Linear Ensemble-Constrained Quantum Monte Carlo: From Dilute Fermi Gas to Flat-Band Ferromagnetism
Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education) School of Physics and Astronomy, Shanghai Jiao Tong University（上海交通大学物理与天文学院人工结构量子控制教育部重点实验室）；Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）；Hefei National Laboratory（合肥国家实验室）
We present a finite-temperature canonical-ensemble determinant quantum Monte Carlo algorithm that enforces an exact fermion number and enables numerically stable simulations of correlated lattice fermions. We propose a stabilized QR update that reduces the computational complexity from standard cubic scaling $O(βN^3)$ to linear scaling $O(βN N_e^2)$ with respect to the system size $N$, where $N_e$ is the particle number. This yields a dramatic speedup in dilute regimes ($N_e \ll N$), opening unbiased access to large-scale simulations of strongly correlated low-density phases. We validate the method on the dilute Fermi gas with onsite Hubbard interactions, observing the suppression of the fermion sign problem in the dilute limit. Furthermore, we apply this approach to a one-dimensional flat-band system, where the canonical ensemble allows for precise control over filling. We reveal a ferromagnetic instability at low temperatures in the half-filling regime. Our linear-scaling approach provides a powerful tool for investigating emergent phenomena in dilute quantum matter.
X-ray Anomalous Scattering of Diluted Magnetic Oxide Semiconductors: Possible Evidence of Lattice Deformation for High Temperature Ferromagnetism
我们研究了在金红石型和金红石型Ti_{1-x} $Co$ _{x} $O$ _{2-delta} $ thin films that exhibit room-temperature ferromagnetism. Intensities of the x-ray Bragg reflection from the films were measured around the $ K $-absorption-edge of Co. If the Co ions randomly substitute on the Ti sites, the intensity should exhibit an anomaly due to the anomalous dispersion of the atomic scattering factor of Co. However, none of the anatase and rutile samples did exhibit an anomaly, unambiguously showing that the Co ions in Ti$ _{1-x} $Co$ _{x} $O$ _{2-delta} $ are not exactly located at the Ti sites of TiO$ _2 $. The absence …
Colossal low-field negative magnetoresistance in CaAl$_{2}$Si$_{2}$-type diluted magnetic semiconductors (Ba,K)(Cd,Mn)$_{2}$As$_{2}$
Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所凝聚态物理国家实验室）；Collaborative Innovation Center of Quantum Matter（量子物质协同创新中心）
