Complex Langevin approach to interacting Bose gases

Heinen, Philipp; Gasenzer, Thomas

doi:10.1103/physreva.106.063308

Cited by 6 publications

(2 citation statements)

References 78 publications

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“…It has been first proposed in the 1980s [7,8] with applications mainly in the realm of lattice simulations for QCD [9][10][11][12]. More recently, the method has been applied to systems of non relativistic fermions and bosons [13][14][15] in one dimension, both at zero [16,17] and finite temperature [18][19][20], as well as the three dimensional unitary Fermi gas [21,22]. In the present contribution we aim at the evaluation of the applicability of this approach, as well as reporting on first results on one-dimensional systems in harmonic trapping potentials.…”

Section: Introductionmentioning

confidence: 99%

Density profiles and correlations of harmonically trapped ultracold fermions via complex Langevin

Bauer¹,

Attanasio²,

Pawlowski³

2023

Proceedings of the 39th International Symposium on Lattice Field Theory — PoS(LATTICE2022)

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Standard lattice formulations of non-relativistic Fermi gases with two spin components suffer from a sign problem in the cases of repulsive contact interactions and attractive contact interactions with spin imbalance. We discuss the nature of this sign problem and the applicability of stochastic quantisation with complex Langevin evolution in both cases. For repulsive interactions, we find that the results converge, using adaptive step size scaling and a Gaussian regulator to modify the lattice action. We present results on density profiles and correlations of a harmonically trapped system in one spatial dimension.

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Section: Introductionmentioning

confidence: 99%

Density profiles and correlations of harmonically trapped ultracold fermions via complex Langevin

Bauer¹,

Attanasio²,

Pawlowski³

2023

Proceedings of the 39th International Symposium on Lattice Field Theory — PoS(LATTICE2022)

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“…The inclusion of interactions, i.e., the more realistic model, requires the solution of a many-body problem. The addition of interactions implies a change in critical temperature [23,24], condensed fraction, heat capacity, and ground-state fluctuations with respect to ideal results [25,26]. To solve these questions in this dissertation we use the perturbation theory which treats the interaction as a perturbation of a non-interacting system.…”

Section: A Brief History About Bose-einstein Condensatementioning

confidence: 99%

Propriedades termodinâmicas de condensados de Bose-Einstein confinados utilizando a abordagem canônica recursiva

Soares

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Primeiro de tudo, quero agradecer a Deus por ter conseguido realizar este trabalho. Meus primeiros agradecimentos vão aos meus pais, que são as pessoas que mais amo na vida e são os meus maiores ídolos, que me ensinaram a ser o que sou, e me deram todo o apoio emocional, intelectual e financeiro, novamente, o meu muito obrigado, tenho muito orgulho e honra de ser filho de vocês, que nunca mediram esforços para que eu estudasse e fizeram a pessoa que sou hoje. Segundo, à minha família, que sempre acreditou em mim e me apoiaram nessa jornada, especialmente minhas tias e meus primos.Ao meu orientador, Prof. Dr. Arnaldo Gammal pela paciência, pelas inúmeras discussões, por ter me ensinado a falar inglês, pela disposição em me ajudar, pelos conselhos e me mostrar de fato a área de pesquisa na qual me apaixonei. Quero agradeçer ao Dr. Axel Pelster pelas inúmeras discussões a respeito de teoria quântica de campos aplicada a mecânica estatística, pelos conselhos, e pela oportunidade de ir para a Alemanha como visitante por um mês, que foi certamente, uma das grandes experiências da minha vida. Também quero agradeçer aos professores Dr. Antonio Piza e Dr. Emerson Passos pelas discussões nos semanais JC.Aos meus amigos, Pedro, David, Will, Gabriel, Bruno, Quinsan e Lucas por serem os melhores amigos que conheci na USP, e por todas as discussões, cafés, conselhos e risadas. Vocês são incríveis e moldaram parte do que sou hoje. Também quero agradeçer aos meus amigos desde o colégio há mais de 10 anos, Marcelo, Alessandro, Jonas, Guilherme por todas as risadas, conselhos e histórias. Também queria agradeçer aos meus colegas de grupo, ao Gustavo, Rafael, Leonardo e Alex pelas inúmeras discussões na nossa sala e no JC.À RPTU Kaiserslautern pelo apoio durante minha estadia na Alemanha.

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Stabilizing complex Langevin for real-time gauge theories with an anisotropic kernel

Boguslavski

Hotzy

Müller

2023

J. High Energ. Phys.

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The complex Langevin (CL) method is a promising approach to overcome the sign problem that occurs in real-time formulations of quantum field theories. Using the Schwinger-Keldysh formalism, we study SU(Nc) gauge theories with CL. We observe that current stabilization techniques are insufficient to obtain correct results. Therefore, we revise the discretization of the CL equations on complex time contours, find a time reflection symmetric formulation and introduce a novel anisotropic kernel that enables CL simulations on discretized complex time paths. Applying it to SU(2) Yang-Mills theory in 3+1 dimensions, we obtain unprecedentedly stable results that we validate using additional observables and that can be systematically improved. For the first time, we are able to simulate non-Abelian gauge theory on time contours whose real-time extent exceeds its inverse temperature. Thus, our approach may pave the way towards an ab-initio real-time framework of QCD in and out of equilibrium with a potentially large impact on the phenomenology of heavy-ion collisions.

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Complex Langevin approach to interacting Bose gases

Cited by 6 publications

References 78 publications

Density profiles and correlations of harmonically trapped ultracold fermions via complex Langevin

Density profiles and correlations of harmonically trapped ultracold fermions via complex Langevin

Propriedades termodinâmicas de condensados de Bose-Einstein confinados utilizando a abordagem canônica recursiva

Stabilizing complex Langevin for real-time gauge theories with an anisotropic kernel

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