arXiv subjects

Peter Riseborough

Publications and source records attributed to Peter Riseborough.

3 recordsLinked to original sources

arXiv2025

Density Matrix Geometry and Sum Rules

Geometry plays a fundamental role in a wide range of physical responses, from anomalous transport coefficients to their related sum rules. Notable examples include the quantization of the Hall conductivity and the Souza-Wilkens-Martin (SWM) sum rule -- both valid at zero temperature, independent of interactions and disorder. The finite-temperature generalization of the SWM sum rule has been explored in the literature, revealing deep connections to the geometry of density matrices. Building on recent advances in time-dependent geometric frameworks, we propose a time-dependent quantum geometric tensor for thermal density matrices. This formalism provides a unified interpretation of known sum rules within the framework of the fluctuation-dissipation theorem, further elucidating their fundamental geometric origin. In addition, it provides experimentally accessible methods to probe quantum geometry beyond the zero-temperature regime.

cond-mat.mes-hall↗

arXiv2024

Relocalization of Uranium 5f Electrons in Antiferromagnetic Heavy Fermion Superconductor UPd$_2$Al$_3$: Insights from Angle-Resolved Photoemission Spectroscopy

We investigate the antiferromagnetic heavy fermion superconductor UPd$_2$Al$_3$, employing angle-resolved photoemission spectroscopy to unravel the complex electronic structure of its U 5f electrons. We observe unexpected characteristics that challenge the conventional temperature-dependent behavior of heavy fermion systems, revealing unexpected characteristics. At temperatures above the anticipated coherence temperature (T$^*$), we observe itinerant U 5f electrons at temperatures higher than previously postulated. Additionally, a previously unidentified dispersionless band emerges around 600 meV below the Fermi energy, potentially linked to spin-orbit splitting within the U 5f states. Hybridization between the 5f electrons and conduction band was observed with an energy dispersion of 10 meV at low temperatures, suggesting that U 5f electrons near and at the Fermi surface have an itinerant nature. Temperature-dependent 5d-5f resonance spectra reveal that the 5f electron spectrum weight increases with lowering temperature and begins to decrease at temperatures significantly higher than the Neel temperature (T$_N$). We further show that the competition between the Kondo effect and Ruderman-Kittel-Kasuya-Yosida (RKKY) interactions may be responsible for the relocalization of 5f electrons, making relocalization a precursor to the establishment of magnetic order at lower temperatures. Our experiments also provide evidence that 5f electrons with the same orbital are involved in both the Kondo effect and RKKY interactions, suggesting that the two coexist at lower temperatures.

cond-mat.str-el↗

arXiv2022

The cumulant Green's functions method for the Hubbard model

We study the single-band Hubbard model under the action of an external magnetic field using the cumulant Green's functions method (CGFM). The starting point of the method is to diagonalize a cluster containing N correlated sites (seed) and employ the cumulants calculated from the cluster solution to obtain the full Green's functions for the lattice. All calculations are done directly, and no self-consistent process is needed. We benchmark the one-dimensional results for the gap, the ground-state energy, and the double occupancy obtained from the CGFM against the corresponding exact results of the thermodynamic Bethe ansatz and the quantum transfer matrix methods. The results for the CGFM tend systematically to the exact one as the cluster size increases. The particle-hole symmetry of the density of states is fulfilled. The method can be applied to any parameter space for one, two, or three-dimensional Hubbard Hamiltonians and can also be extended to other strongly correlated models, like the Anderson Hamiltonian, the t-J, Kondo, and Coqblin-Schrieffer models. We also calculate the effects of positive magnetic fields as a function of the chemical potential, and we identify a finite cluster effect (Phase VI) characterized by a partially filled band and negative magnetization (n_up < n_down). This phase survives for clusters containing up to N=8 sites but tends to disappear as the size of the cluster increases. We include a simple application to spintronics, where we used these clusters as correlated quantum dots to realize a single-electron transistor when connected to Hubbard leads. We calculate the phase diagram, including the new cluster phase, using the magnetic field and chemical potential as parameters for N=7 and N=8.

cond-mat.str-el↗