Quantum robustness of fracton phases

Mühlhauser, M.; Walther, M. R.; Reiss, D. A.; Schmidt, K. P.

doi:10.1103/physrevb.101.054426

Cited by 28 publications

(22 citation statements)

References 81 publications

(118 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Fractons not only represent a fundamentally new type of emergent quasiparticle with striking properties, but also draw connections between a variety of seemingly unrelated topics, from gravity and elasticity to higher-order topological insulators and hole-doped antiferromagnets. While we have covered a wide range of topics, there have been many other exciting advances in the field which we have not discussed here, and we refer the interested reader to the literature for more information [135,[137][138][139][140][141][142][143][144][145][146][147][148].…”

Section: Discussionmentioning

confidence: 99%

Fracton phases of matter

Pretko

Xie

You

2020

Int. J. Mod. Phys. A

343

269

View full text Add to dashboard Cite

Fractons are a new type of quasiparticle which are immobile in isolation, but can often move by forming bound states. Fractons are found in a variety of physical settings, such as spin liquids and elasticity theory, and exhibit unusual phenomenology, such as gravitational physics and localization.The past several years have seen a surge of interest in these exotic particles, which have come to the forefront of modern condensed matter theory. In this review, we provide a broad treatment of fractons, ranging from pedagogical introductory material to discussions of recent advances in the field. We begin by demonstrating how the fracton phenomenon naturally arises as a consequence of higher moment conservation laws, often accompanied by the emergence of tensor gauge theories.We then provide a survey of fracton phases in spin models, along with the various tools used to characterize them, such as the foliation framework. We discuss in detail the manifestation of fracton physics in elasticity theory, as well as the connections of fractons with localization and gravitation.Finally, we provide an overview of some recently proposed platforms for fracton physics, such as Majorana islands and hole-doped antiferromagnets. We conclude with some open questions and an outlook on the field.

show abstract

Section: Discussionmentioning

confidence: 99%

Fracton phases of matter

Pretko

Xie

You

2020

Int. J. Mod. Phys. A

343

269

View full text Add to dashboard Cite

show abstract

“…Furthermore, in three-dimensional topologically-ordered systems point-like anyonic excitations are excluded but nontrivial statistics can be found for extended objects such as membranes. However, in 3D, one must distinguish between two main categories of topologically-ordered long-range entangled ground states [16,17] depending on whether their degeneracy is finite [18][19][20][21] or sub-extensive with the system size [22][23][24][25][26][27][28][29][30][31][32][33][34][35]. The topological order for systems with sub-extensive ground-state degeneracy is called fracton order.…”

Section: Introductionmentioning

confidence: 99%

Competing topological orders in three dimensions

et al. 2022

Self Cite

View full text Add to dashboard Cite

We study the competition between two different topological orders in three dimensions by considering the X-cube model and the three-dimensional toric code. The corresponding Hamiltonian can be decomposed into two commuting parts, one of which displays a self-dual spectrum. To determine the phase diagram, we compute the high-order series expansions of the ground-state energy in all limiting cases. Apart from the topological order related to the toric code and the fractonic order related to the X-cube model, we found two new phases which are adiabatically connected to classical limits with nontrivial sub-extensive degeneracies. All phase transitions are found to be first order.

show abstract

“…their quantum robustness and associated quantum critical properties. High-order series expansions represent one important tool to study these questions [34,35,[52][53][54][55]. In condensed matter physics, multi-site interactions are known to arise in strongly correlated Mott insulators like Hubbard systems in the limit of strong interactions [56][57][58][59].…”

Section: Introductionmentioning

confidence: 99%

Linked Cluster Expansions via Hypergraph Decompositions

Mühlhauser,

Schmidt

2022

Preprint

Self Cite

View full text Add to dashboard Cite

We propose a hypergraph expansion which facilitates the direct treatment of quantum spin models with many-site interactions via perturbative linked cluster expansions. The main idea is to generate all relevant subclusters and sort them into equivalence classes essentially governed by hypergraph isomorphism. Concretely, a reduced König representation of the hypergraphs is used to make the equivalence relation accessible by graph isomorphism. During this procedure we determine the embedding factor for each equivalence class, which is used in the final resummation in order to obtain the final result. As an instructive example we calculate the ground-state energy and a particular excitation gap of the plaquette Ising model in a transverse field on the three-dimensional cubic lattice.

show abstract

Quantum robustness of fracton phases

Cited by 28 publications

References 81 publications

Fracton phases of matter

Fracton phases of matter

Competing topological orders in three dimensions

Linked Cluster Expansions via Hypergraph Decompositions

Contact Info

Product

Resources

About