Ground-state properties of strongly interacting Fermi gases in two dimensions
Abstract
Exact calculations are performed on the two-dimensional strongly interacting unpolarized uniform Fermi gas with a zero-range attractive interaction. Two auxiliary-field approaches are employed which accelerate the sampling of imaginary-time paths using BCS trial wave functions and a force bias technique. Their combination enables calculations on large enough lattices to reliably compute ground-state properties in the thermodynamic limit. An equation of state is obtained with a parametrization provided, which can serve as a benchmark and allow accurate comparisons with experiments. The pressure, contact parameter, and condensate fraction are determined systematically vs $$k_Fa$$ . The momentum distribution, pairing correlation, and the structure of the pair wave function are computed. The use of force bias to accelerate the Metropolis sampling of auxiliary fields in determinantal approaches is discussed.
- Authors:
-
- College of William and Mary, Williamsburg, VA (United States). Dept. of Physics
- Publication Date:
- Research Org.:
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Oak Ridge Leadership Computing Facility (OLCF)
- Sponsoring Org.:
- USDOE Office of Science (SC); National Science Foundation (NSF)
- OSTI Identifier:
- 1565361
- Alternate Identifier(s):
- OSTI ID: 1214347
- Grant/Contract Number:
- AC05-00OR22725; SC0008627; DMR-1409510
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review A - Atomic, Molecular, and Optical Physics
- Additional Journal Information:
- Journal Volume: 92; Journal Issue: 3; Journal ID: ISSN 1050-2947
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Optics; Physics
Citation Formats
Shi, Hao, Chiesa, Simone, and Zhang, Shiwei. Ground-state properties of strongly interacting Fermi gases in two dimensions. United States: N. p., 2015.
Web. doi:10.1103/physreva.92.033603.
Shi, Hao, Chiesa, Simone, & Zhang, Shiwei. Ground-state properties of strongly interacting Fermi gases in two dimensions. United States. https://doi.org/10.1103/physreva.92.033603
Shi, Hao, Chiesa, Simone, and Zhang, Shiwei. Tue .
"Ground-state properties of strongly interacting Fermi gases in two dimensions". United States. https://doi.org/10.1103/physreva.92.033603. https://www.osti.gov/servlets/purl/1565361.
@article{osti_1565361,
title = {Ground-state properties of strongly interacting Fermi gases in two dimensions},
author = {Shi, Hao and Chiesa, Simone and Zhang, Shiwei},
abstractNote = {Exact calculations are performed on the two-dimensional strongly interacting unpolarized uniform Fermi gas with a zero-range attractive interaction. Two auxiliary-field approaches are employed which accelerate the sampling of imaginary-time paths using BCS trial wave functions and a force bias technique. Their combination enables calculations on large enough lattices to reliably compute ground-state properties in the thermodynamic limit. An equation of state is obtained with a parametrization provided, which can serve as a benchmark and allow accurate comparisons with experiments. The pressure, contact parameter, and condensate fraction are determined systematically vs $k_Fa$ . The momentum distribution, pairing correlation, and the structure of the pair wave function are computed. The use of force bias to accelerate the Metropolis sampling of auxiliary fields in determinantal approaches is discussed.},
doi = {10.1103/physreva.92.033603},
journal = {Physical Review A - Atomic, Molecular, and Optical Physics},
number = 3,
volume = 92,
place = {United States},
year = {2015},
month = {9}
}
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Works referenced in this record:
Non-Abelian Topological Order in -Wave Superfluids of Ultracold Fermionic Atoms
journal, July 2009
- Sato, Masatoshi; Takahashi, Yoshiro; Fujimoto, Satoshi
- Physical Review Letters, Vol. 103, Issue 2
Ground-State Pressure of Quasi-2D Fermi and Bose Gases
journal, January 2014
- Makhalov, Vasiliy; Martiyanov, Kirill; Turlapov, Andrey
- Physical Review Letters, Vol. 112, Issue 4
Interaction energy and itinerant ferromagnetism in a strongly interacting Fermi gas in the absence of molecule formation
journal, November 2014
- He, Lianyi
- Physical Review A, Vol. 90, Issue 5
Thermodynamic Measurements in a Strongly Interacting Fermi Gas
journal, November 2008
- Luo, Le; Thomas, J. E.
