Quantum Monte Carlo with QuantumField Monte Carlo Interactions with Chiral Effective Theory Chiral Effective Field Theory Interactions From matter to nuclei Alexandros Gezerlis ECT*-EMMI Workshop Neutron-Rich Matter and Neutron Stars Trento, Italy October 1, 2013
Key Point: Quantum Monte Carlo with Chiral Effective Field Theory Interactions From matter to nuclei
Thanks to my collaborators Joe Carlson (LANL) Joel Lynn (LANL) Evgeny Epelbaum (Bochum) Andreas Nogga (Juelich) Stefano Gandolfi (LANL) Achim Schwenk (Darmstadt) Kai Hebeler (OSU) Ingo Tews (Darmstadt)
(My) equation of state goals Start at low density, where the interaction is pretty standard and find experimental constraints Move to higher density by systematizing our ignorance Graduate to finite nuclei, using the same input concepts
(My) equation of state goals Start at low density, where the interaction is pretty standard and find experimental constraints DMC: Diffusion Monte Carlo (frozen spins) Move to higher density by systematizing our ignorance AFDMC: Auxiliary-Field Diffusion Monte Carlo (spins treated stochastically) Graduate to finite nuclei, using the same input concepts GFMC: nuclear Green's Function Monte Carlo (spins treated explicitly)
Continuum Quantum Monte Carlo Rudiments of Diffusion Monte Carlo:
Continuum Quantum Monte Carlo Rudiments of Diffusion Monte Carlo: Some complications for spin-dependent interactions (hanc marginis exiguitas non caperet)
Start at low densities Simple interaction, rich physics
Connection between the two Neutron matter Cold atoms MeV scale O(1057) neutrons pev scale O(10) or O(105) atoms Credit:UniversityofColorado Very similar Weak to intermediate to strong coupling
Fermionic dictionary Energy of a free Fermi gas: Fermi energy: Fermi wave number: Number density: Scattering length:
Fermionic dictionary Energy of a free Fermi gas: Fermi energy: Fermi wave number: Number density: Scattering length: In what follows, the dimensionless quantity is called the coupling
Pairing gaps: results Results identical at low density Range important at high density Two independent MIT experiments at unitarity NEUTRONS ATOMS A. Gezerlis and J. Carlson, Phys. Rev. C 77, 032801 (2008)
Pairing gaps: comparison Consistent suppression with respect to BCS; similar to Gorkov Disagreement with AFDMC studied extensively Emerging consensus NEUTRONS A. Gezerlis and J. Carlson, Phys. Rev. C 81, 025803 (2010)
The meaning of it all Neutron-star crust consequences Negligible contribution to specific heat consistent with cooling of transients: E. F. Brown and A. Cumming. Astrophys. J. 698, 1020 (2009). Young neutron star cooling curves depend on the magnitude of the gap: D. Page, J. M. Lattimer, M. Prakash, A. W. Steiner, Astrophys. J. 707, 1131 (2009). Superfluid-phonon heat conduction mechanism viable: D. Aguilera, V. Cirigliano, J. Pons, S. Reddy, R. Sharma, Phys. Rev. Lett. 102, 091101 (2009). V. Cirigliano, S. Reddy, R. Sharma, Phys. Rev. C 84, 045809 (2011). Constraints for Skyrme-HFB calculations of neutron-rich nuclei: N. Chamel, S. Goriely, and J. M. Pearson, Nucl. Phys. A 812, 27 (2008).
