arXiv subjects

Shao-Jun Dong

Publications and source records attributed to Shao-Jun Dong.

6 recordsLinked to original sources

arXiv2021

Hybrid convolutional neural network and PEPS wave functions for quantum many-particle states

Neural networks have been used as variational wave functions for quantum many-particle problems. It has been shown that the correct sign structure is crucial to obtain the high accurate ground state energies. In this work, we propose a hybrid wave function combining the convolutional neural network (CNN) and projected entangled pair states (PEPS), in which the sign structures are determined by the PEPS, and the amplitudes of the wave functions are provided by CNN. We benchmark the ansatz on the highly frustrated spin-1/2 $J_1$-$J_2$ model. We show that the achieved ground energies are competitive to state-of-the-art results.

cond-mat.str-el↗

arXiv2019

Stable diagonal stripes in the t-J model at $\bar{n}_h$=1/8 doping from fPEPS calculations

We investigate the 2D t-J model at a hole doping of $\bar{n}_h$=1/8 using recently developed high accuracy fermionic projected entangled pair states(fPEPS) method. By applying stochastic gradient descent method combined with Monte Carlo sampling technique, we obtain the ground state hole energy $E_{\rm hole}$=-1.6186 for $J/t$=0.4. We show that the ground state has stable diagonal stripes instead of vertical stripes with width of 4 unit cells, and stripe filling $ρ_l$=0.5. We further show that the long range superconductivity order is suppressed at this point.

cond-mat.str-el↗

arXiv2019

Gradient optimization of fermionic projected entangled pair states on directed lattices

The recently developed stochastic gradient method combined with Monte Carlo sampling techniques [PRB {\bf 95}, 195154 (2017)] offers a low scaling and accurate method to optimize the projected entangled pair states (PEPS). We extended this method to the fermionic PEPS (fPEPS). To simplify the implementation, we introduce a fermi arrow notation to specify the order of the fermion operators in the virtual entangled EPR pairs. By defining some local operation rules associated with the fermi arrows, one can implement fPEPS algorithms very similar to that of standard PEPS. We benchmark the method for the interacting spinless fermion models, and the t-J models. The numerical calculations show that the gradient optimization greatly improves the results of simple update method. Furthermore, much larger virtual bond dimensions ($D$) and truncation dimensions ($D_c$) than those of boson and spin systems are necessary to converge the results. The method therefore offer a powerful tool to simulate fermion systems because it has much lower scaling than the direct contraction methods.

cond-mat.str-el↗

arXiv2017

TNSPackage: A Fortran2003 library designed for tensor network state methods

Recently, the tensor network states (TNS) methods have proven to be very powerful tools to investigate the strongly correlated many-particle physics in one and two dimensions. The implementation of TNS methods depends heavily on the operations of tensors, including contraction, permutation, reshaping tensors, SVD and son on. Unfortunately, the most popular computer languages for scientific computation, such as Fortran and C/C++ do not have a standard library for such operations, and therefore make the coding of TNS very tedious. We develop a Fortran2003 package that includes all kinds of basic tensor operations designed for TNS. It is user-friendly and flexible for different forms of TNS, and therefore greatly simplifies the coding work for the TNS methods.

cond-mat.str-el↗

arXiv2017

Tunneling frustration induced peculiar supersolid phases in the extended Bose-Hubbard model

By using a state of art tensor network state method, we study the ground-state phase diagram of an extended Bose-Hubbard model on the square lattice with frustrated next-nearest neighboring tunneling. In the hardcore limit, tunneling frustration stabilizes a peculiar half supersolid (HSS) phase with one sublattice being superfluid and the other sublattice being Mott Insulator away from half filling. In the softcore case, the model shows very rich phase diagrams above half filling, including three different types of supersolid phases depending on the interaction parameters. The considered model provides a promising route to experimentally search for novel stable supersolid state induced by frustrated tunneling in below half filling region with dipolar atoms or molecules.

cond-mat.str-el↗

arXiv2017

Gradient optimization of finite projected entangled pair states

The projected entangled pair states (PEPS) methods have been proved to be powerful tools to solve the strongly correlated quantum many-body problems in two-dimension. However, due to the high computational scaling with the virtual bond dimension $D$, in a practical application PEPS are often limited to rather small bond dimensions, which may not be large enough for some highly entangled systems, for instance, the frustrated systems. The optimization of the ground state using time evolution method with simple update scheme may go to a larger bond dimension. However, the accuracy of the rough approximation to the environment of the local tensors is questionable. Here, we demonstrate that combining the time evolution method with simple update, Monte Carlo sampling techniques and gradient optimization will offer an efficient method to calculate the PEPS ground state. By taking the advantages of massive parallel computing, we can study the quantum systems with larger bond dimensions up to $D$=10 without resorting to any symmetry. Benchmark tests of the method on the $J_1$-$J_2$ model give impressive accuracy compared with exact results.

quant-ph↗