- Journal of Low Temperature Physics, Vol. 154, Issue 1-2
Theory of ultracold atomic Fermi gases
journal, October 2008
- Giorgini, Stefano; Pitaevskii, Lev P.; Stringari, Sandro
- Reviews of Modern Physics, Vol. 80, Issue 4
Many-body physics with ultracold gases
journal, July 2008
- Bloch, Immanuel; Dalibard, Jean; Zwerger, Wilhelm
- Reviews of Modern Physics, Vol. 80, Issue 3
Berezinskii-Kosterlitz-Thouless transition in a trapped quasi-two-dimensional Fermi gas near a Feshbach resonance
journal, October 2008
- Zhang, Wei; Lin, G. -D.; Duan, L. -M.
- Physical Review A, Vol. 78, Issue 4
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
Vortex-Antivortex Lattice in Ultracold Fermionic Gases
journal, February 2006
- Botelho, S. S.; Sá de Melo, C. A. R.
- Physical Review Letters, Vol. 96, Issue 4
BCS-BEC Crossover in a Two-Dimensional Fermi Gas
journal, March 2011
- Bertaina, G.; Giorgini, S.
- Physical Review Letters, Vol. 106, Issue 11
Quantum Monte Carlo Method using Phase-Free Random Walks with Slater Determinants
journal, April 2003
- Zhang, Shiwei; Krakauer, Henry
- Physical Review Letters, Vol. 90, Issue 13
Quantum Monte Carlo method for the ground state of many-boson systems
journal, November 2004
- Purwanto, Wirawan; Zhang, Shiwei
- Physical Review E, Vol. 70, Issue 5
Universal Equation of State and Pseudogap in the Two-Dimensional Fermi Gas
journal, April 2014
- Bauer, Marianne; Parish, Meera M.; Enss, Tilman
- Physical Review Letters, Vol. 112, Issue 13
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
Quantum chemistry by random walk. H 2 P , H + 3 D 3 h 1 A ′ 1 , H 2 3 Σ + u , H 4 1 Σ + g , Be 1 S
journal, November 1976
- Anderson, James B.
- The Journal of Chemical Physics, Vol. 65, Issue 10
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
Quasi-Two-Dimensional Superfluid Fermionic Gases
journal, October 2005
- Martikainen, J. -P.; Törmä, P.
- Physical Review Letters, Vol. 95, Issue 17
Revealing the Superfluid Lambda Transition in the Universal Thermodynamics of a Unitary Fermi Gas
journal, January 2012
- Ku, M. J. H.; Sommer, A. T.; Cheuk, L. W.
- Science, Vol. 335, Issue 6068
Superfluidity at the BEC-BCS crossover in two-dimensional Fermi gases with population and mass imbalance
journal, May 2008
- Conduit, G. J.; Conlon, P. H.; Simons, B. D.
- Physical Review A, Vol. 77, Issue 5
Density distribution of a trapped two-dimensional strongly interacting Fermi gas
journal, November 2011
- Orel, Alexey A.; Dyke, Paul; Delehaye, Marion
- New Journal of Physics, Vol. 13, Issue 11
Measurements of Tan’s Contact in an Atomic Bose-Einstein Condensate
journal, April 2012
- Wild, R. J.; Makotyn, P.; Pino, J. M.
- Physical Review Letters, Vol. 108, Issue 14
Lattice Monte Carlo calculations for unitary fermions in a finite box
journal, February 2013
- Endres, Michael G.; Kaplan, David B.; Lee, Jong-Wan
- Physical Review A, Vol. 87, Issue 2
Density matrix formulation for quantum renormalization groups
journal, November 1992
- White, Steven R.
- Physical Review Letters, Vol. 69, Issue 19
BCS-BEC crossover of a quasi-two-dimensional Fermi gas: The significance of dressed molecules
journal, June 2008
- Zhang, Wei; Lin, G. -D.; Duan, L. -M.
