# Impurity lattice Monte Carlo for hypernuclei

## Abstract

Abstract We consider the problem of including $$\varLambda $$ $\Lambda $ hyperons into the ab initio framework of nuclear lattice effective field theory. In order to avoid large sign oscillations in Monte Carlo simulations, we make use of the fact that the number of hyperons is typically small compared to the number of nucleons in the hypernuclei of interest. This allows us to use the impurity lattice Monte Carlo method, where the minority species of fermions in the full nuclear Hamiltonian is integrated out and treated as a worldline in Euclidean projection time. The majority fermions (nucleons) are treated as explicit degrees of freedom, with their mutual interactions described by auxiliary fields. This is the first application of the impurity lattice Monte Carlo method to systems where the majority particles are interacting. Here, we show how the impurity Monte Carlo method can be applied to compute the binding energies of the light hypernuclei. In this exploratory work we use spin-independent nucleon–nucleon and hyperon–nucleon interactions to test the computational power of the method. We find that the computational effort scales approximately linearly in the number of nucleons. The results are very promising for future studies of larger hypernuclear systems using chiral effective field theory and realistic hyperon–nucleon interactions, as well as applications to other quantum many-body systems.

- Authors:

- Publication Date:

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1670510

- Grant/Contract Number:
- SC0018638

- Resource Type:
- Published Article

- Journal Name:
- European Physical Journal. A

- Additional Journal Information:
- Journal Name: European Physical Journal. A Journal Volume: 56 Journal Issue: 10; Journal ID: ISSN 1434-6001

- Publisher:
- Springer Science + Business Media

- Country of Publication:
- Germany

- Language:
- English

### Citation Formats

```
Frame, Dillon, Lähde, Timo A., Lee, Dean, and Meißner, Ulf-G. Impurity lattice Monte Carlo for hypernuclei. Germany: N. p., 2020.
Web. https://doi.org/10.1140/epja/s10050-020-00257-y.
```

```
Frame, Dillon, Lähde, Timo A., Lee, Dean, & Meißner, Ulf-G. Impurity lattice Monte Carlo for hypernuclei. Germany. https://doi.org/10.1140/epja/s10050-020-00257-y
```

```
Frame, Dillon, Lähde, Timo A., Lee, Dean, and Meißner, Ulf-G. Tue .
"Impurity lattice Monte Carlo for hypernuclei". Germany. https://doi.org/10.1140/epja/s10050-020-00257-y.
```

```
@article{osti_1670510,
```

title = {Impurity lattice Monte Carlo for hypernuclei},

author = {Frame, Dillon and Lähde, Timo A. and Lee, Dean and Meißner, Ulf-G.},

abstractNote = {Abstract We consider the problem of including $$\varLambda $$ Λ hyperons into the ab initio framework of nuclear lattice effective field theory. In order to avoid large sign oscillations in Monte Carlo simulations, we make use of the fact that the number of hyperons is typically small compared to the number of nucleons in the hypernuclei of interest. This allows us to use the impurity lattice Monte Carlo method, where the minority species of fermions in the full nuclear Hamiltonian is integrated out and treated as a worldline in Euclidean projection time. The majority fermions (nucleons) are treated as explicit degrees of freedom, with their mutual interactions described by auxiliary fields. This is the first application of the impurity lattice Monte Carlo method to systems where the majority particles are interacting. Here, we show how the impurity Monte Carlo method can be applied to compute the binding energies of the light hypernuclei. In this exploratory work we use spin-independent nucleon–nucleon and hyperon–nucleon interactions to test the computational power of the method. We find that the computational effort scales approximately linearly in the number of nucleons. The results are very promising for future studies of larger hypernuclear systems using chiral effective field theory and realistic hyperon–nucleon interactions, as well as applications to other quantum many-body systems.},

doi = {10.1140/epja/s10050-020-00257-y},

journal = {European Physical Journal. A},

number = 10,

volume = 56,

place = {Germany},

year = {2020},

month = {10}

}

https://doi.org/10.1140/epja/s10050-020-00257-y

Works referenced in this record:

##
Hyperon–nucleon interactions—a chiral effective field theory approach

journal, November 2006

- Polinder, Henk; Haidenbauer, Johann; Meißner, Ulf-G.
- Nuclear Physics A, Vol. 779

##
Baryon-baryon interactions and spin-flavor symmetry from lattice quantum chromodynamics

journal, December 2017

- Wagman, Michael L.; Winter, Frank; Chang, Emmanuel
- Physical Review D, Vol. 96, Issue 11

##
Resolving the $\mathrm{\Lambda}$ Hypernuclear Overbinding Problem in Pionless Effective Field Theory

journal, September 2018

- Contessi, L.; Barnea, N.; Gal, A.
- Physical Review Letters, Vol. 121, Issue 10

##
Structure of single-$$\varLambda $$Λ hypernuclei with chiral hyperon–nucleon potentials

journal, February 2020

- Haidenbauer, Johann; Vidaña, Isaac
- The European Physical Journal A, Vol. 56, Issue 2

##
The hypertriton in effective field theory

journal, July 2002

- Hammer, H. -W.
- Nuclear Physics A, Vol. 705, Issue 1-2

##
A framework for exploring the interactions and decays of hyperons with lattice QCD

journal, January 2005

- Beane, S. R.; Bedaque, P. F.; Parreño, A.
- Nuclear Physics A, Vol. 747, Issue 1

