Entanglement renormalization.

@article{Vidal2007EntanglementR,
  title={Entanglement renormalization.},
  author={Guifr{\'e} Vidal},
  journal={Physical review letters},
  year={2007},
  volume={99 22},
  pages={
          220405
        }
}
  • G. Vidal
  • Published 8 December 2005
  • Physics
  • Physical review letters
We propose a real-space renormalization group (RG) transformation for quantum systems on a D-dimensional lattice. The transformation partially disentangles a block of sites before coarse-graining it into an effective site. Numerical simulations with the ground state of a 1D lattice at criticality show that the resulting coarse-grained sites require a Hilbert space dimension that does not grow with successive RG transformations. As a result we can address, in a quasi-exact way, tens of thousands… 

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References

SHOWING 1-10 OF 28 REFERENCES

Entanglement in quantum critical phenomena.

The results establish a precise connection between concepts of quantum information, condensed matter physics, and quantum field theory, by showing that the behavior of critical entanglement in spin systems is analogous to that of entropy in conformal field theories.

The density-matrix renormalization group

The density-matrix renormalization group (DMRG) is a numerical algorithm for the efficient truncation of the Hilbert space of low-dimensional strongly correlated quantum systems based on a rather

Efficient simulation of one-dimensional quantum many-body systems.

  • G. Vidal
  • Physics
    Physical review letters
  • 2004
Numerical analysis indicates that this method can be used, for instance, to efficiently compute time-dependent properties of low-energy dynamics in sufficiently regular but otherwise arbitrary one-dimensional quantum many-body systems.

Thermodynamic limit of density matrix renormalization.

It is shown that quantum states in the thermodynamic limit with periodic boundary conditions can be represented by a ``matrix product ground state'' with a natural description of Bloch states of elementary excitations and can be rederived through a simple variational ansatz making no reference to a renormalization construction.

Time-dependent density-matrix renormalization-group using adaptive effective Hilbert spaces

An algorithm for the simulation of the evolution of slightly entangled quantum states has been recently proposed as a tool to study time-dependent phenomena in one-dimensional quantum systems. Its

Quantum Spin Chain, Toeplitz Determinants and the Fisher—Hartwig Conjecture

We consider the one-dimensional quantum spin chain, which is called the XX model (XX0 model or isotropic XY model) in a transverse magnetic field. We are mainly interested in the entropy of a block

Finitely correlated states on quantum spin chains

We study a construction that yields a class of translation invariant states on quantum spin chains, characterized by the property that the correlations across any bond can be modeled on a

The renormalization group: Critical phenomena and the Kondo problem

This review covers several topics involving renormalization group ideas. The solution of the $s$-wave Kondo Hamiltonian, describing a single magnetic impurity in a nonmagnetic metal, is explained in

Density matrix formulation for quantum renormalization groups.

  • White
  • Physics
    Physical review letters
  • 1992
A generalization of the numerical renormalization-group procedure used first by Wilson for the Kondo problem is presented. It is shown that this formulation is optimal in a certain sense. As a

Efficient classical simulation of slightly entangled quantum computations.

  • G. Vidal
  • Computer Science, Physics
    Physical review letters
  • 2003
The results imply that a necessary condition for an exponential computational speedup is that the amount of entanglement increases with the size n of the computation, and provide an explicit lower bound on the required growth.