arXiv subjects

Yunqing Ouyang

Publications and source records attributed to Yunqing Ouyang.

3 recordsLinked to original sources

arXiv2021

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

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-$U$ $SU(2N)$ 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 Moiré 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.

cond-mat.str-el↗

arXiv2021

Computing classification of interacting fermionic symmetry-protected topological phases using topological invariants

In recent years, great success has been achieved on the classification of symmetry-protected topological (SPT) phases for interacting fermion systems by using generalized cohomology theory. However, the explicit calculation of generalized cohomology theory is extremely hard due to the difficulty of computing obstruction functions. In this paper, based on the physical picture of topological invariants and mathematical techniques in homotopy algebra, we develop an algorithm to resolve this hard problem. It is well known that cochains in the cohomology of the symmetry group, which are used to enumerate the SPT phases, can be expressed equivalently in different linear bases, known as the resolutions. By expressing the cochains in a reduced resolution containing much fewer basis than the choice commonly used in previous studies, the computational cost is drastically reduced. In particular, it reduces the computational cost for infinite discrete symmetry groups, like the wallpaper groups and space groups, from infinity to finity. As examples, we compute the classification of two-dimensional interacting fermionic SPT phases, for all 17 wallpaper symmetry groups

cond-mat.str-el↗

arXiv2018

Equivalent-neighbor percolation models in two dimensions: crossover between mean-field and short-range behavior

We investigate the influence of the range of interactions in the two-dimensional bond percolation model, by means of Monte Carlo simulations. We locate the phase transitions for several interaction ranges, as expressed by the number $z$ of equivalent neighbors. We also consider the $z \to \infty$ limit, i.e., the complete graph case, where percolation bonds are allowed between each pair of sites, and the model becomes mean-field-like. All investigated models with finite $z$ are found to belong to the short-range universality class. There is no evidence of a tricritical point separating the short-range and long-range behavior, such as is known to occur for $q=3$ and $q=4$ Potts models. We determine the renormalization exponent describing a finite-range perturbation at the mean-field limit as $y_r \approx 2/3$. Its relevance confirms the continuous crossover from mean-field percolation universality to short-range percolation universality. For finite interaction ranges, we find approximate relations between the coordination numbers and the amplitudes of the leading correction terms as found in the finite-size scaling analysis.

cond-mat.stat-mech↗