Research Experiences for Undergraduates in Computational Methods with Applications in Materials Science
MSU Affiliation
College of Arts and Sciences; Department of Physics and Astronomy; Center for Computational Sciences
Research Mentor
Rudolf Torsten Clay
Creation Date
7-25-2025
Abstract
The mechanism of superconductivity (SC) in high critical temperature cuprate superconductors remains an unsolved problem. The simplest electronic model of cuprate superconductors is the one band Hubbard model. It models copper atom positions with lattice sites, omitting oxygen atoms for simplicity, and separates the Hamiltonian into hopping (t,t) and interaction (U) components. The simplest Hubbard model only considers nearest neighbor hopping, t. To account for overlap between oxygen orbitals also requires next nearest neighbor hopping, t'. Exact solutions of the model are computationally prohibitive to find for large systems. Quantum Monte Carlo (QMC) methods such as Constrained Path Monte Carlo (CPMC) can be used in cases where exact methods cannot. Constraining the imaginary time path removes the Fermion sign problem caused by sign degeneracy of Slater determinants. However, an additional approximate technique known as back propagation must also be used to measure any quantity besides the energy within CPMC. A newly proposed released constraint measurement method instead releases the path constraint of CPMC for short intervals. This is more accurate but reintroduces the sign problem. We present the first calculations of superconducting pair-pair correlations in the Hubbard model using the released constraint technique. Our results show that in general back propagation tends to underestimate long- range superconducting pairing in the Hubbard model. Recent work using CPMC has suggested that SC does exist in the lightly doped two-dimensional Hubbard model. Our results show that superconducting pair-pair correlations continuously weaken with increasing U, suggesting that SC is not present.
Presentation Date
Summer 7-31-2025
Keywords
superconductivity, cuprates, Hubbard model, computational physics
Recommended Citation
Roberts, Jodie and Clay, Rudolf Torsten, "Absence of Superconductivity in the lightly doped Hubbard model" (2025). Research Experiences for Undergraduates in Computational Methods with Applications in Materials Science. 8.
https://scholarsjunction.msstate.edu/ccs-reu/8
