AI 中文总结
该研究对比ghost-Gutzwiller方法的迭代嵌入与直接极小化方案，发现前者在莫特相及塞曼场中存在缺陷，后者可稳定顺磁解，对称性破缺时迭代方案更可靠，明确了两种方法的适用条件。
AI 中文摘要
准确描述假设的对称不变莫特绝缘体是迭代量子嵌入方法中长期存在的挑战。我们在ghost-Gutzwiller方法框架内解决该问题，该方法既可通过类似动力学平均场理论的迭代嵌入方案求解，也可通过直接极小化其变分能量泛函求解。在单带哈伯德模型的莫特相变过程中，这两种形式等价的方法表现差异显著：迭代方案计算高效但脆弱，在莫特相需要特设处理方案，该方案在塞曼场中失效，会导致不连续能量和虚假的完全极化绝缘体；直接极小化可避免这些伪影，稳定得到真正的顺磁解。相反，当允许对称性破缺（如反铁磁相）时，迭代方案能得到与动力学平均场理论高度吻合的正确解。我们的研究明确了迭代嵌入可信赖的条件，以及需采用直接极小化的情形。
英文摘要
Accurately describing a hypothetical symmetry-invariant Mott insulator presents a long-standing ing challenge in iterative quantum embedding methods. We address this issue within the ghost- Gutzwiller method, which can be solved either through an iterative embedding scheme, analogous to dynamical mean-field theory, or by directly minimizing its variational energy functional. Across the Mott transition of the single-band Hubbard model, these formally equivalent approaches behave very differently: the iterative scheme is computationally efficient but fragile, necessitating ad-hoc recipes in the Mott phase that fail in a Zeeman field, leading to a discontinuous energy and a spurious fully-polarized insulator. Direct minimization avoids these artifacts, stabilizing a genuinely paramagnetic solution. Conversely, when symmetry breaking is allowed, as in an antiferromagnetic phase, the iterative scheme yields the correct solution, closely aligning with dynamical mean-field theory. Our findings delineate the conditions under which the iterative embedding can be trusted and when direct minimization is instead required.