- Physical Review A, Vol. 77, Issue 6
Large momentum part of a strongly correlated Fermi gas
journal, December 2008
- Tan, Shina
- Annals of Physics, Vol. 323, Issue 12
Energetics of a strongly correlated Fermi gas
journal, December 2008
- Tan, Shina
- Annals of Physics, Vol. 323, Issue 12
Landau f function for the dilute Fermi gas in two dimensions
journal, May 1992
- Engelbrecht, Jan R.; Randeria, Mohit; Zhang, Lizeng
- Physical Review B, Vol. 45, Issue 17
Quantum Monte Carlo for molecules: Green’s function and nodal release
journal, December 1984
- Ceperley, D. M.; Alder, B. J.
- The Journal of Chemical Physics, Vol. 81, Issue 12
Observation of a Two-Dimensional Fermi Gas of Atoms
journal, July 2010
- Martiyanov, Kirill; Makhalov, Vasiliy; Turlapov, Andrey
- Physical Review Letters, Vol. 105, Issue 3
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
Two-Dimensional System of Hard-Core Bosons
journal, March 1971
- Schick, M.
- Physical Review A, Vol. 3, Issue 3
Ground-state energy of the unitary Fermi gas from the expansion
journal, January 2009
- Nishida, Yusuke
- Physical Review A, Vol. 79, Issue 1
Imbalanced Fermi superfluid in a one-dimensional optical potential
journal, May 2007
- Tempere, J.; Wouters, M.; Devreese, J. T.
- Physical Review B, Vol. 75, Issue 18
Many-Body Physics with Ultracold Gases
text, January 2007
- Bloch, Immanuel; Dalibard, Jean; Zwerger, Wilhelm
- arXiv
BCS-BEC Crossover of a Quasi-two-dimensional Fermi Gas: the Significance of Dressed Molecules
text, January 2008
- Zhang, Wei; Lin, G. -D.; Duan, L. -M.
- arXiv
Superfluidity at the BEC-BCS crossover in two-dimensional Fermi gases with population and mass imbalance
text, January 2008
- Conduit, G. J.; Conlon, P. H.; Simons, B. D.
- arXiv
Thermodynamic Measurements in a Strongly Interacting Fermi Gas
text, January 2008
- Luo, Le; Thomas, John E.
- arXiv
Momentum Distribution and Contact of the Unitary Fermi gas
text, January 2010
- Drut, Joaquín E.; Lähde, Timo A.; Ten, Timour
- arXiv
Revealing the Superfluid Lambda Transition in the Universal Thermodynamics of a Unitary Fermi Gas
text, January 2011
- Ku, Mark J. H.; Sommer, Ariel T.; Cheuk, Lawrence W.
- arXiv
Lattice Monte Carlo calculations for unitary fermions in a finite box
text, January 2012
- Endres, Michael G.; Kaplan, David B.; Lee, Jong-Wan
- arXiv
Interaction energy and itinerant ferromagnetism in a strongly interacting Fermi gas in the absence of molecule formation
text, January 2014
- He, Lianyi
- arXiv
Quantum Monte Carlo method using phase-free random walks with Slater determinants
text, January 2002
- Zhang, Shiwei; Krakauer, Henry
- arXiv
Quasi two-dimensional superfluid Fermi gases
text, January 2005
- Martikainen, J. -P.; Torma, Paivi
- arXiv
Imbalanced Fermi superfluid in a one-dimensional optical potential
text, January 2007
- Tempere, J.; Wouters, M.; Devreese, J. T.
- arXiv
A Constrained Path Quantum Monte Carlo Method for Fermion Ground States
text, January 1995
- Zhang, Shiwei; Carlson, J.; Gubernatis, J. E.
