both the measurement and gate costs significantly without adding extra algorithm errors in the QITE. Then, the classical numerical simulation of the deterministic QITE using tensor networks is performed, and the results are compared with the density matrix renormalization group (DMRG) to evaluate the accuracy of the algorithm. Specifically, we investigate the coupling and system size dependence, and find that the deterministic QITE can achieve a relative error of less than $0.1\%$ up to a twelve-plaquette system and coupling values in a regime that we study. Furthermore, the error dependence on the number of time steps is studied and discussed.

Nucleon-nucleon systems in the $^3S_1$ and the $^1S_0$ channels are studied in lattice quantum chromodynamics at a pion mass of approximately $m_{\pi}\approx292$ MeV, employing three $N_f = 2+1$ ensembles with the same pion mass and lattice spacing $a=0.10530(18)$ fm but different spatial volumes. Finite-volume energies of the nucleon-nucleon systems are determined in both the rest frame and a moving frame. The distillation quark smearing method is applied to improve the precision and to ensure the symmetric correlators by using the same interpolating operators at sink and source. The scattering amplitudes are extracted from the finite-volume spectra using the Lüscher's finite-volume method. At the studied pion mass, both the $^3S_1$ (deuteron) and $^1S_0$(di-neutron) channels exhibit a virtual state pole, with binding energies of $6^{+5}_{-3}$ MeV and $11^{+6}_{-5}$ MeV, respectively. To investigate the effects of the left-hand cut, an alternative method -- the Non-Perturbative Hamiltonian framework (NPHF) -- is used for the scattering analysis and yields consistent results with those from the Lüscher method.