Symmetry-Broken Perturbation Theory to Large Orders in Antiferromagnetic Phases

Year: 2024

Authors: Garioud R., Simkovic F., Rossi R., Spada G., Schdfer T., Werner F., Ferrero M.

Autors Affiliation: Ecole Polytech, Inst Polytech Paris, CPHT, CNRS, F-91128 Palaiseau, France; Coll France, 11 Pl Marcelin Berthelot, F-75005 Paris, France; Ecole Polytech Fed Lausanne EPFL, Inst Phys, CH-1015 Lausanne, Switzerland; Sorbonne Univ, CNRS, Lab Phys Theor Matiere Condensee, LPTMC, F-75005 Paris, France; Sorbonne Univ, Univ PSL, Ecole Normale Super, Lab Kastler Brossel,Coll France,CNRS, F-75005 Paris, France; Univ Trento, Pitaevskii BEC Ctr, CNR INO, I-38123 Trento, Italy; Univ Trento, Dipartimento Fis, I-38123 Trento, Italy; Max Planck Inst Festkorperforsch, Heisenbergstr 1, D-70569 Stuttgart, Germany.

Abstract: We introduce a spin-symmetry-broken extension of the connected determinant algorithm [Riccardo Rossi, Determinant diagrammatic Monte Carlo algorithm in the thermodynamic limit, Phys. Rev. Lett. 119, 045701 (2017).]. The resulting systematic perturbative expansions around an antiferromagnetic state allow for numerically exact calculations directly inside a magnetically ordered phase. We show new precise results for the magnetic phase diagram and thermodynamics of the three-dimensional cubic Hubbard model at halffilling. With detailed computations of the order parameter in the low to intermediate-coupling regime, we establish the Neel phase boundary. The critical behavior in its vicinity is shown to be compatible with the O(3) Heisenberg universality class. By determining the evolution of the entropy with decreasing temperature through the phase transition we identify the different physical regimes at U=t = 4. We provide quantitative results for several thermodynamic quantities deep inside the antiferromagnetic dome up to large interaction strengths and investigate the crossover between the Slater and Heisenberg regimes.

Journal/Review: PHYSICAL REVIEW LETTERS

Volume: 132 (24)      Pages from: 246505-1  to: 246505-8

More Information: The authors are grateful to A. Georges, A. J. Kim, E. Kozik, C. Lenihan, G. Rohringer, and J. Stobbe for valuable discussions. This work was granted access to the HPC resources of TGCC and IDRIS under the allocations A0150510609 attributed by GENCI (Grand Equipement National de Calcul Intensif). It has also used high performance computing resources of IDCS (Infrastructure, Donnces, Calcul Scientifique) under the allocation CPHT (Centre de Physique Thcorique) 2023. This work has been supp orted by the Simons Foundation within the Many Electron Collaboration framework. G. S. acknowledges support from Provincia Autonoma di Trento.
KeyWords: Hubbard-model; Electron Correlations; Transition; Quantum; Ferromagnetism; Diagram
DOI: 10.1103/PhysRevLett.132.246505