Cellular Dynamical Mean-field Theory in large Impurity Clusters

Even after decades of intense research, the single band Hubbard model representing the fundamental model for interacting quantum systems and electronic correlations remains an unsolved cornerstone paradigm in theoretical solid state physics. Within the non-perturbative dynamical mean-field theory (DMFT), the lattice problem is mapped to a self-consistent auxiliary quantum impurity model leading to a local approximation of the self-energy. Nonlocal correlations can be included by the real-space cluster extension of the DMFT (CDMFT). Enlarging the unit cell makes the calculation of a numerically exact solution in CDMFT very challenging. We here use a quantum Monte-Carlo approach in the imaginary-time space in order to solve the self-consistency equations for different cluster sizes. In order to restore the broken translational symmetry re-periodization schemes for the Green function, the self-energy, or its cumulants have been introduced. However, these suffer from ambiguity and may even lead to convergence problems when attempted inside the self-consistency loop. The comparison to numerically exact diagrammatic quantum Monte Carlo calculations shows that introducing a so-called centerfocused extrapolation (CFE) to approximate the lattice self-energy yields very accurate results. Moreover, the CFE converges faster with the cluster size than previous periodization schemes. We here perform a detailed CDMFT analysis for the single-band Hubbard model on the 2D square lattice, reaching real-space cluster sizes of up to 9x9 sites. In addition to spectral properties, we also compute two-particle correlation functions which are not accessible in DMFT. Using benchmarks against diagrammatic Monte Carlo at high temperature, we show that the cluster spin susceptibility can be extrapolated to the exact result at large cluster size. In particular, the exponential decay of spin-spin correlations is very well captured by CDMFT calculations, even when correlations extend beyond the size of the cluster. We further present results at lower temperature T and larger $U$ than the range currently accessible with diagrammatic Monte Carlo methods techniques. The CDMFT+CFE represents therefore a powerful computational tool to access the physics of non-local correlations beyond dynamical mean-field theory

Topological edge states in the Su-Schrieffer-Heeger model subject to balanced particle gain and loss

We investigate the Su-Schrieffer-Heeger model in presence of an injection and removal of particles, introduced via a master equation in Lindblad form. It is shown that the dynamics of the density matrix follows the predictions of calculations in which the gain and loss are modeled by complex $\mathcal{PT}$-symmetric potentials. In particular it is found that there is a clear distinction in the dynamics between the topologically different cases known from the stationary eigenstates.Comment: 8 pages, 6 figures, minor changes in the text, additional reference

Mott transition and pseudogap of the square-lattice Hubbard model: results from center-focused cellular dynamical mean-field theory

The recently proposed center-focused post-processing procedure [Phys. Rev. Research 2, 033476 (2020)] of cellular dynamical mean-field theory suggests that central sites of large impurity clusters are closer to the exact solution of the Hubbard model than the edge sites. In this paper, we systematically investigate results in the spirit of this center-focused scheme for several cluster sizes up to $8\times 8$ in and out of particle-hole symmetry. First we analyze the metal-insulator crossovers and transitions of the half-filled Hubbard model on a simple square lattice. We find that the critical interaction of the crossover is reduced with increasing cluster sizes and the critical temperature abruptly drops for the $4\times 4$ cluster. Second, for this cluster size, we apply the center-focused scheme to a system with more realistic tight-binding parameters, investigating its pseudogap regime as a function of temperature and doping, where we find doping dependent metal-insulator crossovers, Lifshitz transitions and a strongly renormalized Fermi-liquid regime. Additionally to diagnosing the real space origin of the suppressed antinodal spectral weight in the pseudogap regime, we can infer hints towards underlying charge ordering tendencies.Comment: 29 pages, 15 figure

Single- and two-particle observables in the Emery model: a dynamical mean-field perspective

We compare the dynamical mean-field descriptions of the single-band Hubbard model and the three-band Emery model at the one- and two-particle level for parameters relevant to high-Tc superconductors. We show that even within dynamical mean-field theory, accounting solely for temporal fluctuations, the intrinsic multi-orbital nature of the Emery model introduces effective non-local correlations. These lead to a non-Curie-like temperature-dependence of the magnetic susceptibility, also seen in nuclear magnetic resonance experiments in the pseudogap regime by M. Avramovska, et al. [Journal of Superconductivity and Novel Magnetism 33, 2621 (2020)]. We demonstrate the agreement of our results with these experiments for a large range of dopings and trace back the effective non-local correlations to an emerging oxygen-copper singlet by analyzing a minimal finite-size cluster model. Despite this correct description of the hallmark of the pseudogap at the two-particle level, i.e., the drop in the Knight shift of nuclear magnetic resonance, dynamical mean-field theory fails to properly describe the spectral properties of the pseudogap.Comment: 7 pages, 7 figure

Magnetism and Metallicity in Moir\'e Transition Metal Dichalcogenides

The ability to control the properties of twisted bilayer transition metal dichalcogenides in situ makes them an ideal platform for investigating the interplay of strong correlations and geometric frustration. Of particular interest are the low energy scales, which make it possible to experimentally access both temperature and magnetic fields that are of the order of the bandwidth or the correlation scale. In this manuscript we analyze the moir\'e Hubbard model, believed to describe the low energy physics of an important subclass of the twisted bilayer compounds. We establish its magnetic and the metal-insulator phase diagram for the full range of magnetic fields up to the fully spin polarized state. We find a rich phase diagram including fully and partially polarized insulating and metallic phases of which we determine the interplay of magnetic order, Zeeman-field, and metallicity, and make connection to recent experiments.Comment: 7 (+9) pages, 4 (+8) figure