- arXiv
Works referencing / citing this record:
Ab initio computations of molecular systems by the auxiliary-field quantum Monte Carlo method
journal, May 2018
- Motta, Mario; Zhang, Shiwei
- Wiley Interdisciplinary Reviews: Computational Molecular Science, Vol. 8, Issue 5
Fermions in Two Dimensions: Scattering and Many-Body Properties
journal, August 2017
- Galea, Alexander; Zielinski, Tash; Gandolfi, Stefano
- Journal of Low Temperature Physics, Vol. 189, Issue 5-6
Dynamical BCS Theory of a Two-Dimensional Attractive Fermi Gas: Effective Interactions from Quantum Monte Carlo Calculations
journal, August 2019
- Vitali, Ettore; Gonzalez, Jimmy
- Journal of Low Temperature Physics, Vol. 197, Issue 5-6
Fermi-to-Bose crossover in a trapped quasi-2D gas of fermionic atoms
journal, August 2017
- Turlapov, A. V.; Yu Kagan, M.
- Journal of Physics: Condensed Matter, Vol. 29, Issue 38
Calculating ground-state properties of correlated fermionic systems with BCS trial wave functions in Slater determinant path-integral approaches
journal, August 2019
- Vitali, Ettore; Rosenberg, Peter; Zhang, Shiwei
- Physical Review A, Vol. 100, Issue 2
Diffusion Monte Carlo study of a spin-imbalanced two-dimensional Fermi gas with attractive interactions
journal, December 2019
- Foo, D. C. W.; Conduit, G. J.
- Physical Review A, Vol. 100, Issue 6
Chiral two-dimensional -wave superfluid from -wave pairing in the Bose-Einstein-condensate regime
journal, January 2020
- Thompson, K.; Brand, J.; Zülicke, U.
- Physical Review A, Vol. 101, Issue 1
Effective-range dependence of two-dimensional Fermi gases
journal, August 2017
- Schonenberg, L. M.; Verpoort, P. C.; Conduit, G. J.
- Physical Review A, Vol. 96, Issue 2
Dimensional crossover in a strongly interacting ultracold atomic Fermi gas
journal, October 2017
- Toniolo, Umberto; Mulkerin, Brendan C.; Vale, Chris J.
- Physical Review A, Vol. 96, Issue 4
Visualizing the BEC-BCS crossover in a two-dimensional Fermi gas: Pairing gaps and dynamical response functions from ab initio computations
journal, December 2017
- Vitali, Ettore; Shi, Hao; Qin, Mingpu
- Physical Review A, Vol. 96, Issue 6
Numerically exact study of Weyl superconductivity
journal, September 2019
- Rosenberg, Peter; Aryal, Niraj; Manousakis, Efstratios
- Physical Review B, Vol. 100, Issue 10
Benchmark study of the two-dimensional Hubbard model with auxiliary-field quantum Monte Carlo method
journal, August 2016
- Qin, Mingpu; Shi, Hao; Zhang, Shiwei
- Physical Review B, Vol. 94, Issue 8
Computation of dynamical correlation functions for many-fermion systems with auxiliary-field quantum Monte Carlo
journal, August 2016
- Vitali, Ettore; Shi, Hao; Qin, Mingpu
- Physical Review B, Vol. 94, Issue 8
Cluster size convergence of the density matrix embedding theory and its dynamical cluster formulation: A study with an auxiliary-field quantum Monte Carlo solver
journal, January 2017
- Zheng, Bo-Xiao; Kretchmer, Joshua S.; Shi, Hao
- Physical Review B, Vol. 95, Issue 4
Rashba Spin-Orbit Coupling, Strong Interactions, and the BCS-BEC Crossover in the Ground State of the Two-Dimensional Fermi Gas
journal, July 2016
- Shi, Hao; Rosenberg, Peter; Chiesa, Simone
- Physical Review Letters, Vol. 117, Issue 4
Quantum Anomaly and 2D-3D Crossover in Strongly Interacting Fermi Gases
journal, September 2018
- Peppler, T.; Dyke, P.; Zamorano, M.
