arXiv subjects

Boyuan Shi

Publications and source records attributed to Boyuan Shi.

5 recordsLinked to original sources

arXiv2026

Diagrammatic Monte Carlo for Fermionic R\'enyi Entanglement Entropy

We develop a direct diagrammatic Monte Carlo framework for the Renyi entanglement entropy of interacting lattice fermions. The method starts from the fermionic graded-swap representation of Z_n[A]=Tr_A\rho_A^n, which converts the entropy problem into a replicated path integral with mixed temporal boundary conditions on the entangling region. In this representation the replica momenta are half-shifted, q_m=(2m+1)\pi/n, and the interaction expansion has a determinant form suitable for connected-determinant summation. We combine this expansion with a many-configuration Markov-chain Monte Carlo sampler to obtain order-by-order corrections for very large systems to very high orders. As a benchmark, we compare the order-by-order coefficients of a 3*3 Hubbard cluster with exact diagonalization. We then report a production calculation for a large periodic lattice with a square subregions. The dominant system-size limitation is therefore memory rather than a conventional auxiliary-field sign problem. The results provide a step toward diagrammatic calculations of fermionic entanglement observables in regimes where direct quantum Monte Carlo sampling is costly or sign-problem limited.

cond-mat.str-el↗

arXiv2025

CoS++: Towards More General and Explicit Implementations for Sampling High-Order Feynman Diagrammatic Series

Diagrammatic Monte Carlo methods provide robust routines for accurate computations of correlated electronic systems in the thermodynamical limit. Recently, its versatility was extended to SU(N) Hubbard model, where the core is a novel dynamical programming approach to the summation of all connected Feynman diagrams. We present several generalizations of it with more interaction vertices and symmetry broken terms. The framework treats SU(N) symmetry breaking both from nonuniform, flavor-dependent chemical potentials and from spontaneously broken phases induced by shift parameters. We also provide an end-to-end GPU acceleration path with dedicated CUDA C++ optimizations independent of a previous CUDA acceleration approach, where the parallelization strategy is different. We performed detailed numerical study of new algorithms involved in this article and exposed numerical instabilities of connected determinant formalism, which we solved in multiple ways. Together, these advances establish a scalable, high-performance DiagMC toolbox for multi-flavor correlated systems with and without symmetry breaking.

cond-mat.str-el↗

arXiv2025

Fast summation of fermionic Feynman diagrams beyond Bravais Lattices and on-site Hubbard interactions

We designed new algorithms for summing bold-line Feynman diagrams in arbitrary channels, where it can be readily modified for bare interaction series as well. When applied to magnetic channel bold-line series with on-site Hubbard interactions, the algorithm achieves competitive performance compared with the state-of-art RPADet. We then generalize it beyond square lattice and on-site Hubbard interactions and achieve better scaling in the number of sites within a unit cell, while there is substantial increase when there are more types of interactions. This work paves the way of diagrammatic Monte Carlo simulations for real materials, holding the premise for a robust replacement of state-of-art simulation tools in the thermodynamical limit.

cond-mat.str-el↗

arXiv2024

Semi-Deterministic and Stochastic Sampling of Feynman Diagrams with 1/N$_f$ Expansions

We introduce a family of (semi) bold-line series, assisted with $1/\text{N}_{f}$ expansions, with $\text{N}_{f}$ being the number of fermion flavours. If there is no additional $\mathrm{N}_{f}$ cut, the series reduces to the RPA series in the density-density channel, complementary to the particle-hole and particle-particle channels introduced in [Phys. Rev. B $\textbf{102}$, 195122 (2020)]. We performed extensive benchmarks for density, energy and pressure with $\mathrm{t}-\mathrm{t}'$ $\mathrm{SU}(\mathrm{N}_{f})$ Hubbard model on square lattice and honeycomb lattices over a wide range of numerical methods. For benchmark purposes, we also implement bare-$\mathrm{U}$ symmetry-broken perturbation series for the 2D SU(2) Hubbard model on the honeycomb lattice, where we found encouraging results from weak to intermediate couplings.

cond-mat.str-el↗

arXiv2024

Quantum simulations of time-dependent Hamiltonians beyond the quasi-static approximation

Existing approaches to analogue quantum simulations of time-dependent quantum systems rely on perturbative corrections to quantum simulations of time-independent quantum systems. We overcome this restriction to perturbative treatments with an approach based on flow equations and a multi-mode Fourier expansion. The potential of the quantum simulations that can be achieved with our approach is demonstrated with the pedagogical example of a Lambda-system and the quench in finite time through a quantum phase transition of a Chern insulator in a driven non-interacting Hubbard system. The example of the Lambda-system demonstrates the ability of our approach to describe situations beyond the validity of adiabatic approximations.

quant-ph↗