Topological phases in the Haldane model with spin–spin on-site interactions

Rubio-García, Álvaro; García-Ripoll, Juan José

doi:10.1088/1367-2630/aabb1a

Cited by 5 publications

(4 citation statements)

References 35 publications

(92 reference statements)

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“…We want to remark that the actual phase diagram of the Haldane Hubbard model in the moderate interacting regime has been highly debated over the past several years, namely different methods predicted quite different results [45][46][47][48][49][50][51][52][53][54][55][56][57]. In particular, even whether the intermediate phases exist has not come to an agreement, let alone their physical properties.…”

Section: Summary and Discussionmentioning

confidence: 99%

“…In this article we focus on the scheme of applying quantum cluster approaches to the determination of topological invariants in correlated Chern insulators. The prototype is the half-filled Haldane Hubbard model [46][47][48][49][50][51][52][53][54][55][56][57], which exhibits quantum anomalous Hall effect with weak Coulomb interactions and is antiferromagnetically ordered in the strong coupling limit. Previous quantum cluster methods [45] predicted a topological Neel antiferromagnet and/or a topological nonmagnetic Mott insulator in the moderate interacting regime.…”

Section: Introductionmentioning

confidence: 99%

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Quantum cluster approach to the topological invariants in correlated Chern insulators

2019

New J. Phys.

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We detect the topological properties of Chern insulators with strong Coulomb interactions by use of cluster perturbation theory and variational cluster approach. The common scheme in previous studies only involves the calculation of the interacting bulk Chern number within the natural-unit cell by means of the so-called topological Hamiltonian. With close investigations on a prototype model, the half-filled Haldane Hubbard model, which is subject to both periodic and open boundary conditions, we uncover the unexpected failure of this scheme due to the explicit breaking of the translation symmetry. Instead, we assert that the faithful interacting bulk Chern number in the framework of quantum cluster approaches can be computed in the enlarged unit cell, which is free of the fault caused by the explicit translation symmetry breaking and consistent with the interacting bulk-edge correspondence.

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Section: Summary and Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Quantum cluster approach to the topological invariants in correlated Chern insulators

2019

New J. Phys.

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“…This feature, combined with the L-Lipschitz continuity of ESG risk-performance functions, allows Bayesian optimization to optimize various ESG criteria with minimal prior knowledge and minimal assumptions about the function's structure, making it a highly adaptable and flexible approach for ESG portfolio management. Prior in the literature, other black-box models -including metaheuristics such as Genetic algorithm (GA) [17] or Simulated Annealing (SA) [18]have also been proposed as alternative portfolio optimization techniques [44][45][46][47][48][49][50][51][52][53]. Bayesian optimization (BO) is a state-of-the-art class of methods that optimize black-boxes.…”

Section: State Of the Art In Portfolio Optimization With Esg And Baye...mentioning

confidence: 99%

Bayesian optimization of ESG (Environmental Social Governance) financial investments

Garrido-Merchán¹,

Piris²,

Vaca³

2023

Environ. Res. Commun.

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Financial experts seek to predict the variability of financial markets to ensure investors’ successful investments. However, there hasbeen a big trend in finance in the last few years, which are the ESG (Economic, Social and Governance) criteria, due to the growing importance of investments being socially responsible, and because of the financial impact companies suffer when not complying with them. Consequently, creating a stock portfolio should consider not only its financial performance but compliance with ESG criteria. Portfolio optimization (PO) techniques previously applied to ESG portfolios, are all closed-form analytical ones. But the real world is rather a black box with unknown analytical expressions. Thus, in this paper we use Bayesian optimization (BO), a sequential state-of-the-art design strategy to optimize black-boxes with unknown analytical and costly-to-compute expressions, to maximize the performance of a stock portfolio under the presence of ESG criteria soft constraints incorporated into the objective function.And we compare it to two other black-box techniques widely applied for the optimization of “conventional portfolios” (non-ESG ones): the metaheuristics Genetic Algorithm (GA) and Simulated Annealing (SA). Although BO has many theoretical advantages over GA and SA, it has never been applied to PO. Thus, this paper investigates whether BO can be used in the ESG PO framework as an alternative and compares it with GA and SA. This is the research gap to which this paper responds. To show the empirical performance of BO, we carry out four illustrative experiments and find evidence of BO outperforming the baselines. Thus we add another different optimization approach to the world of ESG investing: a black-box non-heuristic optimization approach through BO. Our study is the first paper that leverages BO and ESG scores into a PO technique. This paper opens the door to many new research lines in (ESG) portfolio optimization

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“…Related interaction effects in static models can be found in Refs. [30][31][32][33]. For weak interaction, using the Hartree-Fock (HF) approximation and HF plus the second-order perturbation correction (HF+2nd), respectively, we plot the phase diagram in Fig.…”

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confidence: 99%

Measuring an interaction-induced topological phase transition via the single-particle density matrix

et al. 2020

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We discuss the topological phase transition of the spin-1 2 fermionic Haldane model with repulsive on-site interaction. We show that the Berry curvature of the topological Hamiltonian, the first Chern number, and the topological phase transition point can be extracted from the single-particle density matrix for this interacting system. Furthermore, we design a tomography scheme for the single-particle density matrix of interacting fermionic two-band models in experimental realizations with cold atoms in optical lattices.

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Topological phases in the Haldane model with spin–spin on-site interactions

Cited by 5 publications

References 35 publications

Quantum cluster approach to the topological invariants in correlated Chern insulators

Quantum cluster approach to the topological invariants in correlated Chern insulators

Bayesian optimization of ESG (Environmental Social Governance) financial investments

Measuring an interaction-induced topological phase transition via the single-particle density matrix

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