New Developments in Diagrammatic Monte Carlo for Interacting Lattice Fermions: Efficient Algorithms and Applications
Abstract
This thesis develops diagrammatic methods for thermodynamic and subsystem quantities of interacting lattice fermions, providing reference calculations for quantum simulators and many-body approximations. I formulate an inverse-flavour expansion about a self-consistent Hartree saddle, enumerate non-Gaussian diagrams, and use a discrete Lehmann representation to integrate selected internal vertices analytically. Density results cover 31 state points of the six-flavour Hubbard model on a 70×70 lattice at T/t=0.15. I generalize combinatorial summation to flavour-dependent propagators and expansion shifts. CoS++ combines partial contractions to obtain connected sums for interaction subsets. A determinant-polynomial sieve evaluates the same sums through local coefficient filters; at ninth order it is 24--25 times faster than the specified CoS baselines in three-flavour dense-random-matrix benchmarks. Thermodynamic applications include a 2048-site honeycomb lattice and a three-flavour square lattice with 1024 sites. For the second Renyi entropy, I derive a fermionic replica path integral and a stable evaluation of its two-time Green functions. The connected-determinant calculation reaches tenth order on a 3×3 cluster and ninth order on larger lattices. On 50×50 sites at (U/t,μ/t,βt)=(3,1,8), the ninth-order continuation at shift α=1.3 gives S2/Ns=0.06695 with propagated Monte Carlo uncertainty 3.0×10−5. Comparing two expansion shifts at their respective retained orders gives an endpoint difference of 2.6×10−4.
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BibTeX
@misc{shi2026developments,
title = {{New Developments in Diagrammatic Monte Carlo for Interacting Lattice Fermions: Efficient Algorithms and Applications}},
author = {Boyuan Shi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.37505},
eprint = {2610.37505},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.37505},
}
RIS
TY - UNPB
TI - New Developments in Diagrammatic Monte Carlo for Interacting Lattice Fermions: Efficient Algorithms and Applications
AU - Boyuan Shi
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.37505
UR - https://arxiv.org/abs/2610.37505
AB - This thesis develops diagrammatic methods for thermodynamic and subsystem quantities of interacting lattice fermions, providing reference calculations for quantum simulators and many-body approximations. I formulate an inverse-flavour expansion about a self-consistent Hartree saddle, enumerate non-Gaussian diagrams, and use a discrete Lehmann representation to integrate selected internal vertices analytically. Density results cover 31 state points of the six-flavour Hubbard model on a 70×70 lattice at T/t=0.15. I generalize combinatorial summation to flavour-dependent propagators and expansion shifts. CoS++ combines partial contractions to obtain connected sums for interaction subsets. A determinant-polynomial sieve evaluates the same sums through local coefficient filters; at ninth order it is 24--25 times faster than the specified CoS baselines in three-flavour dense-random-matrix benchmarks. Thermodynamic applications include a 2048-site honeycomb lattice and a three-flavour square lattice with 1024 sites. For the second Renyi entropy, I derive a fermionic replica path integral and a stable evaluation of its two-time Green functions. The connected-determinant calculation reaches tenth order on a 3×3 cluster and ninth order on larger lattices. On 50×50 sites at (U/t,μ/t,βt)=(3,1,8), the ninth-order continuation at shift α=1.3 gives S_2/N_s=0.06695 with propagated Monte Carlo uncertainty 3.0×10^−5. Comparing two expansion shifts at their respective retained orders gives an endpoint difference of 2.6×10^−4.
ER -