Cluster Density Matrix Embedding Theory for Quantum Spin Systems

Abstract

We applied cluster density matrix embedding theory, with some modifications, to a spin lattice system. The reduced density matrix of the impurity cluster is embedded in the bath states, which are a set of block-product states. The ground state of the impurity model is formulated using a variational wave function. We tested this theory in a two-dimensional (2-D) spin-1/2 J1-J2 model for a square lattice. The ground-state energy (GSE) and the location of the phase boundaries agree well with the most accurate previous results obtained using the quantum Monte Carlo and coupled cluster methods. Moreover, this cluster density matrix embedding theory is cost-effective and convenient for calculating the von Neumann entropy, which is related to the quantum phase transition.

24 pages, 5figs, accepted by Phys. Rev. B

References in corpus (36)

• Entanglement in quantum critical phenomena
• "Deconfined" quantum critical points
• Cellular Dynamical Mean Field Approach to Strongly Correlated Systems
• Density matrix embedding: A simple alternative to dynamical mean-field theory
• Finite-Size Scaling of the Ground State Parameters of the Two-Dimensional Heisenberg Model
• Spin Liquid Ground State of the Spin-1/2 Square $J_1$-$J_2$ Heisenberg Model
• Cluster Dynamical Mean Field Theory of the Mott Transition
• Resonating Valence Bond Wave Functions for Strongly Frustrated Spin Systems
• Plaquette valence bond solid in the frustrated Heisenberg quantum antiferromagnet on the square lattice
• Dimer Order with Striped Correlations in the J_1-J_2 Heisenberg Model
• Spontaneous plaquette dimerization in the $J_1-J_2$ Heisenberg model
• Ground-state phases of the spin-1/2 J_1-J_2 Heisenberg antiferromagnet on the square lattice: A high-order coupled cluster treatment
• Cluster Dynamical Mean Field analysis of the Mott transition
• Two-site entropy and quantum phase transitions in low-dimensional models
• New valence bond crystal phase of a frustrated spin-1/2 square lattice antiferromagnet
• Exploring frustrated spin-systems using Projected Entangled Pair States (PEPS)
• Truncated Configuration Interaction expansions as solvers for correlated quantum impurity models and dynamical mean field theory
• Dynamical mean-field theory from a quantum chemical perspective
• Density Matrix Embedding from Broken Symmetry Lattice Mean-Fields
• Dynamical Mean Field Theory with the Density Matrix Renormalization Group
• Hierarchical mean-field approach to the $J_1$-$J_2$ Heisenberg model on a square lattice
• Cluster Dynamical Mean-Field Theory of the density-driven Mott transition in the one-dimensional Hubbard model
• A note on cluster methods for strongly correlated electron systems
• Low-energy singlet and triplet excitations in the spin-liquid phase of the two-dimensional J1-J2 model
• Block-block entanglement and quantum phase transitions in one-dimensional extended Hubbard model
• Spin-1/2 J1-J2 Heisenberg antiferromagnet on a square lattice: a plaquette renormalized tensor network study
• The frustrated spin-1/2 J1-J2 Heisenberg ferromagnet on the square lattice: Exact diagonalization and Coupled-Cluster study
• The intermediate and spin-liquid phase of the half-filled honeycomb Hubbard model
• Nonlinear Sigma model method for the J1-J2 Heisenberg model: disordered ground state with plaquette symmetry
• Ising transition in the two-dimensional quantum $J_1-J_2$ Heisenberg model
• Incorporation of Density Matrix Wavefunctions in Monte Carlo Simulations: Application to the Frustrated Heisenberg Model
• Quantum Entanglement in the S=1/2 Spin Ladder with Ring Exchange
• Frustrated Quantum Antiferromagnets: Application of High-Order Coupled Cluster Method
• Quantum phase transition in easy-axis antiferromagnetic Heisenberg spin-1 chain
• Dynamical mean-field theory for quantum spin systems: Test of solutions for magnetically ordered states
• Approximating the ground state of fermion system by multiple determinant states: matching pursuit approach

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