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arXiv:1702.04285 · Physical review. B./Physical review. B

Block product density matrix embedding theory for strongly correlated spin systems

Klaas Gunst, Sebastian Wouters, Stijn De Baerdemacker, Dimitri Van Neck

Published May 11, 2017• 26 citations
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Abstract

Density matrix embedding theory (DMET) is a relatively new technique for the calculation of strongly correlated systems. Recently, block product DMET (BPDMET) was introduced for the study of spin systems such as the antiferromagnetic ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ model on the square lattice. In this paper, we extend the variational Ansatz of BPDMET using spin-state optimization, yielding improved results. We apply the same techniques to the Kitaev-Heisenberg model on the honeycomb lattice, comparing the results when using several types of clusters. Energy profiles and correlation functions are investigated. A diagonalization in the tangent space of the variational approach yields information on the excited states and the corresponding spectral functions.

DOI
10.1103/physrevb.95.195127

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Density matrix embedding theory (DMET) is a relatively new technique for the calculation of strongly correlated systems. Recently, block product DMET (BPDMET) was introduced for the study of spin systems such as the antiferromagnetic J1\ensuremath-J2{J}_{1}\text{\ensuremath{-}}{J}_{2}J1​\ensuremath-J2​ model on the square lattice. In this paper, we extend the variational Ansatz of BPDMET using spin-state optimization, yielding improved results. We apply the same techniques to the Kitaev-Heisenberg model on the honeycomb lattice, comparing the results when using several types of clusters. Energy profiles and correlation functions are investigated. A diagonalization in the tangent space of the variational approach yields information on the excited states and the corresponding spectral functions.
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 spin-1/2 ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ 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.
Density matrix embedding theory (DMET) provides a framework to describe ground-state expectation values in strongly correlated systems, but its extension to dynamical quantities is still an open problem. We show one route to obtaining excitations and dynamical spectral functions by using the techniques of DMET to approximate the matrix elements that arise in a single-mode inspired excitation ansatz. We demonstrate this approach in the 1D Hubbard model, comparing the neutral excitations, single-particle density of states, charge, and spin dynamical structure factors to benchmarks from the Bethe ansatz and density matrix renormalization group. Our work highlights the potential of these ideas in building computationally efficient approaches for dynamical quantities.
We describe an efficient quantum embedding framework for realistic ab initio density matrix embedding theory (DMET) calculations in solids. We discuss in detail the choice of orbitals and mapping to a lattice, treatment of the virtual space and bath truncation, and the lattice-to-embedded integral transformation. We apply DMET in this ab initio framework to a hexagonal boron nitride monolayer, crystalline silicon, and nickel monoxide in the antiferromagnetic phase, using large embedded clusters with up to 300 embedding orbitals. We demonstrate our formulation of ab initio DMET in the computation of ground-state properties such as the total energy, equation of state, magnetic moment, and correlation functions.
We propose an optimized cluster density matrix embedding theory (CDMET). It reduces the computational cost of CDMET with simpler bath states. And the result is as accurate as the original one. As a demonstration, we study the distant correlations of the Heisenberg J 1–J 2 model on the square lattice. We find that the intermediate phase (0.43 ≲ J 2 ≲ 0.62) is divided into two parts. One part is a near-critical region (0.43 ≲ J 2 ≲ 0.50). The other part is the plaquette valence bond solid (PVB) state (0.51 ≲ J 2 ≲ 0.62). The spin correlations decay exponentially as a function of distance in the PVB.
We developed a periodic version of density matrix embedding theory, DMET, with which it is possible to perform electronic structure calculations on periodic systems and compute the band structure of solid-state materials. Electron correlation can be captured by means of a local impurity model using various wave function methods, such as full configuration interaction, coupled cluster, and multiconfigurational methods. The method is able to describe not only the ground-state energy but also the quasiparticle band picture via the real space-momentum space implementation. We investigate the performance of periodic DMET in describing the ground-state energy as well as the electronic band structure for one-dimensional solids. Our results show that DMET is in good agreement with other many-body techniques at a cheaper computational cost. We anticipate that periodic DMET can be a promising first principle method for strongly correlated materials.
We propose a class of variational wave functions, namely the correlated valence bond states, for the frustrated Hamiltonian in the paramagnetic phase. This class of wave functions admits negative amplitude and the same sub-lattice pairing when a bipartite lattice is considered, thus suffers from the negative sign problem. However if applied to small systems, the sign problem is manageable using the standard variational Monte Carlo method. We optimize the wave functions for the J1-J2 Anti ferromagnetic Heisenberg model on a square lattice in the coupling region J2/J1 \in [0.45 : 0.56] for system sizes L = 4, 6, 8. To calculate the correlation functions and the order parameters for larger systems, we make the extensive Monte Carlo samplings using the variational parameters optimized at system size L = 8. We find that the paramagnetic phase is a gap-less spin liquid in the entire range of J2/J1 \in [0.45 : 0.56] with a gap-less singlet excitation and a gaped triplet excitation.