Operator product expansion beyond leading order for two-component fermions
Abstract
Here, we consider a homogeneous, balanced gas of strongly interacting fermions in two spin states interacting through a large scattering length. Finite-range corrections are needed for a quantitative description of data which experiments and numerical simulations have provided. We use a perturbative field-theoretical framework and a tool called the operator product expansion (OPE), which together allow for the expression of finite-range corrections to the universal relations and momentum distribution. By using the OPE, we derive the 1/k6 part of the momentum tail, which is related to the sum of the derivative of the energy with respect to the finite range and the averaged kinetic energy of opposite spin pairs. By comparing the 1/k4 term and the 1/k6 correction in the momentum distribution to provided quantum Monte Carlo (QMC) data, we show that including the 1/k6 part offers marked improvements. Our field-theoretical approach enables for a clear understanding of the role of the scattering length and finite effective range in the universal relations and the momentum distribution.
- Authors:
-
- Univ. of Tennessee, Knoxville, TN (United States)
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- Univ. of Tennessee, Knoxville, TN (United States) ; Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
- Publication Date:
- Research Org.:
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Nuclear Physics (NP)
- OSTI Identifier:
- 1564233
- Alternate Identifier(s):
- OSTI ID: 1328512
- Grant/Contract Number:
- AC05-00OR22725; AC52-06NA25396
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review A
- Additional Journal Information:
- Journal Volume: 94; Journal Issue: 4; Journal ID: ISSN 2469-9926
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 74 ATOMIC AND MOLECULAR PHYSICS
Citation Formats
Emmons, Samuel B., Kang, Daekyoung, and Platter, Lucas. Operator product expansion beyond leading order for two-component fermions. United States: N. p., 2016.
Web. doi:10.1103/PhysRevA.94.043615.
Emmons, Samuel B., Kang, Daekyoung, & Platter, Lucas. Operator product expansion beyond leading order for two-component fermions. United States. https://doi.org/10.1103/PhysRevA.94.043615
Emmons, Samuel B., Kang, Daekyoung, and Platter, Lucas. Mon .
"Operator product expansion beyond leading order for two-component fermions". United States. https://doi.org/10.1103/PhysRevA.94.043615. https://www.osti.gov/servlets/purl/1564233.
@article{osti_1564233,
title = {Operator product expansion beyond leading order for two-component fermions},
author = {Emmons, Samuel B. and Kang, Daekyoung and Platter, Lucas},
abstractNote = {Here, we consider a homogeneous, balanced gas of strongly interacting fermions in two spin states interacting through a large scattering length. Finite-range corrections are needed for a quantitative description of data which experiments and numerical simulations have provided. We use a perturbative field-theoretical framework and a tool called the operator product expansion (OPE), which together allow for the expression of finite-range corrections to the universal relations and momentum distribution. By using the OPE, we derive the 1/k6 part of the momentum tail, which is related to the sum of the derivative of the energy with respect to the finite range and the averaged kinetic energy of opposite spin pairs. By comparing the 1/k4 term and the 1/k6 correction in the momentum distribution to provided quantum Monte Carlo (QMC) data, we show that including the 1/k6 part offers marked improvements. Our field-theoretical approach enables for a clear understanding of the role of the scattering length and finite effective range in the universal relations and the momentum distribution.},
doi = {10.1103/PhysRevA.94.043615},
journal = {Physical Review A},
number = 4,
volume = 94,
place = {United States},
year = {Mon Oct 10 00:00:00 EDT 2016},
month = {Mon Oct 10 00:00:00 EDT 2016}
}
Free Publicly Available Full Text
Publisher's Version of Record
Other availability
Search WorldCat to find libraries that may hold this journal
Cited by: 9 works
Citation information provided by
Web of Science
Web of Science
Figures / Tables:
FIG. 1: Scattering amplitude at leading order.
All figures and tables
(11 total)
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.
Works referenced in this record:
Universal Behavior of Pair Correlations in a Strongly Interacting Fermi Gas
journal, August 2010
- Kuhnle, E. D.; Hu, H.; Liu, X. -J.
- Physical Review Letters, Vol. 105, Issue 7
Two-Body and Three-Body Contacts for Identical Bosons near Unitarity
journal, March 2014
- Smith, D. Hudson; Braaten, Eric; Kang, Daekyoung
- Physical Review Letters, Vol. 112, Issue 11
Virial theorems for trapped cold atoms
journal, August 2008
- Werner, Félix
- Physical Review A, Vol. 78, Issue 2
Nucleon-nucleon scattering from effective field theory
journal, November 1996
- Kaplan, David B.; Savage, Martin J.; Wise, Mark B.