Now turn to larger densities
Nuclear potentials Local high-quality phenomenology is hard
Nuclear potentials Local high-quality phenomenology is hard Consubstantial with the successes of nuclear QMC, difficult to use in most other many-body methods
Nuclear potentials Local high-quality phenomenology is hard Consubstantial with the successes of nuclear QMC, difficult to use in most other many-body methods Chiral EFT a) is connected to symmetries of QCD b) has consistent many-body forces, and c) allows us to produce systematic uncertainty bands also happens to be non-local (such are the sumbebekota)
Nuclear potentials Local high-quality phenomenology is hard Consubstantial with the successes of nuclear QMC, difficult to use in most other many-body methods Chiral EFT a) is connected to symmetries of QCD b) has consistent many-body forces, and c) allows us to produce systematic uncertainty bands also happens to be non-local (such are the sumbebekota) Heavily used in other methods, but not used in nuclear QMC
Nuclear Hamiltonian: chiral EFT Long-studied two-pion exchange Contains couplings from πn scattering Regulatoranddictionary:
What is more Successful nuclear QMC program constrained to use local potentials as input. What does local mean?
What is more Successful nuclear QMC program constrained to use local potentials as input. What does local mean? In particle physics: potential is defined at one point in space-time (contact)
What is more Successful nuclear QMC program constrained to use local potentials as input. What does local mean? In particle physics: potential is defined at one point in space-time (contact) In nuclear physics: which is equivalent to
What is more Successful nuclear QMC program constrained to use local potentials as input. What does local mean? In particle physics: potential is defined at one point in space-time (contact) In nuclear physics: which is equivalent to Reminder: in our terminology local is function of only
Local chiral EFT Combine power of Quantum Monte Carlo with consistency of chiral Effective Field Theory Write down a local energy-independent NN potential Use local pion-exchange regulator cf.
Local chiral EFT Combine power of Quantum Monte Carlo with consistency of chiral Effective Field Theory Write down a local energy-independent NN potential Use local pion-exchange regulator Pick 7 different contacts at NLO, just make sure that when antisymmetrized they lead to a set obeying the required symmetry principles cf.
Chiral EFT in QMC Use Auxiliary-Field Diffusion Monte Carlo to handle the full interaction First ever non-perturbative systematic error bands Band sizes to be expected Many-body forces will emerge systematically NEUTRONS A. Gezerlis, I. Tews, E. Epelbaum, S. Gandolfi, K. Hebeler, A. Nogga, A. Schwenk, Phys. Rev. Lett. 111, 032501 (2013).
Chiral EFT in lattice QMC Complementary Quantum Monte Carlo approach that has already been using chiral EFT forces Preliminary results NEUTRONS Dean Lee/nuclear lattice EFT collaboration
QMC vs MBPT Comparison with manybody perturbation approach MBPT bands come from diff. single-particle spectra Soft potential in excellent agreement with AFDMC Hard potential slower to converge NEUTRONS A. Gezerlis, I. Tews, E. Epelbaum, S. Gandolfi, K. Hebeler, A. Nogga, A. Schwenk, Phys. Rev. Lett. 111, 032501 (2013).
Newer results e Pr New, better fits to higher energies Spectral-function regularization cutoff (kept fixed before) now varied Clearly shows lack of dependence ry a in m li NEUTRONS
Newer results Comparison with many-body perturbation approach Once again, soft potential is nearly identical to AFDMC Once again, SFR cutoff does not matter ry a in m eli r P NEUTRONS
Finally, turn to finite nuclei
Phenomenological Hamiltonian Green's Function Monte Carlo is a very accurate method Credit:StevePieper
New results with chiral forces e Pr Binding energy of 4He First-ever non-perturbative systematic error bands All results are strong force + Coulomb, no NNN ry a in m li NUCLEONS
New results with chiral forces Two-nucleon densities in 4He Appropriately normalized: Quantifies softness of potential ry a in m eli r P NUCLEONS
New results with chiral forces One-nucleon densities in 4He Defined from the center of mass Indistinguishable beyond 1 fm ry a in m eli r P NUCLEONS
Conclusions Chiral EFT can now be used in continuum Quantum Monte Carlo methods (matter and nuclei) The perturbativeness of different orders can be directly tested Non-perturbative systematic error bands can be produced
Conclusions Chiral EFT can now be used in continuum Quantum Monte Carlo methods (matter and nuclei) The perturbativeness of different orders can be directly tested Non-perturbative systematic error bands can be produced Jt is ywrite that every thing Hymself sheweth in the tastyng