Augmenting Density Matrix Renormalization Group with Disentanglers
Xiangjian Qian and Mingpu Qin*
Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
Abstract：Density matrix renormalization group (DMRG) and its extensions in the form of matrix product states are arguably the choice for the study of one-dimensional quantum systems in the last three decades. However, due to the limited entanglement encoded in the wave-function ansatz, to maintain the accuracy of DMRG with the increase of the system size in the study of two-dimensional systems, exponentially increased resources are required, which limits the applicability of DMRG to only narrow systems. We introduce a new ansatz in which DMRG is augmented with disentanglers to encode area-law-like entanglement entropy (entanglement entropy supported in the new ansatz scales as $l$ for an $l \times l$ system). In the new method, the $O(D^3)$ low computational cost of DMRG is kept (with an overhead of $O(d^4)$ and $d$ the dimension of the physical degrees of freedom). We perform benchmark calculations with this approach on the two-dimensional transverse Ising and Heisenberg models. This new ansatz extends the power of DMRG in the study of two-dimensional quantum systems.
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By contracting the additional disentangler layer in Fig. (c) into the original MPS wave-function, the effective bond dimension for the resulting MPS is much larger than the original MPS. Thus, the FAMPS is a more entangled wave-function than the MPS.
2023, Vol. 40 
