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.

arXiv comment5 pages, 4 figures, with supplementary materials, close to the published version

References in corpus (67)

• The density-matrix renormalization group in the age of matrix product states
• The density-matrix renormalization group
• Area laws for the entanglement entropy - a review
• Entanglement in quantum critical phenomena
• Entropy and Area
• Real time evolution using the density matrix renormalization group
• Spin Liquid Ground State of the $S=1/2$ Kagome Heisenberg Model
• Entanglement renormalization
• Thermodynamic limit of the density matrix renormalization for the spin-1 Heisenberg chain
• A class of quantum many-body states that can be efficiently simulated
• Matrix Product States and Projected Entangled Pair States: Concepts, Symmetries, and Theorems
• Quantum Monte Carlo with Directed Loops
• Time-evolution methods for matrix-product states
• Criticality, the area law, and the computational power of PEPS
• Stripe order in the underdoped region of the two-dimensional Hubbard model
• Tensor networks for complex quantum systems
• Finite-Size Scaling of the Ground State Parameters of the Two-Dimensional Heisenberg Model
• Solutions of the Two Dimensional Hubbard Model: Benchmarks and Results from a Wide Range of Numerical Algorithms
• Exactly solvable Richardson-Gaudin models for many-body quantum systems
• Hand-waving and Interpretive Dance: An Introductory Course on Tensor Networks
• Entropy, entanglement, and area: analytical results for harmonic lattice systems
• Studying Two Dimensional Systems With the Density Matrix Renormalization Group
• Gapless spin-liquid ground state in the $S=1/2$ kagome antiferromagnet
• Algorithms for entanglement renormalization
• Absence of superconductivity in the pure two-dimensional Hubbard model
• Tensor network states and algorithms in the presence of a global U(1) symmetry
• Plaquette Ordered Phase and Quantum Phase Diagram in the Spin-1/2 J1-J2 Square Heisenberg Model
• Fractional excitations in the square-lattice quantum antiferromagnet
• Study of the Two-Dimensional Frustrated J1-J2 Model with Neural Network Quantum States
• Differentiable Programming Tensor Networks
• Unbiasing Fermionic Quantum Monte Carlo with a Quantum Computer
• Algorithms for finite Projected Entangled Pair States
• Direct evidence for a gapless $Z_2$ spin liquid by frustrating Néel antiferromagnetism
• Frustrated antiferromagnets with entanglement renormalization: ground state of the spin-1/2 Heisenberg model on a kagome lattice
• Matrix Product States for dynamical simulation of infinite chains
• Crystals of bound states in the magnetization plateaus of the Shastry-Sutherland model
• Entanglement renormalization in two spatial dimensions
• Encoding of Matrix Product States into Quantum Circuits of One- and Two-Qubit Gates
• Tensor renormalization of quantum many-body systems using projected entangled simplex states
• The Tensor Networks Anthology: Simulation techniques for many-body quantum lattice systems
• Dirac-type nodal spin liquid revealed by refined quantum many-body solver using neural-network wave function, correlation ratio, and level spectroscopy
• Ground State Phase Diagram of the $t$-$t^{\prime }$-$J$ model
• Faster Methods for Contracting Infinite 2D Tensor Networks
• High Temperature Superconductivity in a Lightly Doped Quantum Spin Liquid
• Robust d-wave superconductivity in the square-lattice $t$-$J$ model
• Gapless quantum spin liquid and global phase diagram of the spin-1/2 $J_1$-$J_2$ square antiferromagnetic Heisenberg model
• One-dimensional Continuum Electronic Structure with the Density Matrix Renormalization Group and Its Implications For Density Functional Theory
• A two-dimensional algorithm of the density matrix renormalization group
• Fractional entropy of multichannel Kondo systems from conductance-charge relations
• Efficient Tensor Network ansatz for high-dimensional quantum many-body problems
• Density Matrix Renormalization Group Study of the Haldane Phase in Random One-Dimensional Antiferromagnets
• Two-dimensional quantum liquids from interacting non-Abelian anyons
• Optimized contraction scheme for tensor-network states
• Accurate simulation for finite projected entangled pair states in two dimensions
• MERA for Spin Chains with Continuously Varying Criticality
• Variational methods for contracting projected entangled-pair states
• Long-range phase order in two dimensions under shear flow
• Hilbert curve vs Hilbert space: exploiting fractal 2D covering to increase tensor network efficiency
• Exactly Solvable Points and Symmetry-Protected Topological Phases of Quantum Spins on a Zig-Zag Lattice
• Projected Entangled Pair States: Fundamental analytical and numerical limitations
• Quantum phase transition of a two-dimensional quadrupolar system
• Abelian and non-abelian symmetries in infinite projected entangled pair states
• Matrix Product States with Backflow correlations
• Molecular Impurities as a Realization of Anyons on the Two-Sphere
• From Tree Tensor Network to Multiscale Entanglement Renormalization Ansatz
• Combination of Tensor Network States and Green's function Monte Carlo
• Exact solution of an integrable anisotropic $J_1-J_2$ spin chain model

Cited by in corpus (11)

• Augmenting Density Matrix Renormalization Group with Clifford Circuits
• Absence of spin liquid phase in the $J_1-J_2$ Heisenberg model on the square lattice
• Stabilizer disentangling of conformal field theories
• Variational optimization of the amplitude of neural-network quantum many-body ground states
• 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