# Simulating both parity sectors of the Hubbard model with tensor networks

@article{Schneider2021SimulatingBP, title={Simulating both parity sectors of the Hubbard model with tensor networks}, author={Manuel Schneider and Johann Ostmeyer and Karl Jansen and Thomas C. Luu and Carsten Urbach}, journal={Physical Review B}, year={2021} }

Tensor networks are a powerful tool to simulate a variety of different physical models, including those that suffer from the sign problem in Monte Carlo simulations. The Hubbard model on the honeycomb lattice with nonzero chemical potential is one such problem. Our method is based on projected entangled pair states using imaginary-time evolution. We demonstrate that it provides accurate estimators for the ground state of the model, including cases where Monte Carlo simulations fail miserably…

## 7 Citations

### The Hubbard model with fermionic tensor networks

- PhysicsProceedings of The 38th International Symposium on Lattice Field Theory — PoS(LATTICE2021)
- 2022

Many electromagnetic properties of graphene can be described by the Hubbard model on a honeycomb lattice. However, this system suﬀers strongly from the sign problem if a chemical potential is…

### Stochastic and Tensor Network simulations of the Hubbard Model

- PhysicsProceedings of The 39th International Symposium on Lattice Field Theory — PoS(LATTICE2022)
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The Hubbard model is an important tool to understand the electrical properties of various materials. More specifically, on the honeycomb lattice it is used to describe graphene predicting a quantum…

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Efficient discretisations of gauge groups are crucial with the long term perspective of using tensor networks or quantum computers for lattice gauge theory simulations. For any Lie group other than…

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Motivated by the recent discovery of ferromagnetic quantum criticality in the heavy fermion compound CeRh 6 Ge 4 , we develop a numerical algorithm of inﬁnite projected entangled pair states for the…

### Optimised Trotter Decompositions for Classical and Quantum Computing

- Computer Science
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It is demonstrated how highly optimised schemes originally derived for exactly two operators A 1, 2 can be applied to such generic Suzuki-Trotter decompositions, providing a formal proof of correctness as well as numerical evidence of eﬃciency.

### Detecting coherence with respect to general quantum measurements

- Physics
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Quantum coherence is a crucial resource in quantum resource theory. Previous study mainly fo-cused on standard coherence under a complete orthogonal reference basis. The standard coherence has…

### Diverse Soliton wave solutions of for the nonlinear potential Kadomtsev–Petviashvili and Calogero–Degasperis equations

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## 57 References

### Site-resolved observations of antiferromagnetic correlations in the Hubbard model

- Physics
- 2016

Quantum many-body systems exhibiting magnetic correlations underlie a wide variety of phenomena. High-temperature superconductivity, for example, can arise from the correlated motion of holes on an…

### Unifying projected entangled pair state contractions

- Computer Science
- 2013

A new strategy is introduced, based on the idea of clusters, that unifies previous methods for the approximate contraction of a tensor network of projected entangled pair states and interpolates naturally between the cheapest and most imprecise and the most costly and most precise method.

### REVIEW ARTICLE: The Hubbard model - an introduction and selected rigorous results

- Physics
- 1998

The Hubbard model is a `highly oversimplified model' for electrons in a solid which interact with each other through extremely short-ranged repulsive (Coulomb) interaction. The Hamiltonian of the…

### Renormalization group on a triad network

- Computer Science
- 2019

The proposed renormalization scheme of tensor networks made only of third order tensors is tested in three dimensional Ising model and finds that the numerical results are obtained for large $D$s with reasonable errors.

### The rise of graphene.

- PhysicsNature materials
- 2007

Owing to its unusual electronic spectrum, graphene has led to the emergence of a new paradigm of 'relativistic' condensed-matter physics, where quantum relativistic phenomena can now be mimicked and tested in table-top experiments.

### Matrix product states, projected entangled pair states, and variational renormalization group methods for quantum spin systems

- Physics
- 2008

This article reviews recent developments in the theoretical understanding and the numerical implementation of variational renormalization group methods using matrix product states and projected…

### A METHOD FOR THE SOLUTION OF CERTAIN NON – LINEAR PROBLEMS IN LEAST SQUARES

- Mathematics
- 1944

The standard method for solving least squares problems which lead to non-linear normal equations depends upon a reduction of the residuals to linear form by first order Taylor approximations taken…

### Physical Review B 81

- 174411
- 2010