2017
DOI: 10.48550/arxiv.1712.02188
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Path integral representation for the Hubbard model with reduced number of Lefschetz thimbles

Abstract: The concept of Lefschetz thimble decomposition is one of the most promising possible modifications of Quantum Monte Carlo (QMC) algorithms aimed at alleviating the sign problem which appears in many interesting physical situations, e.g. in the Hubbard model away from half filling. In this approach one utilizes the fact that the integral over real variables with an integrand containing a complex fluctuating phase is equivalent to the sum of integrals over special manifolds in complex space ("Lefschetz thimbles"… Show more

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Cited by 6 publications
(21 citation statements)
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“…where (18) and the pair (α, β) parametrizes the surface of constant observable O in 3D space (x 1 ; x 2 ; x2 ).…”
Section: Toy Modelmentioning
confidence: 99%
See 1 more Smart Citation
“…where (18) and the pair (α, β) parametrizes the surface of constant observable O in 3D space (x 1 ; x 2 ; x2 ).…”
Section: Toy Modelmentioning
confidence: 99%
“…Here, the zeros of the determinant form "domain walls" in configuration space such that the dimensionality the zero-manifolds is given V L τ − 1, where V L τ corresponds to the number of auxiliary fields. The connection to the power law in heavytailed distributions was considered in details in [18] and for the particular case of zeros of the determinant forming domain walls, ξ = 5/2. A detailed proof is given in Appendix B.…”
Section: Formalism For the Repulsive Hubbard Modelmentioning
confidence: 99%
“…This form can be advantageous for preserving some symmetries of the original Hamiltonian (6) at the level of the discretized path integral [13]. However, since the Trotter decomposition anyway introduces a discretization error of order O ∆τ 2 in the partition function (4) and observables (5), one can also expand the exponential in (14) to the leading order in ∆τ :…”
Section: The Structure Of the Fermionic Matrix For Tight-binding Mode...mentioning
confidence: 99%
“…In practice, we have found that also many elements of the non-sparse matrix (14) are numerically very small, of order 10 −5 and smaller, and can be set to zero without introducing any noticeable error in the results of Monte-Carlo simulations. This allows to use sparse linear algebra to speed up the algorithm even for the exponential representation (14).…”
Section: The Structure Of the Fermionic Matrix For Tight-binding Mode...mentioning
confidence: 99%
“…All our calculations here are performed with m s = 0 . (In [25] it was pointed out that certain fermion operator discretizations with m s = 0 suffer from ergodicity issues. We stress that our discretization in eq.…”
Section: The Systemmentioning
confidence: 99%