The sign problem limits determinant quantum Monte Carlo studies of strongly correlated fermion systems. In the spin-channel Hubbard-Stratonovich decoupling, spin correlations are exactly related to auxiliary-field correlations. This relation implies that an antiferromagnetic transition reorganizes auxiliary-field configurations and thereby changes the statistical structure of the resulting fermion matrices. We use the adjacent gap ratio of low-lying singular values of the space-time fermion matrix to probe interaction-driven transitions in two half-filled honeycomb-lattice Hubbard models. In the sign-free honeycomb Hubbard model, the statistic tracks the established transition from a Dirac semimetal to an antiferromagnetic Mott insulator. In the complex-weight Haldane-Hubbard model, the transition-sensitive feature remains visible in the phase-quenched reference ensemble and occurs near previous estimates of the transition. Moreover, phase reweighting only weakly modifies the gap ratio over the regimes investigated, despite the rapid suppression of the average phase. These results establish singular-value statistics as a sign-problem-resilient probe of interaction-driven transitions in determinant quantum Monte Carlo.The sign problem limits determinant quantum Monte Carlo studies of strongly correlated fermion systems. In the spin-channel Hubbard-Stratonovich decoupling, spin correlations are exactly related to auxiliary-field correlations. This relation implies that an antiferromagnetic transition reorganizes auxiliary-field configurations and thereby changes the statistical structure of the resulting fermion matrices. We use the adjacent gap ratio of low-lying singular values of the space-time fermion matrix to probe interaction-driven transitions in two half-filled honeycomb-lattice Hubbard models. In the sign-free honeycomb Hubbard model, the statistic tracks the established transition from a Dirac semimetal to an antiferromagnetic Mott insulator. In the complex-weight Haldane-Hubbard model, the transition-sensitive feature remains visible in the phase-quenched reference ensemble and occurs near previous estimates of the transition. Moreover, phase reweighting only weakly modifies the gap ratio over the regimes investigated, despite the rapid suppression of the average phase. These results establish singular-value statistics as a sign-problem-resilient probe of interaction-driven transitions in determinant quantum Monte Carlo.

arXiv:2608.19028Aug 19, 20260 citations

Mitigating the sign problem for non-relativistic fermions on the lattice

Andrei B. Kryjevski

APSFeb 1, 20100 citations

Solution to new sign problems with Hamiltonian Lattice Fermions

Emilie Huffman

We present a solution to the sign problem in a class of particle-hole symmetric Hamiltonian lattice fermion models on bipartite lattices using the idea of fermion bags. The solution remains valid when the particle-hole symmetry is broken through a staggered chemical potential term. This solution allows, for the first time, simulations of some massless four-fermion models with minimal fermion doubling and with an odd number of fermion flavors using ultra-local actions. One can thus study a variety of quantum phase transitions that have remained unexplored so far due to sign problems.We present a solution to the sign problem in a class of particle-hole symmetric Hamiltonian lattice fermion models on bipartite lattices using the idea of fermion bags. The solution remains valid when the particle-hole symmetry is broken through a staggered chemical potential term. This solution allows, for the first time, simulations of some massless four-fermion models with minimal fermion doubling and with an odd number of fermion flavors using ultra-local actions. One can thus study a variety of quantum phase transitions that have remained unexplored so far due to sign problems.

arXiv:1411.7147International Symposium on Lattice Field Theory (LATTICE)May 21, 20150 citations

Mott Transition in Strongly Correlated Fermionic Systems: Hubbard Model Review

Moukouri Mikano Jonas, Ndjacka Jean-Marie Bienvenu, Jeannot Mane Mane +8 more

International Journal of Scientific and Research PublicationsOct 24, 20220 citations

Projection of infinite- U Hubbard model and algebraic sign structure

Yunqing Ouyang, Xiao Yan Xu

We propose a projection approach to perform quantum Monte Carlo (QMC) simulation on the infinite- $U$ Hubbard model at some integer fillings where either it is sign problem free or surprisingly has an algebraic sign structure---a power law dependence of average sign on system size. We demonstrate our scheme on the infinite- $U\phantom{\rule{4pt}{0ex}}SU(2N)$ fermionic Hubbard model on both a square and honeycomb lattice at half filling, where it is sign problem free, and suggest possible correlated ground states. The method can be generalized to study certain extended Hubbard models applying to cluster Mott insulators or two-dimensional Moir\'e systems; among one of them at certain non-half-integer filling, the sign has an algebraic behavior such that it can be numerically solved within a polynomial time. Further, our projection scheme can also be generalized to implement the Gutzwiller projection to spin basis such that $SU(2N)$ quantum spin models and Kondo lattice models may be studied in the framework of fermionic QMC simulations.We propose a projection approach to perform quantum Monte Carlo (QMC) simulation on the infinite-$U$ Hubbard model at some integer fillings where either it is sign problem free or surprisingly has an algebraic sign structure---a power law dependence of average sign on system size. We demonstrate our scheme on the infinite-$U\phantom{\rule{4pt}{0ex}}SU(2N)$ fermionic Hubbard model on both a square and honeycomb lattice at half filling, where it is sign problem free, and suggest possible correlated ground states. The method can be generalized to study certain extended Hubbard models applying to cluster Mott insulators or two-dimensional Moir\'e systems; among one of them at certain non-half-integer filling, the sign has an algebraic behavior such that it can be numerically solved within a polynomial time. Further, our projection scheme can also be generalized to implement the Gutzwiller projection to spin basis such that $SU(2N)$ quantum spin models and Kondo lattice models may be studied in the framework of fermionic QMC simulations.

arXiv:2108.04832Physical review. B./Physical review. BDec 14, 202115 citations

We propose a projection approach to perform quantum Monte Carlo (QMC) simulation on the infinite-

U

Hubbard model at some integer fillings where either it is sign problem free or surprisingly has an algebraic sign structure---a power law dependence of average sign on system size. We demonstrate our scheme on the infinite-

U\phantom{\rule{4pt}{0ex}}SU(2N)

fermionic Hubbard model on both a square and honeycomb lattice at half filling, where it is sign problem free, and suggest possible correlated ground states. The method can be generalized to study certain extended Hubbard models applying to cluster Mott insulators or two-dimensional Moir\'e systems; among one of them at certain non-half-integer filling, the sign has an algebraic behavior such that it can be numerically solved within a polynomial time. Further, our projection scheme can also be generalized to implement the Gutzwiller projection to spin basis such that

SU(2N)

quantum spin models and Kondo lattice models may be studied in the framework of fermionic QMC simulations.