Quantum Monte Carlo Simulation of Generalized Kitaev Models

Sato, Toshihiro; Assaad, Fakher F.

doi:10.48550/arxiv.2012.12283

Cited by 1 publication

(3 citation statements)

References 33 publications

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“…The results indicate that the asymptotic Lefschetz thimbles evolve from the real axis in each projection along the flows shown by the light blue points. As expected, the total average sign increases with t as S total = 0.8155 (8) and S total = 0.8304(4) for t = 0.04 and t = 0.08, respectively. The internal energy obtained by the ALT-QMC simulations reproduce the exact result as E ALT-QMC = −2.754(3) for t = 0.04 and E ALT-QMC = −2.749(2) for t = 0.08.…”

Section: Alleviation Of Sign Problemsupporting

confidence: 73%

“…The light and dark red points represent the samples on the asymptotic Lefschetz thimbles obtained at t = 0.04 and at t = 0.08, respectively. The average sign S total is alleviated from S total = 0.7933(2) in the D-QMC result (t = 0) to S total = 0.8155 (8) and S total = 0.8304(4) on the asymptotic Lefschetz thimbles at t = 0.04 and t = 0.08, respectively. All the data are obtained for N β = 1 with β = 3.125.…”

Section: B Visualization Of the Asymptotic Lefschetz Thimblesmentioning

confidence: 79%

“…where A ReS(ϕ) denotes the thermal average of A obtained with the weight of e −ReS(ϕ) . This reweighting is used in a broad range of the research fields; for instance, it has been used in the so-called determinant QMC (D-QMC) method for many fermionic models in solid state physics [1][2][3][4][5][6][7][8]. The problem is that the practical evaluation of Eq.…”

Section: Introductionmentioning

confidence: 99%

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A quantum Monte Carlo method on asymptotic Lefschetz thimbles for quantum spin systems: An application to the Kitaev model in a magnetic field

Mishchenko,

Kato,

Motome

2021

Preprint

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The quantum Monte Carlo method on asymptotic Lefschetz thimbles is a numerical algorithm devised specifically for alleviation of the sign problem appearing in the simulations of quantum many-body systems. In this method, the sign problem is alleviated by shifting the integration domain for the auxiliary fields, appearing for example in the conventional determinant quantum Monte Carlo method, from real space to an appropriate manifold in complex space. Here we extend this method to quantum spin models with generic two-spin interactions, by using the Hubbard-Stratonovich transformation to decouple the exchange interactions and the Popov-Fedotov transformation to map the quantum spins to complex fermions. As a demonstration, we apply the method to the Kitaev model in a magnetic field whose ground state is predicted to deliver a topological quantum spin liquid with non-Abelian anyonic excitations. To illustrate how the sign problem is alleviated in this method, we visualize the asymptotic Lefschetz thimbles in complex space, together with the saddle points and the zeros of the fermion determinant. We benchmark our method in the low-temperature region in a magnetic field and show that the sign of the action is recovered considerably and unbiased numerical results are obtained with sufficient precision.

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Section: Alleviation Of Sign Problemsupporting

confidence: 73%

Section: B Visualization Of the Asymptotic Lefschetz Thimblesmentioning

confidence: 79%