Error estimates for extrapolations with matrix-product states

@article{Hubig2017ErrorEF,
  title={Error estimates for extrapolations with matrix-product states},
  author={Claudius Hubig and Jutho Haegeman and Ulrich Schollwock},
  journal={Physical Review B},
  year={2017},
  volume={97},
  pages={045125}
}
We introduce an error measure for matrix-product states without requiring the relatively costly two-site density-matrix renormalization group (2DMRG). This error measure is based on an approximation of the full variance . When applied to a series of matrix-product states at different bond dimensions obtained from a single-site density-matrix renormalization group (1DMRG) calculation, it allows for the extrapolation of observables towards the zero-error case representing the exact ground state… 
View PDF on arXiv
26 Citations
Highly Influential Citations
1
Background Citations
7
Methods Citations
8
Results Citations
1

26 Citations

Optimization of highly excited matrix product states with an application to vibrational spectroscopy.

Two variants of the DMRG algorithm are introduced that allows us to target directly specific energy regions and therefore highly excited states and can accurately calculate prominent spectral features of large molecules such as the sarcosine-glycine dipeptide and the Coulomb Hamiltonian to address X-ray spectra.

Topological phases in the Fermi-Hofstadter-Hubbard model on hybrid-space ladders

In recent experiments with ultracold atoms, both two-dimensional (2d) Chern insulators and one-dimensional (1d) topological charge pumps have been realized. Without interactions, both systems can be…

Absence of Superconductivity in the Pure Two-Dimensional Hubbard Model

We study the superconducting pairing correlations in the ground state of the doped Hubbard model -- in its original form without hopping beyond nearest neighbor or other perturbing parameters -- in…

Time-evolution methods for matrix-product states

Time-dependent variational principle with controlled bond expansion for matrix product states

We present a controlled bond expansion (CBE) approach to simulate quantum dynamics based on the time-dependent variational principle (TDVP) for matrix product states. Our method alleviates the…

The importance of the spectral gap in estimating ground-state energies

It is shown that the full complexity of the high precision case only comes about when the spectral gap is exponentially small, which is a surprising result that the complexity of LocalHamiltonian is magnified from QMA to PSPACE, the class of problems solvable in polynomial space.

Four-Spin Terms and the Origin of the Chiral Spin Liquid in Mott Insulators on the Triangular Lattice.

This work studies the effect of the additional four-spin interactions naturally generated from the underlying Mott-insulator physics of electrons as the repulsion decreases and finds that they stabilize a chiral spin liquid of Kalmeyer-Laughlin (KL) type, clarifying observations in recent studies of the Hubbard model.

Possible Inversion Symmetry Breaking in the S=1/2 Pyrochlore Heisenberg Magnet.

A robust spontaneous inversion symmetry breaking is found, reflected in an energy density difference between the two sublattices of tetrahedra, familiar as a starting point of earlier perturbative treatments, and suggest a scenario in which a finite-temperature spin liquid regime gives way to a symmetry-broken state at low temperatures.

Tangent-space methods for uniform matrix product states

In these lecture notes we give a technical overview of tangent-space methods for matrix product states in the thermodynamic limit. We introduce the manifold of uniform matrix product states, show how…

Efficient and flexible approach to simulate low-dimensional quantum lattice models with large local Hilbert spaces

This work introduces a mapping that allows to construct artificial $U(1)$ symmetries for any type of lattice model and reveals an intimate connection between the Schmidt values of the corresponding matrix-product-state representation and the single-site reduced density matrix.

References

SHOWING 1-10 OF 33 REFERENCES

Solutions of the Two-Dimensional Hubbard Model: Benchmarks and Results from a Wide Range of Numerical Algorithms

Numerical results for ground-state and excited-state properties (energies, double occupancies, and Matsubara-axis self-energies) of the single-orbital Hubbard model on a two-dimensional square…

Accuracy of the density-matrix renormalization-group method.

  • LegezaFáth
  • Physics
    Physical review. B, Condensed matter
  • 1996
White's density-matrix renormalization-group method is applied to the one-dimensional Ising model in a transverse field and a detailed picture is obtained of how errors behave as functions of the various model and algorithm parameters.

Efficient DMFT impurity solver using real-time dynamics with matrix product states

We propose to calculate spectral functions of quantum impurity models using the time evolving block decimation (TEBD) for matrix product states. The resolution of the spectral function is improved by…

The density-matrix renormalization group in the age of matrix product states

Imaginary-time matrix product state impurity solver for dynamical mean-field theory

We present a new impurity solver for dynamical mean-field theory based on imaginary-time evolution of matrix product states. This converges the self-consistency loop on the imaginary-frequency axis…

Hybrid-space density matrix renormalization group study of the doped two-dimensional Hubbard model

The performance of the density matrix renormalization group (DMRG) is strongly influenced by the choice of the local basis of the underlying physical lattice. We demonstrate that, for the…

Density-matrix renormalization group for a gapless system of free fermions

We investigate convergence of the density matrix renormalization group (DMRG) in the thermodynamic limit for gapless systems. Although the DMRG correlations always decay exponentially in the…

Fork Tensor Product States - Efficient Three Orbital Real Time DMFT Solver

We present a tensor network especially suited for multi-orbital Anderson impurity models and as an impurity solver for multi-orbital dynamical mean-field theory (DMFT). The solver works directly on…

Matrix product operators, matrix product states, and ab initio density matrix renormalization group algorithms.

This work describes how to efficiently implement the ab initio DMRG sweep using a matrix product operator based code, and the equivalence to the original renormalized operator implementation, and discusses two improvements of the abinitio D MRG sweep algorithm motivated by matrix product operators language: Hamiltonian compression, and a sum over operators representation that allows for perfect computational parallelism.

Density Matrix Embedding: A Strong-Coupling Quantum Embedding Theory.

It is found that DMET correctly describes the notoriously difficult symmetric dissociation of a 4 × 3 hydrogen atom grid, even when the treated fragments are as small as single hydrogen atoms.