##
Light neutron-rich hypernuclei from the importance-truncated no-core shell model

journal, April 2018

- Wirth, Roland; Roth, Robert
- Physics Letters B, Vol. 779

##
On the Consequences of the Symmetry of the Nuclear Hamiltonian on the Spectroscopy of Nuclei

journal, January 1937

- Wigner, E.
- Physical Review, Vol. 51, Issue 2

##
Implications of an increased Λ-separation energy of the hypertriton

journal, February 2020

- Le, Hoai; Haidenbauer, Johann; Meißner, Ulf-G.
- Physics Letters B, Vol. 801

##
Nuclear Binding Near a Quantum Phase Transition

journal, September 2016

- Elhatisari, Serdar; Li, Ning; Rokash, Alexander
- Physical Review Letters, Vol. 117, Issue 13

##
Strangeness S = − 2 baryon–baryon interactions using chiral effective field theory

journal, September 2007

- Polinder, H.; Haidenbauer, J.; Meißner, U. -G.
- Physics Letters B, Vol. 653, Issue 1

##
Charge symmetry breaking in the A = 4 hypernuclei

journal, October 2016

- Gazda, Daniel; Gal, Avraham
- Nuclear Physics A, Vol. 954

##
A determination of the binding-energy values of light hypernuclei

journal, March 1968

- Bohm, G.; Klabuhn, J.; Krecker, U.
- Nuclear Physics B, Vol. 4, Issue 6

##
Hyperon–nucleon interaction at next-to-leading order in chiral effective field theory

journal, October 2013

- Haidenbauer, J.; Petschauer, S.; Kaiser, N.
- Nuclear Physics A, Vol. 915

##
A brief review of emulsion results on hypernuclei

conference, January 1991

- Davis, D. H.
- LAMPF workshop on (π, , AIP Conference Proceedings

##
Excited states of light hypernuclei

journal, January 1973

- Bamberger, A.; Faessler, M. A.; Lynen, U.
- Nuclear Physics B, Vol. 60

##
*Ab initio* Calculations of the Isotopic Dependence of Nuclear Clustering

journal, December 2017

- Elhatisari, Serdar; Epelbaum, Evgeny; Krebs, Hermann
- Physical Review Letters, Vol. 119, Issue 22

##
Neutron-proton scattering with lattice chiral effective field theory at next-to-next-to-next-to-leading order

journal, October 2018

- Li, Ning; Elhatisari, Serdar; Epelbaum, Evgeny
- Physical Review C, Vol. 98, Issue 4

##
Structure of *S* =−2 Hypernuclei and Hyperon–Hyperon Interactions

journal, October 2018

- Hiyama, Emiko; Nakazawa, Kazuma
- Annual Review of Nuclear and Particle Science, Vol. 68, Issue 1

##
The symmetric heavy-light ansatz

journal, February 2008

- Lee, D.
- The European Physical Journal A, Vol. 35, Issue 2

##
Further investigation of the γ-transitions in Λ4H and Λ4 hypernuclei

journal, May 1979

- Bedjidian, M.; Descroix, E.; Grossiord, J. Y.
- Physics Letters B, Vol. 83, Issue 2

##
A new determination of the binding-energy values of the light hypernuclei (A ⩽ 15)

journal, January 1973

- Jurič, M.; Bohm, G.; Klabuhn, J.
- Nuclear Physics B, Vol. 52, Issue 1

##
Lattice simulations for few- and many-body systems

journal, July 2009

- Lee, Dean
- Progress in Particle and Nuclear Physics, Vol. 63, Issue 1

##
Fermion-dimer scattering using an impurity lattice Monte Carlo approach and the adiabatic projection method

journal, December 2014

- Elhatisari, Serdar; Lee, Dean
- Physical Review C, Vol. 90, Issue 6

##
A survey of hypernuclear physics

journal, June 1995

- Gibson, B. F.; Hungerford, E. V.
- Physics Reports, Vol. 257, Issue 6

##
Two-particle states on a torus and their relation to the scattering matrix

journal, May 1991

- Lüscher, Martin
- Nuclear Physics B, Vol. 354, Issue 2-3

##
Volume Dependence of Bound States with Angular Momentum

journal, September 2011

- König, Sebastian; Lee, Dean; Hammer, H. -W.
- Physical Review Letters, Vol. 107, Issue 11

##
Strangeness S = −2 baryon–baryon interaction at next-to-leading order in chiral effective field theory

journal, October 2016

- Haidenbauer, J.; Meißner, Ulf-G.; Petschauer, S.
- Nuclear Physics A, Vol. 954

##
Hyperon–nucleon interaction within chiral effective field theory revisited

journal, March 2020

- Haidenbauer, J.; Meißner, U. -G.; Nogga, A.
- The European Physical Journal A, Vol. 56, Issue 3

##
Essential elements for nuclear binding

journal, October 2019

- Lu, Bing-Nan; Li, Ning; Elhatisari, Serdar
- Physics Letters B, Vol. 797

##
*Ab initio* Lattice Results for Fermi Polarons in Two Dimensions

journal, October 2015

- Bour, Shahin; Lee, Dean; Hammer, H. -W.
- Physical Review Letters, Vol. 115, Issue 18

##
Volume dependence of N -body bound states

journal, April 2018

- König, Sebastian; Lee, Dean
- Physics Letters B, Vol. 779

##
Hyperon-nucleon scattering and hyperon masses in the nuclear medium

journal, December 2001

- Korpa, C. L.; Dieperink, A. E. L.; Timmermans, R. G. E.
- Physical Review C, Vol. 65, Issue 1

##
Effects of the two-body and three-body hyperon-nucleon interactions in $\Lambda $ hypernuclei

journal, April 2013

- Lonardoni, D.; Gandolfi, S.; Pederiva, F.
- Physical Review C, Vol. 87, Issue 4