Detecting a Z2 topologically ordered phase from unbiased infinite projected entangled-pair state simulations

@article{Crone2019DetectingA,
  title={Detecting a 
Z2
 topologically ordered phase from unbiased infinite projected entangled-pair state simulations},
  author={Sven Crone and Philippe Corboz},
  journal={Physical Review B},
  year={2019}
}
We present an approach to identify topological order based on unbiased infinite projected entangled-pair states (iPEPS) simulations, i.e. where we do not impose a virtual symmetry on the tensors during the optimization of the tensor network ansatz. As an example we consider the ground state of the toric code model in a magnetic field exhibiting $Z_2$ topological order. The optimization is done by an efficient energy minimization approach based on a summation of tensor environments to compute… 

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References

SHOWING 1-10 OF 76 REFERENCES

Determining topological order from infinite projected entangled pair states

The algorithm is shown to be robust against a perturbation driving string-net toric code across a phase transition to a ferromagnetic phase and provides accurate results near quantum phase transition, where the correlation length is prohibitively large for other numerical methods.

Infinite projected entangled-pair state algorithm for ruby and triangle-honeycomb lattices

The infinite Projected Entangled-Pair State (iPEPS) algorithm is one of the most efficient techniques for studying the ground-state properties of two-dimensional quantum lattice Hamiltonians in the

Variational optimization with infinite projected entangled-pair states

An infinite projected entangled-pair state (iPEPS) is a powerful variational tensor network ansatz for two-dimensional ground states in the thermodynamic limit, and can be seen as a natural

Characterizing topological order by studying the ground States on an infinite cylinder.

A thorough characterization of the hard-core boson Haldane model by using the two-dimensional density matrix renormalization group shows that it realizes a ν=1/2 bosonic fractional quantum Hall state.

Topological transitions from multipartite entanglement with tensor networks: a procedure for sharper and faster characterization.

This work presents an efficient tensor network algorithm based on projected entangled pair states to compute this quantity for a torus partitioned into cylinders and uses this method to find sharp evidence of topological phase transitions in 2D systems with a string-tension perturbation.

Finite correlation length scaling with infinite projected entangled-pair states

We show how to accurately study 2D quantum critical phenomena using infinite projected entangled-pair states (iPEPS). We identify the presence of a finite correlation length in the optimal iPEPS

Modular matrices as topological order parameter by a gauge-symmetry-preserved tensor renormalization approach

A systematic numerical method based on tensor network to calculate modular matrices in 2D systems is introduced, which can fully identify topological order with gapped edge and it is shown numerically that modularMatrices, including S and T matrices, are robust characterization to describe phase transitions between topologically ordered states and trivial states.

Finite Correlation Length Scaling in Lorentz-Invariant Gapless iPEPS Wave Functions

It is an open question how well tensor network states in the form of an infinite projected entangled pair states (iPEPS) tensor network can approximate gapless quantum states of matter. Here we

Gradient methods for variational optimization of projected entangled-pair states

We present a conjugate-gradient method for the ground-state optimization of projected entangled-pair states (PEPS) in the thermodynamic limit, as a direct implementation of the variational principle
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