Simulation of two-dimensional quantum systems on an infinite lattice revisited: Corner transfer matrix for tensor contraction

By Roman Orus, Guifré Vidal. 2009

288 citations recorded by the source corpus.

An extension of the projected entangled-pair states (PEPS) algorithm to infinite systems, known as the iPEPS algorithm, was recently proposed to compute the ground state of quantum systems on an infinite two dimensional lattice. Here we investigate a modification of the iPEPS algorithm, where the environment is computed using the corner transfer matrix renormalization group (CTMRG) method, instead of using one-dimensional transfer matrix methods as in the original proposal. We describe a variant of the CTMRG that addresses different directions of the lattice independently, and use it combined with imaginary time evolution to compute the ground state of the two dimensional quantum Ising model. Near criticality, the modified iPEPS algorithm is seen to provide a better estimation of the order parameter and correlators.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics, Condensed Matter Physics

View Paper: https://www.semanticscholar.org/paper/5010c00815b18145c9c650f75c8f9ecedd13b4c8

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. J. Haegeman
2. L. Vanderstraeten
3. Frank Verstraete
4. S. White
5. B. Zheng
6. Garnet Kin-Lic Chan
7. Philippe Corboz
8. Andrew J. Daley

In Atomic and Molecular Physics, and Optics

1. Frank Verstraete
2. L. Vanderstraeten
3. S. White
4. J. Haegeman
5. Garnet Kin-Lic Chan
6. B. Zheng
7. Shiwei Zhang
8. Philippe Corboz

In Condensed Matter Physics

1. L. Vanderstraeten
2. S. White
3. J. Haegeman
4. Frank Verstraete
5. Hao Shi
6. Chia-Min Chung
7. B. Zheng
8. Shiwei Zhang

Citations in the corpus

• Gradient methods for variational optimization of projected entangled-pair states (2016, methodology): “The model has been extensively studied with the PEPS ansatz [18,20,50], and we use the model as a benchmark for our conjugate-gradient method.”
• Stripe order in the underdoped region of the two-dimensional Hubbard model (2016, methodology): “Observables are evaluated by contracting the two-dimensional tensor network in a controlled, approximate way, using a variant (18, 61) of the corner-transfer matrix (CTM) method (62,63).”
• Tangent-space methods for uniform matrix product states (2018, methodology): “Ten years later these works led to contraction algorithms based on the time-evolving block decimation [17] or the corner transfer matrix renormalization group [56].”