Augmenting Density Matrix Renormalization Group with Disentanglers

Abstract

Density Matrix Renormalization Group (DMRG) and its extensions in the form of Matrix Product States (MPS) 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. In this work, 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 a $l\times l$ 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 degree 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.

5 pages, 4 figures, with supplementary materials, close to the published version

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• Disentangling critical quantum spin chains with Clifford circuits
• Disentangling Interacting Systems with Fermionic Gaussian Circuits: Application to Quantum Impurity Models
• On the Magnetization of the $120^{\circ }$ order of the Spin-1/2 Triangular Lattice Heisenberg Model: a DMRG revisit
• Designs from magic-augmented Clifford circuits
• Plaquette-type valence bond solid state in the $J_1$-$J_2$ square-lattice Heisenberg model
• From the Shastry-Sutherland model to the $J_1$-$J_2$ Heisenberg model
• Parent Hamiltonian for Fully-augmented Matrix Product States