- Nuclear Physics B, Vol. 478, Issue 3
Measurement of the Homogeneous Contact of a Unitary Fermi Gas
journal, November 2012
- Sagi, Yoav; Drake, Tara E.; Paudel, Rabin
- Physical Review Letters, Vol. 109, Issue 22
Exact Relations for a Strongly Interacting Fermi Gas from the Operator Product Expansion
journal, May 2008
- Braaten, Eric; Platter, Lucas
- Physical Review Letters, Vol. 100, Issue 20
Short-distance and short-time structure of a unitary Fermi gas
journal, June 2010
- Son, Dam T.; Thompson, Ethan G.
- Physical Review A, Vol. 81, Issue 6
Momentum Distribution and Contact of the Unitary Fermi Gas
journal, May 2011
- Drut, Joaquín E.; Lähde, Timo A.; Ten, Timour
- Physical Review Letters, Vol. 106, Issue 20
Universal relation for the inelastic two-body loss rate
journal, October 2013
- Braaten, Eric; Hammer, H-W
- Journal of Physics B: Atomic, Molecular and Optical Physics, Vol. 46, Issue 21
Auxiliary-field quantum Monte Carlo method for strongly paired fermions
journal, December 2011
- Carlson, J.; Gandolfi, Stefano; Schmidt, Kevin E.
- Physical Review A, Vol. 84, Issue 6
Structure-function sum rules for systems with large scattering lengths
journal, January 2012
- Goldberger, Walter D.; Rothstein, Ira Z.
- Physical Review A, Vol. 85, Issue 1
Temperature and coupling dependence of the universal contact intensity for an ultracold Fermi gas
journal, August 2010
- Palestini, F.; Perali, A.; Pieri, P.
- Physical Review A, Vol. 82, Issue 2
From low-density neutron matter to the unitary limit
journal, May 2009
- Abe, T.; Seki, R.
- Physical Review C, Vol. 79, Issue 5
Quantum Monte Carlo approaches to nuclear and atomic physics
journal, January 2012
- Carlson, J.; Gandolfi, Stefano; Gezerlis, Alexandros
- Progress of Theoretical and Experimental Physics, Vol. 2012, Issue 1
Number of closed-channel molecules in the BEC-BCS crossover
journal, February 2009
- Werner, F.; Tarruell, L.; Castin, Y.
- The European Physical Journal B, Vol. 68, Issue 3
Generalized virial theorem and pressure relation for a strongly correlated Fermi gas
journal, December 2008
- Tan, Shina
- Annals of Physics, Vol. 323, Issue 12
Verification of Universal Relations in a Strongly Interacting Fermi Gas
journal, June 2010
- Stewart, J. T.; Gaebler, J. P.; Drake, T. E.
- Physical Review Letters, Vol. 104, Issue 23
BEC-BCS crossover in the expansion
journal, April 2007
- Chen, Jiunn-Wei; Nakano, Eiji
- Physical Review A, Vol. 75, Issue 4
Dynamical cluster quantum Monte Carlo study of the single-particle spectra of strongly interacting fermion gases
journal, May 2010
- Su, Shi-Quan; Sheehy, Daniel E.; Moreno, Juana
- Physical Review A, Vol. 81, Issue 5
Current response, structure factor and hydrodynamic quantities of a two- and three-dimensional Fermi gas from the operator-product expansion
journal, October 2011
- Hofmann, Johannes
- Physical Review A, Vol. 84, Issue 4
Molecular Probe of Pairing in the BEC-BCS Crossover
journal, July 2005
- Partridge, G. B.; Strecker, K. E.; Kamar, R. I.
- Physical Review Letters, Vol. 95, Issue 2
Universal Relations for Identical Bosons from Three-Body Physics
journal, April 2011
- Braaten, Eric; Kang, Daekyoung; Platter, Lucas
- Physical Review Letters, Vol. 106, Issue 15
Single-particle spectral density of the unitary Fermi gas: Novel approach based on the operator product expansion, sum rules and the maximum entropy method
journal, May 2015
- Gubler, Philipp; Yamamoto, Naoki; Hatsuda, Tetsuo
- Annals of Physics, Vol. 356
Pair Correlations of an Expanding Superfluid Fermi Gas
journal, September 2006
- Lobo, C.; Carusotto, I.; Giorgini, S.
