# 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…

## 12 Citations

### Determining non-Abelian topological order from infinite projected entangled pair states

- MathematicsPhysical Review B
- 2020

The iPEPS tensor network, which is free of the sign problem notorious for the quantum Monte Carlo, is the method of choice to search for topological order in two-dimensional strongly correlated…

### Variational tensor network operator

- PhysicsPhysical Review Research
- 2022

We propose a simple and generic construction of the variational tensor network operators to study the quantum spin systems by the synergy of ideas from the imaginary-time evolution and variational…

### Finding the ground state of a lattice gauge theory with fermionic tensor networks: a $2+1d$ $\mathbb{Z}_2$ demonstration

- Physics
- 2022

Tensor network states, and in particular Projected Entangled Pair States (PEPS) have been a strong ansatz for the variational study of complicated quantum many-body systems, thanks to their built-in…

### Extracting Wilson loop operators and fractional statistics from a single bulk ground state

- Mathematics
- 2022

An essential aspect of topological phases of matter is the existence of Wilson loop operators that keep the ground state subspace invariant. Here we present and implement an unbiased numerical…

### Automatic differentiation applied to excitations with projected entangled pair states

- PhysicsSciPost Physics
- 2022

The excitation ansatz for tensor networks is a powerful tool for simulating the low-lying quasiparticle excitations above ground states of strongly correlated quantum many-body systems. Recently, the…

### Variational methods for characterizing matrix product operator symmetries

- MathematicsPhysical Review B
- 2021

We present a method of extracting information about topological order from the ground state of a strongly correlated two-dimensional system represented by an infinite projected entangled pair state…

### Unsupervised mapping of phase diagrams of 2D systems from infinite projected entangled-pair states via deep anomaly detection

- Computer ScienceSciPost Physics
- 2021

We demonstrate how to map out the phase diagram of a two dimensional quantum many body system with no prior physical knowledge by applying deep anomaly detection to ground states from infinite…

### Gauge Invariant Autoregressive Neural Networks for Quantum Lattice Models

- Materials ScienceArXiv
- 2021

This paper presents a probabilistic procedure for estimating the response of the immune system to TSPs, a type of “spatially aggregating immune cell” that responds to Tau.

### On the stability of topological order in tensor network states

- PhysicsPhysical Review B
- 2021

Stanford Institute for Theoretical Physics, Stanford University, Stanford, CA 94305, USA Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Straße 1, 85748 Garching, Germany Munich Center for…

### Order parameters and critical exponents for topological phase transitions through tensor networks

- Physics
- 2020

Order parameters are key to our understanding of phases of matter. Not only do they allow to classify phases, but they also enable the study of phase transitions through their critical exponents…

## References

SHOWING 1-10 OF 76 REFERENCES

### Determining topological order from infinite projected entangled pair states

- Computer SciencePhysical Review B
- 2020

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

- Physics
- 2018

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

- Physics
- 2016

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.

- PhysicsPhysical review letters
- 2013

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.

- Physics, Computer SciencePhysical review letters
- 2014

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

- Physics
- 2018

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

- Computer Science, Mathematics
- 2014

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

- PhysicsPhysical Review X
- 2018

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

- Physics
- 2016

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…