12 research outputs found
Block product density matrix embedding theory for strongly correlated spin systems
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 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.Comment: 12 pages, 12 figure
T3NS: three-legged tree tensor network states
We present a new variational tree tensor network state (TTNS) ansatz, the
three-legged tree tensor network state (T3NS). Physical tensors are
interspersed with branching tensors. Physical tensors have one physical index
and at most two virtual indices, as in the matrix product state (MPS) ansatz of
the density matrix renormalization group (DMRG). Branching tensors have no
physical index, but up to three virtual indices. In this way, advantages of
DMRG, in particular a low computational cost and a simple implementation of
symmetries, are combined with advantages of TTNS, namely incorporating more
entanglement. Our code is capable of simulating quantum chemical Hamiltonians,
and we present several proof-of-principle calculations on LiF, N and the
bis(-oxo) and peroxo isomers of
.Comment: 14 pages, 8 figure
The Three-Legged Tree Tensor Networks with SU(2)- and molecular point group symmetry
We extend the three-legged tree tensor network state (T3NS) [J. Chem. Theory
Comput. 2018, 14, 2026-2033] by including spin and the real abelian point group
symmetries. T3NS intersperses physical tensors with branching tensors. Physical
tensors have one physical index and at most two virtual indices. Branching
tensors have up to three virtual indices and no physical index. In this way,
T3NS combines the low computational cost of matrix product states and their
simplicity for implementing symmetries, with the better entanglement
representation of tree tensor networks. By including spin and point group
symmetries, more accurate calculations can be obtained with lower computational
effort. We illustrate this by presenting calculations on the bis(-oxo) and
peroxo isomers of . The
used implementation is available on github.Comment: 20 pages, 13 figure
Method For Making 2-Electron Response Reduced Density Matrices Approximately N-representable
In methods like geminal-based approaches or coupled cluster that are solved
using the projected Schr\"odinger equation, direct computation of the
2-electron reduced density matrix (2-RDM) is impractical and one falls back to
a 2-RDM based on response theory. However, the 2-RDMs from response theory are
not -representable. That is, the response 2-RDM does not correspond to an
actual physical -electron wave function. We present a new algorithm for
making these non--representable 2-RDMs approximately -representable, i.e.
it has the right symmetry and normalization and it fulfills the -, - and
-conditions. Next to an algorithm which can be applied to any 2-RDM, we have
also developed a 2-RDM optimization procedure specifically for seniority-zero
2-RDMs. We aim to find the 2-RDM with the right properties that is the closest
(in the sense of the Frobenius norm) to the non-N-representable 2-RDM by
minimizing the square norm of the difference between the initial 2-RDM and the
targeted 2-RDM under the constraint that the trace is normalized and the 2-RDM,
- and -matrices are positive semidefinite, i.e. their eigenvalues are
non-negative. Our method is suitable for fixing non-N-respresentable 2-RDMs
which are close to being N-representable. Through the N-representability
optimization algorithm we add a small correction to the initial 2-RDM such that
it fulfills the most important N-representability conditions.Comment: 13 pages, 8 figure
The Fermionic Quantum Emulator
The fermionic quantum emulator (FQE) is a collection of protocols for emulating quantum dynamics of fermions efficiently taking advantage of common symmetries present in chemical, materials, and condensed-matter systems. The library is fully integrated with the OpenFermion software package and serves as the simulation backend. The FQE reduces memory footprint by exploiting number and spin symmetry along with custom evolution routines for sparse and dense Hamiltonians, allowing us to study significantly larger quantum circuits at modest computational cost when compared against qubit state vector simulators. This release paper outlines the technical details of the simulation methods and key technical advantages
Matrix product states with large sites
We explore various ways to group orbitals into clusters in a matrix product
state (MPS). We explain how a generic cluster MPS can often lead to an increase
in computational cost and instead propose a special cluster structure,
involving only the first and last orbitals/sites, with a wider scope for
computational advantage. This structure is a natural formalism to describe
correlated multireference (MR) theories. We demonstrate the flexibility and
usefulness of this approach by implementing various uncontracted MR
configuration interaction, perturbation and linearized coupled cluster theories
using an MPS with large cluster sites. Applications to the nitrogen dimer, the
chromium dimer, and benzene, including up to triple excitations in the external
space, demonstrate the utility of an MPS with up to two large sites. We use our
results to analyze the quality of different multireference approximations
Study of strongly correlated spin systems using density matrix embedding theory /
Master of Science in Engineering Physic