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Projection of Infinite-$U$ Hubbard Model and Algebraic Sign Structure

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 Added by Xiao Yan Xu
 Publication date 2021
  fields Physics
and research's language is English




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The repulsive fermionic Hubbard model is a typical model describing correlated electronic systems. Although it is a simple model with only a kinetic term and a local interaction term, their competition generates rich phases. When the interaction part is significant, usually in many strongly correlated, flat or narrow band systems, lots of novel correlated phases may emerge. One way to understand the possible correlated phases is to go beyond finite interaction and solve the infinite-$U$ Hubbard model. Solving infinite-$U$ Hubbard model is usually extremely hard, and a large-scale unbiased numerical study is still missing. In this Letter, we propose a projection approach, such that a controllable quantum Monte Carlo (QMC) simulation on infinite-$U$ Hubbard model may be done 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-$U$ $SU(2N)$ fermionic Hubbard model on both 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 2D Morie 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.



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We demonstrate that the sign structure of the t-J model on a hypercubic lattice is entirely different from that of a Fermi gas, by inspecting the high temperature expansion of the partition function up to all orders, as well as the multi-hole propagator of the half-filled state and the perturbative expansion of the ground state energy. We show that while the fermion signs can be completely gauged away by a Marshall sign transformation at half-filling, the bulk of the signs can be also gauged away in a doped case, leaving behind a rarified irreducible sign structure that can be enumerated easily by counting exchanges of holes with themselves and spins on their real space paths. Such a sparse sign structure implies a mutual statistics for the quantum states of the doped Mott insulator.
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