Symmetry-broken perturbation theory to large orders in antiferromagnetic phases

TL;DR

This paper develops a symmetry-broken perturbation theory for antiferromagnetic phases, enabling precise, numerically exact calculations of the magnetic phase diagram and thermodynamics of the 3D Hubbard model, revealing insights into phase boundaries and critical behavior.

Contribution

It introduces a spin-symmetry-broken extension of the connected determinant algorithm for accurate calculations within magnetically ordered phases.

Findings

Determined the N{é}el phase boundary in the 3D Hubbard model.

Established the critical behavior aligns with the $O(3)$ Heisenberg universality class.

Provided detailed thermodynamic data across the antiferromagnetic dome.

Abstract

We introduce a spin-symmetry-broken extension of the connected determinant algorithm [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 half-filling. With detailed computations of the order parameter in the low to intermediate-coupling regime, we establish the N{\'e}el 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.