Sarcoma classification by DNA methylation profiling

Sarcomas are malignant soft tissue and bone tumours affecting adults, adolescents and children. They represent a morphologically heterogeneous class of tumours and some entities lack defining histopathological features. Therefore, the diagnosis of sarcomas is burdened with a high inter-observer variability and misclassification rate. Here, we demonstrate classification of soft tissue and bone tumours using a machine learning classifier algorithm based on array-generated DNA methylation data. This sarcoma classifier is trained using a dataset of 1077 methylation profiles from comprehensively pre-characterized cases comprising 62 tumour methylation classes constituting a broad range of soft tissue and bone sarcoma subtypes across the entire age spectrum. The performance is validated in a cohort of 428 sarcomatous tumours, of which 322 cases were classified by the sarcoma classifier. Our results demonstrate the potential of the DNA methylation-based sarcoma classification for research and future diagnostic applications

Gene expression profiling of mucinous ovarian tumors and comparison with upper and lower gastrointestinal tumors identifies markers associated with adverse outcomes.

PURPOSE: Advanced-stage mucinous ovarian carcinoma (MOC) has poor chemotherapy response and prognosis and lacks biomarkers to aid stage I adjuvant treatment. Differentiating primary MOC from gastrointestinal (GI) metastases to the ovary is also challenging due to phenotypic similarities. Clinicopathologic and gene-expression data were analyzed to identify prognostic and diagnostic features. EXPERIMENTAL DESIGN: Discovery analyses selected 19 genes with prognostic/diagnostic potential. Validation was performed through the Ovarian Tumor Tissue Analysis consortium and GI cancer biobanks comprising 604 patients with MOC (n = 333), mucinous borderline ovarian tumors (MBOT, n = 151), and upper GI (n = 65) and lower GI tumors (n = 55). RESULTS: Infiltrative pattern of invasion was associated with decreased overall survival (OS) within 2 years from diagnosis, compared with expansile pattern in stage I MOC [hazard ratio (HR), 2.77; 95% confidence interval (CI), 1.04–7.41, P = 0.042]. Increased expression of THBS2 and TAGLN was associated with shorter OS in MOC patients (HR, 1.25; 95% CI, 1.04–1.51, P = 0.016) and (HR, 1.21; 95% CI, 1.01–1.45, P = 0.043), respectively. ERBB2 (HER2) amplification or high mRNA expression was evident in 64 of 243 (26%) of MOCs, but only 8 of 243 (3%) were also infiltrative (4/39, 10%) or stage III/IV (4/31, 13%). CONCLUSIONS: An infiltrative growth pattern infers poor prognosis within 2 years from diagnosis and may help select stage I patients for adjuvant therapy. High expression of THBS2 and TAGLN in MOC confers an adverse prognosis and is upregulated in the infiltrative subtype, which warrants further investigation. Anti-HER2 therapy should be investigated in a subset of patients. MOC samples clustered with upper GI, yet markers to differentiate these entities remain elusive, suggesting similar underlying biology and shared treatment strategies

The global retinoblastoma outcome study : a prospective, cluster-based analysis of 4064 patients from 149 countries

DATA SHARING : The study data will become available online once all analyses are complete.BACKGROUND : Retinoblastoma is the most common intraocular cancer worldwide. There is some evidence to suggest that major differences exist in treatment outcomes for children with retinoblastoma from different regions, but these differences have not been assessed on a global scale. We aimed to report 3-year outcomes for children with retinoblastoma globally and to investigate factors associated with survival. METHODS : We did a prospective cluster-based analysis of treatment-naive patients with retinoblastoma who were diagnosed between Jan 1, 2017, and Dec 31, 2017, then treated and followed up for 3 years. Patients were recruited from 260 specialised treatment centres worldwide. Data were obtained from participating centres on primary and additional treatments, duration of follow-up, metastasis, eye globe salvage, and survival outcome. We analysed time to death and time to enucleation with Cox regression models. FINDINGS : The cohort included 4064 children from 149 countries. The median age at diagnosis was 23·2 months (IQR 11·0–36·5). Extraocular tumour spread (cT4 of the cTNMH classification) at diagnosis was reported in five (0·8%) of 636 children from high-income countries, 55 (5·4%) of 1027 children from upper-middle-income countries, 342 (19·7%) of 1738 children from lower-middle-income countries, and 196 (42·9%) of 457 children from low-income countries. Enucleation surgery was available for all children and intravenous chemotherapy was available for 4014 (98·8%) of 4064 children. The 3-year survival rate was 99·5% (95% CI 98·8–100·0) for children from high-income countries, 91·2% (89·5–93·0) for children from upper-middle-income countries, 80·3% (78·3–82·3) for children from lower-middle-income countries, and 57·3% (52·1-63·0) for children from low-income countries. On analysis, independent factors for worse survival were residence in low-income countries compared to high-income countries (hazard ratio 16·67; 95% CI 4·76–50·00), cT4 advanced tumour compared to cT1 (8·98; 4·44–18·18), and older age at diagnosis in children up to 3 years (1·38 per year; 1·23–1·56). For children aged 3–7 years, the mortality risk decreased slightly (p=0·0104 for the change in slope). INTERPRETATION : This study, estimated to include approximately half of all new retinoblastoma cases worldwide in 2017, shows profound inequity in survival of children depending on the national income level of their country of residence. In high-income countries, death from retinoblastoma is rare, whereas in low-income countries estimated 3-year survival is just over 50%. Although essential treatments are available in nearly all countries, early diagnosis and treatment in low-income countries are key to improving survival outcomes.The Queen Elizabeth Diamond Jubilee Trust and the Wellcome Trust.https://www.thelancet.com/journals/langlo/homeam2023Paediatrics and Child Healt