- Physical Review Letters, Vol. 121, Issue 12
Few-Body Perspective of a Quantum Anomaly in Two-Dimensional Fermi Gases
journal, January 2020
- Yin, X. Y.; Hu, Hui; Liu, Xia-Ji
- Physical Review Letters, Vol. 124, Issue 1
Solutions of the Two-Dimensional Hubbard Model: Benchmarks and Results from a Wide Range of Numerical Algorithms
journal, December 2015
- LeBlanc, J. P. F.; Antipov, Andrey E.; Becca, Federico
- Physical Review X, Vol. 5, Issue 4
Quantum scale anomaly and spatial coherence in a 2D Fermi superfluid
journal, July 2019
- Murthy, Puneet A.; Defenu, Nicolò; Bayha, Luca
- Science, Vol. 365, Issue 6450
Effective-range dependence of two-dimensional Fermi gases
text, January 2017
- Schonenberg, Lm; Verpoort, Philipp; Conduit, Gareth
- Apollo - University of Cambridge Repository
Diffusion Monte Carlo study of a spin-imbalanced two-dimensional Fermi gas with attractive interactions
text, January 2019
- Foo, Darryl; Conduit, Gareth
- Apollo - University of Cambridge Repository
Equation of State of Ultracold Fermions in the 2D BEC-BCS Crossover Region
text, January 2015
- Boettcher, I.; Bayha, L.; Kedar, D.
- arXiv
Diffusion Monte Carlo study of strongly interacting two-dimensional Fermi gases
text, January 2015
- Galea, Alexander; Dawkins, Hillary; Gandolfi, Stefano
- arXiv
Rashba spin-orbit coupling, strong interactions, and the BCS-BEC crossover in the ground state of the two-dimensional Fermi Gas
text, January 2016
- Shi, Hao; Rosenberg, Peter; Chiesa, Simone
- arXiv
Benchmark study of the two-dimensional Hubbard model with auxiliary-field quantum Monte Carlo method
text, January 2016
- Qin, Mingpu; Shi, Hao; Zhang, Shiwei
- arXiv
Computation of dynamical correlation functions for many fermion systems with auxiliary-field quantum Monte Carlo
text, January 2016
- Vitali, Ettore; Shi, Hao; Qin, Mingpu
- arXiv
Pressure profiles of nonuniform two-dimensional atomic Fermi gases
text, January 2016
- Martiyanov, Kirill; Barmashova, Tatiana; Makhalov, Vasiliy
- arXiv
Dimensional crossover in a strongly interacting ultracold atomic Fermi gas
text, January 2017
- Toniolo, Umberto; Mulkerin, Brendan C.; Vale, Chris J.
- arXiv
Fermi-to-Bose crossover in a trapped quasi-2D gas of fermionic atoms
text, January 2017
- Turlapov, A. V.; Kagan, M. Yu.
- arXiv
Visualizing the BEC-BCS crossover in the two-dimensional Fermi gas: pairing gaps and dynamical response functions from ab initio computations
text, January 2017
- Vitali, Ettore; Shi, Hao; Qin, Mingpu
- arXiv
Path Integral Monte Carlo study of particles obeying quantum mechanics and classical statistics
text, January 2017
- Dawkins, William G.; Gezerlis, Alexandros
- arXiv
Effective-range dependence of two-dimensional Fermi gases
text, January 2017
- Schonenberg, L. M.; Verpoort, P. C.; Conduit, G. J.
- arXiv
Quantum anomaly and thermodynamics of one-dimensional fermions with three-body interactions
text, January 2018
- Drut, Joaquín E.; McKenney, Joshua R.; Daza, Wilder S.
- arXiv
Quantum anomaly and 2D-3D crossover in strongly interacting Fermi gases
text, January 2018
- Peppler, T.; Dyke, P.; Zamorano, M.
- arXiv
Calculating ground state properties of correlated fermionic systems with BCS trial wave functions in Slater determinant path-integral approaches
text, January 2019
- Vitali, Ettore; Rosenberg, Peter; Zhang, Shiwei
- arXiv
Dynamical BCS theory of a two-dimensional attractive Fermi gas: effective interactions from Quantum Monte Carlo calculations
text, January 2019
- Vitali, Ettore; Nunez, Jimmy Gonzalez
- arXiv
Few-body perspective of a quantum anomaly in two-dimensional Fermi gases
text, January 2019
- Yin, X. Y.; Hu, Hui; Liu, Xia-Ji
- arXiv