Year: 2026
Type: preprint
Abstract: The two-dimensional Majorana-Hubbard model on the $π$-flux lattice involves the most local interaction possible for a lattice with one relativistic Majorana fermion per site. It is predicted to host a Majorana semimetal, dimerized phases, and quantum-critical points with an emergent $U(1)$ symmetry. Nonperturbative lattice calculations for this model remain a major open challenge, thus far limited to zero hopping. We present quantum Monte Carlo simulations of the model at finite hopping using Hamiltonian fermion bags, which are based on a continuous-time expansion with Boltzmann weights that are Pfaffians of a matrix with dimension set by the expansion order, and which give the sign of the weight. Sign problem severity is related to the location of zero modes in the free hopping matrix, and for couplings $g\lesssim 0.7$ and $β=L/4$ it is fully removed for lattices up to at least $256$ sites. The interaction strength $g>0$ enhances the $U(1)$-charged dimerization doublet and suppresses the neutral channel, as the renormalization group predicts. Increasing the interactions also restores $U(1)$ symmetry in the component of the dimerization correlator that is even under bond orientation exchange, but not its odd component. There is a persistent anisotropy in the odd component with the symmetry of a lattice nematic. The data is consistent with a gapless semimetal throughout the sign-problem-minimal window.
Source: arXiv (Cornell University)
Authors: Johnston, Mark, Huffman, Emilie
Institution: Wake Forest University
Language: English
Subfield: Condensed Matter Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Awards: G1453181110, Track 4: Advanced CI Coordination Ecosystem: Monitoring and Measurement Services, G3562386289, Track 1: ACCESS Resource Allocations Marketplace and Platform Services (RAMPS), G4010157413, ACO: An Open CI Ecosystem to Advance Scientific Discovery (OpenCI), Track 3: COre National Ecosystem for CyberinfrasTructure (CONECT), G5367127336, G5398731249, G5464919783, Track 2: Customized Multi-tier Assistance, Training, and Computational Help (MATCH) for End User ACCESS to CI
OpenAlex ID: W7214151717