Fermion bag study of the two-dimensional Majorana-Hubbard model at finite hopping
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≲ 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.
Related
- Superconductivity in the Repulsive Hubbard Model on Different Geometries Induced by Density-Assisted Hopping
- Transport theory for a generic two-arm co-propagating Majorana interferometer with Majorana fermion and edge vortex tunneling
- Soft Breaking Naturalness in Majorana Fermion Loop induced Scalar and Majoron Amplitudes
- Exact SU(N) symmetry resolution of bosonic Hubbard models: general boson-fermion mappings and flat-band singlet-cluster states
- Vortex-core Majorana coupling to a chiral edge in a px+ipy superconductor: Nonmonotonic spectral reorganization and coherent fermion-parity dynamics
BibTeX
@misc{johnston2026fermion,
title = {{Fermion bag study of the two-dimensional Majorana-Hubbard model at finite hopping}},
author = {Mark Johnston and Emilie Huffman},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.26881},
eprint = {2609.26881},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.26881},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Fermion bag study of the two-dimensional Majorana-Hubbard model at finite hopping
AU - Mark Johnston
AU - Emilie Huffman
PY - 2026
DA - 2026/09/22
PB - arXiv
DO - 10.48550/arxiv.2609.26881
UR - https://arxiv.org/abs/2609.26881
AB - 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≲ 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.
ER -