Lattice QCD at Strong Coupling
Final Report Abstract
Within the funding period, the important goals dened in the proposal have been achieved. The world-line representation of lattice QCD for staggered fermions based on a set of integer (dual) variables has been formulated and Monte Carlo simulations, combining a Worm algorithm with plaquette updates have been successfully implemented and tested. In the strong coupling regime, we investigated the µB-T phase diagram, the equation of state and the nuclear potential. In order to do so unambiguously, it was necessary to determine the anisotropy ξ = a/at (that is needed to vary the temperature at xed lattice spacing) in a non-perturbative way to improve on the previously used Meaneld denitions. This improved scheme corrected the critical line Tc (µ) by about 20%. We have also determined ξ as a function of the quark mass and β. The sign problem in the dual representation turns out to become severe for β > 1. We investigated how this plaquette-induced sign problem can be made milder by considering another basis for the link states, based on a resummation of invariants via so-called decoupling operators into tensor networks. These have been computed up to O(β6 ). We developed further the Hamiltonian formulation in the continuous time limit. This gives rise to Quantum Monte Carlo, the corresponding Worm algorithm in the continuous time limit makes use of creation and annihilation operators. It has been implemented and used to investigate mesonic temporal correlators to extract pole masses as a function of temperature. We have measured the grand-canonical and canonical phase diagram via the Wang-Landau method. We measured Taylor coecients in terms of dual variables up to O((µ B /T )12 ) at zero chemical potential and found that the radius of convergence agreed suciently with the phase boundary. We have also derived the Hamiltonian of the 2-avor dual formulation, which gives more insight in the nature of nuclear interactions based on pion exchange. Following the ideas of the 3-dimensional Polyakov effective theory for Wilson fermions that is under investigation, we have made progress in the formulation of a 3-dimensional effective theory for staggered fermions, which we can study analytically via a linked cluster expansion. There are still many open questions that can be addressed via the strong coupling expansion of lattice QCD. Extensions to larger β via a character expansion (highly non-trivial with dynamical fermions) could provide strong hints that the critical end-point also exists in the continuum limit. We investigate how machine learning can help to evaluate the tensor networks in corresponding Monte Carlo simulations.
Publications
- Quark Mass Dependence of the QCD Critical End Point in the Strong Coupling Limit contribution to the lattice conference 2016, PoS LATTICE 2016 (2017) 035
J. Kim and W. Unger
- Thermodynamics of Strongly-Coupled Lattice QCD in the Chiral Limit contribution to the lattice conference 2016, PoS LATTICE 2016 (2017) 086
P. de Forcrand, P. Romatschke, W. Unger, and H. Vairinhos
- Dual Formulation and Phase Diagram of Lattice QCD in the Strong Coupling Regime. Web of Conferences, 175 (2018) 07047
G. Gagliardi, J. Kim, and W. Unger
(See online at https://doi.org/10.1051/epjconf/201817507047) - Strong-coupling lattice QCD on anisotropic lattices. Phys. Rev. D 97 (2018) 034512
P. de Forcrand, W. Unger, and H. Vairinhos
(See online at https://doi.org/10.1103/PhysRevD.97.034512) - Temporal Correlators in the Continuous Time Formulation of Strong Coupling Lattice QCD contribution to the lattice conference 2018, PoS LATTICE 2018 (2018) 182
M. Klegrewe and W. Unger
- Thermodynamics at Strong Coupling on Anisotropic Lattices contribution to the lattice conference 2018, PoS LATTICE 2018 (2018) 181
D. Bollweg, M. Klegrewe, and W. Unger
- Towards a Dual Representation of Lattice QCD contribution to the lattice conference 2018, PoS LATTICE 2018 (2018) 224
G. Gagliardi and W. Unger
- On the β- and Quark Mass Dependence of the Nuclear Transition in the Strong Coupling Regime contribution to the lattice conference 2019, PoS LATTICE 2019 (2020) 210
J. Kim, O. Philipsen, and W. Unger
- Gauge Corrections to Strong Coupling LQCD on Anisotropic Lattices contribution to the lattice conference 2019, PoS LATTICE 2019 (2020) 210
M. Klegrewe, J. Kim, and W. Unger
- New Dual Representation for Staggered Lattice QCD. Phys. Rev. D 101 (2020) 034509
G. Gagliardi and W. Unger
(See online at https://doi.org/10.1103/PhysRevD.101.034509) - Strong Coupling Lattice QCD in the Continuous Time Limit. Phys. Rev. D 102 (2020) 034505
M. Klegrewe and W. Unger
(See online at https://doi.org/10.1103/PhysRevD.102.034505)
