Thermodynamics of three-dimensional Kitaev quantum spin liquids via tensor networks

Jahromi, Saeed S.; Yarloo, H.; Orús, Román

doi:10.1103/physrevresearch.3.033205

Cited by 9 publications

(2 citation statements)

References 86 publications

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“…A common method for performing gate evolution of a TNS is the simple update (SU) method [116,123,[178][179][180], which we summarize in Fig. 5a and Appendix A.…”

Section: Approximate Gate Application With Belief Propagationmentioning

confidence: 99%

Gauging tensor networks with belief propagation

Tindall,

Fishman

2023

SciPost Phys.

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Effectively compressing and optimizing tensor networks requires reliable methods for fixing the latent degrees of freedom of the tensors, known as the gauge. Here we introduce a new algorithm for gauging tensor networks using belief propagation, a method that was originally formulated for performing statistical inference on graphical models and has recently found applications in tensor network algorithms. We show that this method is closely related to known tensor network gauging methods. It has the practical advantage, however, that existing belief propagation implementations can be repurposed for tensor network gauging, and that belief propagation is a very simple algorithm based on just tensor contractions so it can be easier to implement, optimize, and generalize. We present numerical evidence and scaling arguments that this algorithm is faster than existing gauging algorithms, demonstrating its usage on structured, unstructured, and infinite tensor networks. Additionally, we apply this method to improve the accuracy of the widely used simple update gate evolution algorithm.

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“…A common method for performing gate evolution of a TNS is the simple update (SU) method [116,123,[178][179][180], which we summarize in Fig. 5a and Appendix A.…”

Section: Approximate Gate Application With Belief Propagationmentioning

confidence: 99%

Gauging tensor networks with belief propagation

Tindall,

Fishman

2023

SciPost Phys.

View full text Add to dashboard Cite

show abstract

“…Tensor-Network methods.-Tensor-Network (TN) methods [40][41][42][43][44][45] provide efficient representations for ground states of local Hamiltonians based on their entanglement structure [40]. In particular, the projected entangled-pair state (PEPS) method and its infinite version in the thermodynamic limit (iPEPS) [40,41,45,46], have played a major role in the characterization and discovery of many exotic phases, ranging from magnetically ordered states [47][48][49] to QSLs [19,21,50,51] and valence-bond crystals [52,53]. In particular, the modified version of the iPEPS algorithm, designed for the honeycomb structures [54], has been shown to be very successful for simulating and characterizing the Kitaev model and its variants, such as the Kitaev-Heisenberg model, in the thermodynamic limit [55][56][57].…”

mentioning

confidence: 99%