- Physical Review Letters, Vol. 97, Issue 10
BEC-BCS crossover and universal relations in unitary Fermi gases
journal, April 2011
- Gandolfi, S.; Schmidt, K. E.; Carlson, J.
- Physical Review A, Vol. 83, Issue 4
Large momentum part of a strongly correlated Fermi gas
journal, December 2008
- Tan, Shina
- Annals of Physics, Vol. 323, Issue 12
Effective field theory of short-range forces
journal, January 1999
- van Kolck, U.
- Nuclear Physics A, Vol. 645, Issue 2
Energetics of a strongly correlated Fermi gas
journal, December 2008
- Tan, Shina
- Annals of Physics, Vol. 323, Issue 12
Operator Algebra and the Determination of Critical Indices
journal, December 1969
- Kadanoff, Leo P.
- Physical Review Letters, Vol. 23, Issue 25
Scattering models for ultracold atoms
journal, July 2008
- Braaten, Eric; Kusunoki, Masaoki; Zhang, Dongqing
- Annals of Physics, Vol. 323, Issue 7
Short-Time Operator Product Expansion for rf Spectroscopy of a Strongly Interacting Fermi Gas
journal, June 2010
- Braaten, Eric; Kang, Daekyoung; Platter, Lucas
- Physical Review Letters, Vol. 104, Issue 22
Universal Relations for a Fermi Gas Close to a -Wave Interaction Resonance
journal, September 2015
- Yu, Zhenhua; Thywissen, Joseph H.; Zhang, Shizhong
- Physical Review Letters, Vol. 115, Issue 13
Molecular signatures in the structure factor of an interacting Fermi gas
journal, September 2006
- Combescot, R.; Giorgini, S.; Stringari, S.
- Europhysics Letters (EPL), Vol. 75, Issue 5
Viscosity sum rules at large scattering lengths
journal, January 2012
- Goldberger, Walter D.; Khandker, Zuhair U.
- Physical Review A, Vol. 85, Issue 1
Quantum Anomaly, Universal Relations, and Breathing Mode of a Two-Dimensional Fermi Gas
journal, May 2012
- Hofmann, Johannes
- Physical Review Letters, Vol. 108, Issue 18
General relations for quantum gases in two and three dimensions: Two-component fermions
journal, July 2012
- Werner, Félix; Castin, Yvan
- Physical Review A, Vol. 86, Issue 1
The Equation of State of a Low-Temperature Fermi Gas with Tunable Interactions
journal, April 2010
- Navon, N.; Nascimbene, S.; Chevy, F.
- Science, Vol. 328, Issue 5979
Universal relations for a strongly interacting Fermi gas near a Feshbach resonance
journal, November 2008
- Braaten, Eric; Kang, Daekyoung; Platter, Lucas
- Physical Review A, Vol. 78, Issue 5
Precise Determination of the Structure Factor and Contact in a Unitary Fermi Gas
journal, January 2013
- Hoinka, Sascha; Lingham, Marcus; Fenech, Kristian
- Physical Review Letters, Vol. 110, Issue 5
Bragg Spectroscopy of a Strongly Interacting Fermi Gas
journal, December 2008
- Veeravalli, G.; Kuhnle, E.; Dyke, P.
- Physical Review Letters, Vol. 101, Issue 25
Non-Lagrangian Models of Current Algebra
journal, March 1969
- Wilson, Kenneth G.
- Physical Review, Vol. 179, Issue 5
Erratum: Universal Relations for a Fermi Gas Close to a -Wave Interaction Resonance [Phys. Rev. Lett. 115 , 135304 (2015)]
journal, June 2016
- Yu, Zhenhua; Thywissen, Joseph H.; Zhang, Shizhong
- Physical Review Letters, Vol. 117, Issue 1
Probing strongly interacting atomic gases with energetic atoms
journal, May 2012
- Nishida, Yusuke
- Physical Review A, Vol. 85, Issue 5
Works referencing / citing this record:
Cold atom quantum simulator for dilute neutron matter
journal, February 2019
- Horikoshi, Munekazu; Kuwata-Gonokami, Makoto
- International Journal of Modern Physics E, Vol. 28, Issue 01n02
Cold Atom Quantum Simulator for Dilute Neutron Matter
text, January 2019
- Horikoshi, Munekazu; Kuwata-Gonokami, Makoto
- arXiv
Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.