Few-fermion systems in one dimension: Ground- and excited-state energies and contacts

Rammelmüller, Lukas; Porter, William; Loheac, Andrew C.; Drut, Joaquín E.

doi:10.1103/physreva.92.013631

Cited by 20 publications

(36 citation statements)

References 52 publications

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“…In particular, we compare our results to those previously obtained with HMC in Ref. [13] for attractive systems which have also been found to agree with exact results from the Bethe ansatz. Additionally, we show results from a renormalization-group approach to density functional theory based on the microscopic interactions defining our model [51].…”

Section: Mass Balanced Case: Arbitrary Interactionsupporting

confidence: 75%

Surmounting the sign problem in nonrelativistic calculations: A case study with mass-imbalanced fermions

et al. 2017

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The calculation of the ground state and thermodynamics of mass-imbalanced Fermi systems is a challenging many-body problem. Even in one spatial dimension, analytic solutions are limited to special configurations and numerical progress with standard Monte Carlo approaches is hindered by the sign problem. The focus of the present work is on the further development of methods to study imbalanced systems in a fully nonperturbative fashion. We report our calculations of the ground-state energy of mass-imbalanced fermions using two different approaches which are also very popular in the context of the theory of the strong interaction (quantum chromodynamics, QCD): (a) the hybrid Monte Carlo algorithm with imaginary mass imbalance, followed by an analytic continuation to the real axis; and (b) the complex Langevin algorithm. We cover a range of on-site interaction strengths that includes strongly attractive as well as strongly repulsive cases which we verify with nonperturbative renormalization group methods and perturbation theory. Our findings indicate that, for strong repulsive couplings, the energy starts to flatten out, implying interesting consequences for short-range and high-frequency correlation functions. Overall, our results clearly indicate that the Complex Langevin approach is very versatile and works very well for imbalanced Fermi gases with both attractive and repulsive interactions. arXiv:1708.03149v2 [cond-mat.quant-gas]

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Section: Mass Balanced Case: Arbitrary Interactionsupporting

confidence: 75%

Surmounting the sign problem in nonrelativistic calculations: A case study with mass-imbalanced fermions

et al. 2017

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“…the ground state energy of this system in the zero-temperature limit is given by the (N ↑ + N ↓ )/2 times the binding energy of the associated two-body bound state (see, e.g., Refs. [8,[28][29][30]). Thus, even in the limit of small dimensionless couplingḡ, bound states are formed.…”

Section: A Pairing Effectsmentioning

confidence: 99%

Thermal equation of state of polarized fermions in one dimension via complex chemical potentials

Loheac¹,

Braun

Drut³

et al. 2015

Phys. Rev. A

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We present a nonperturbative computation of the equation of state of polarized, attractively interacting, nonrelativistic fermions in one spatial dimension at finite temperature. We show results for the density, spin magnetization, magnetic susceptibility, and Tan's contact. We compare with the second-order virial expansion, a next-to-leading-order lattice perturbation theory calculation, and interpret our results in terms of pairing correlations. Our lattice Monte Carlo calculations implement an imaginary chemical potential difference to avoid the sign problem. The thermodynamic results on the imaginary side are analytically continued to obtain results on the real axis. We focus on an intermediate-to strong-coupling regime, and cover a wide range of temperatures and spin imbalances.

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“…Such oscillations are typically associated with so-called shell effects and have been seen in 1D and 3D analogues of this system (see e.g. [51] and [52]). In order to better understand the strong coupling regime, we N ε F .…”

Section: Resultsmentioning

confidence: 99%

“…Indeed, it has been shown that C controls the high-momentum tail of the momentum distribution (see below) [54], as well as multiple sum rules of real-time response functions [55]. The calculation of C itself, however, involves a many-body problem that requires computational approaches [51,56]. The contact obeys an adiabatic theorem (see [57,58] (1), the scattering length enters fully through the bare coupling g (and, of course, the UV lattice cutoff, which we hold constant).…”

Section: Resultsmentioning

confidence: 99%

Ground state of the two-dimensional attractive Fermi gas: Essential properties from few to many body

2016

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We calculate the ground-state properties of unpolarized two-dimensional attractive fermions in the range from few to many particles. Using first-principles lattice Monte Carlo methods, we determine the ground-state energy, Tan's contact, momentum distribution, and single-particle correlation function. We investigate those properties for systems of N = 4, 8, ..., 40 particles and for a wide range of attractive couplings. As the attractive coupling is increased, the thermodynamic limit is reached at progressively lower N due to the dominance of the two-body sector. At large momenta k, the momentum distribution displays the expected k −4 behavior, but its onset shifts from k ≃ 1.8k F at weak coupling towards higher k at strong coupling.

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Few-fermion systems in one dimension: Ground- and excited-state energies and contacts

Cited by 20 publications

References 52 publications

Surmounting the sign problem in nonrelativistic calculations: A case study with mass-imbalanced fermions

Surmounting the sign problem in nonrelativistic calculations: A case study with mass-imbalanced fermions

Thermal equation of state of polarized fermions in one dimension via complex chemical potentials

Ground state of the two-dimensional attractive Fermi gas: Essential properties from few to many body

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