Feynman diagrams versus Fermi-gas Feynman emulator

Houcke, Kris Van; Werner, Félix; Kozik, Evgeny; Prokof’ev, Nikolay; Svistunov, Boris; Ku, Mark; Sommer, Ariel; Cheuk, Lawrence; Schirotzek, André; Zwierlein, Martin

doi:10.1038/nphys2273

Cited by 218 publications

(279 citation statements)

References 29 publications

Supporting

Mentioning

254

Contrasting

Unclassified

Order By: Relevance

“…15, 20 and 26, characterized by a very strong suppression of higher-order self-energy contributions, whereas weaker resummation methods did not yield a unique answer. Although the extrapolated results seemed to agree within the (small) error bars, this is at best a hint, and ultimately, only "nature can provide the proof" 15 .…”

Section: Expansion Techniquementioning

confidence: 99%

Diagrammatic Monte Carlo study of quasi-two-dimensional Fermi polarons

Kroiß

Pollet

2014

Phys. Rev. B

View full text Add to dashboard Cite

We apply a diagrammatic Monte Carlo method to the problem of an impurity interacting resonantly with a homogeneous Fermi bath for a quasi-two-dimensional setup. Notwithstanding the series divergence, we can show numerically that the three particle-hole diagrammatic contributions are not contributing significantly to the final answer, thus demonstrating a nearly perfect destructive interference of contributions in subspaces with higher-order particle-hole lines. Consequently, for strong enough confinement in the third direction, the transition between the polaron and the molecule ground state is found to be in good agreement with the pure two-dimensional case and agrees very well with the one found by the wave-function approach in the two-particle-hole subspace.

show abstract

Section: Expansion Techniquementioning

confidence: 99%

Diagrammatic Monte Carlo study of quasi-two-dimensional Fermi polarons

Kroiß

Pollet

2014

Phys. Rev. B

View full text Add to dashboard Cite

show abstract

“…Experimentalists have succeeded in obtaining highly degenerate and strongly interacting samples, providing new perspectives in the study of Fermi superfluidity, including BCS-BEC crossover: Thanks to magnetic Feshbach resonance techniques one can indeed control at will the interaction strength and even reach the unitary limit, where interaction effects are maximal [1,2]. Furthermore very precise measurements of the many body properties of these systems are at reach: Recently the equation of state of the gas at the unitary limit or within the whole BEC-BCS crossover was measured with an uncertainty at a few percent level [3][4][5].…”

Section: Introductionmentioning

confidence: 99%

Impurity in a Fermi sea on a narrow Feshbach resonance: A variational study of the polaronic and dimeronic branches

Trefzger

Castin

2012

Phys. Rev. A

View full text Add to dashboard Cite

We study the problem of a single impurity of mass M immersed in a Fermi sea of particles of mass m. The impurity and the fermions interact through a s-wave narrow Feshbach resonance, so that the Feshbach length R * naturally appears in the system. We use simple variational ansatz, limited to at most one pair of particle-hole excitations of the Fermi sea and we determine for the polaronic and dimeronic branches the phase diagram between absolute ground state, local minimum, thermodynamically unstable regions (with negative effective mass), and regions of complex energies (with negative imaginary part). We also determine the closed channel population which is experimentally accessible. Finally we identify a non-trivial weakly attractive limit where analytical results can be obtained, in particular for the crossing point between the polaronic and dimeronic energy branches.

show abstract

“…At the moment, there are two numerical methods to evaluate diagrammatic expansions at high order, Determinant Diagrammatic Monte Carlo (DDMC), and Diagrammatic Monte Carlo (DiagMC). Major recent achievements of DiagMC are the study of the normal phase of the unitary fermi gas [13], the determination of the ground state phase diagram of the Hubbard model up to filling factor 0.7 and interactions U/t ≤ 4 [14], and the settlement of the Bose-metal issue [15]. Given the power and the versatility of the technique, systematic diagrammatic extensions of Dynamical Mean Field Theory are now being studied [16,17].…”

mentioning

confidence: 99%

Determinant Diagrammatic Monte Carlo Algorithm in the Thermodynamic Limit

Rossi¹

2017

Phys. Rev. Lett.

106

161

View full text Add to dashboard Cite

We present a simple trick that allows to consider the sum of all connected Feynman diagrams at fixed position of interaction vertices for general fermionic models, such that the thermodynamic limit can be taken analytically. With our approach one can achieve superior performance compared to conventional Diagrammatic Monte Carlo, while rendering the algorithmic part dramatically simpler. By considering the sum of all connected diagrams at once, we allow for massive cancellations between different diagrams, greatly reducing the sign problem. In the end, the computational effort increase only exponentially with the order of the expansion, which should be contrasted with the factorial growth of the standard diagrammatic technique. We illustrate the efficiency of the technique for the two-dimensional Fermi-Hubbard model. Finding an efficient method to solve the quantum many-body problem is of fundamental physical importance. A promising strategy to gain insight is represented by quantum simulators. For example, experimentalists working with cold atoms in optical lattices are able to realise one of the most prominent models of stronglycorrelated electrons, the Hubbard model. A study of its equation of state at low-temperature has been reported in [1]. Moreover, short-range antiferromagnetic correlations have been observed [2][3][4][5][6], and, very recently, even a long-range antiferromagnetic state was realized [7].From the theoretical side, making predictions for strongly-correlated fermionic systems is a very challenging problem. Quantum Monte Carlo methods are affected by the infamous sign problem when dealing with fermionic models, which in general precludes reaching low-temperature and large system sizes (see [8,9] and references therein). The simulation time to obtain a given precision scales exponentially with the system size and the inverse of the temperature. In the strongly correlated regime, it is then very difficult to extrapolate to the Thermodynamic Limit (TL). However, the fermionic sign gives an unexpected advantage when considering fermionic perturbation theory. For bosonic theories, typically, the perturbative expansion has a zero radius of convergence. This is due to the factorial number of Feynman diagrams all contributing with the same sign. For fermions, strong cancellations between different diagrams at fixed order lead in general to a finite convergence radius on a lattice at finite temperature. This happens because for sufficiently small interactions of whatever sign (or phase) the system is stable on a lattice at non-zero temperature. This was seen numerically [10,11], and even proved mathematically for the Hubbard model at high enough temperature [12]. Perturbation theory is therefore a powerful tool to study fermionic theories. By * riccardo.rossi@ens.fr analytic continuation, any point of the phase diagram which is in the same phase as the perturbative starting point can be reached in principle, provided that one has a method to compute the diagrammatic series to high order. At the moment...

show abstract

Feynman diagrams versus Fermi-gas Feynman emulator

Cited by 218 publications

References 29 publications

Diagrammatic Monte Carlo study of quasi-two-dimensional Fermi polarons

Diagrammatic Monte Carlo study of quasi-two-dimensional Fermi polarons

Impurity in a Fermi sea on a narrow Feshbach resonance: A variational study of the polaronic and dimeronic branches

Determinant Diagrammatic Monte Carlo Algorithm in the Thermodynamic Limit

Contact Info

Product

Resources

About