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arXiv:2106.15631 · Physical review. B./Physical review. B

Spectroscopic fingerprints of gapless type-II fracton phases

Oliver Hart, Rahul Nandkishore

Published May 31, 2022• 10 citations
arXivHTMLPDF

Abstract

Fracton phases feature elementary excitations with fractionalized mobility and are exciting interest from multiple areas of theoretical physics. However, the most exotic type-II fracton phases, like the Haah codes, currently have no known experimental diagnostics. Here, we explain how type-II fracton phases with gapless gauge modes, such as the $\text{U}(1)$ Haah code, may be identified experimentally. Our analysis makes use of the multipole gauge theory description of type-II fracton phases, which exhibits ultraviolet-infrared (UV-IR) mixing. We show that neutron scattering experiments on gapless type-II fracton phases should generically exhibit exotic pinch points in the structure factor, with distinctive anisotropic contours as a direct consequence of UV-IR mixing. This characteristic pinch point structure provides a clean diagnostic of type-II fracton phases. We also identify distinctive signatures of the ($3+1$)-D $\text{U}(1)$ Haah code in the low-temperature specific heat.

DOI
10.1103/physrevb.105.l180416

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Fracton phases feature elementary excitations with fractionalized mobility and are exciting interest from multiple areas of theoretical physics. However, the most exotic type-II fracton phases, like the Haah codes, currently have no known experimental diagnostics. Here, we explain how type-II fracton phases with gapless gauge modes, such as the U(1)\text{U}(1)U(1) Haah code, may be identified experimentally. Our analysis makes use of the multipole gauge theory description of type-II fracton phases, which exhibits ultraviolet-infrared (UV-IR) mixing. We show that neutron scattering experiments on gapless type-II fracton phases should generically exhibit exotic pinch points in the structure factor, with distinctive anisotropic contours as a direct consequence of UV-IR mixing. This characteristic pinch point structure provides a clean diagnostic of type-II fracton phases. We also identify distinctive signatures of the (3+13+13+1)-D U(1)\text{U}(1)U(1) Haah code in the low-temperature specific heat.
Fracton phases feature elementary excitations with fractionalized mobility, and are exciting interest from multiple areas of theoretical physics. However, the most exotic `type II' fracton phases, like the Haah codes, currently have no known experimental diagnostic. Here we explain how gapless type II fracton phases, such as the U(1) Haah code, may be identified experimentally. Our analysis makes use of the `multipole gauge theory' description of type II fracton phases, which exhibits ultraviolet-infrared (UV-IR) mixing. We show that neutron scattering experiments on gapless type II fracton phases should generically exhibit pinch points in the structure factor, with distinctive parabolic contours as a result of UV-IR mixing. This distinctive pinch point structure provides a clean diagnostic of type II fracton phases. We also identify distinctive signatures of the (3+1)-D U(1) Haah code in the low temperature specific heat.
Fracton phases are a particularly exotic type of quantum spin liquids where the elementary quasiparticles are intrinsically immobile. These phases may be described by unconventional gauge theories known as tensor or multipolar gauge theories, characteristic for so-called type-I or type-II fracton phases, respectively. Both variants have been associated with distinctive singular patterns in the spin structure factor, such as multifold pinch points for type-I and quadratic pinch points for type-II fracton phases. Here, we assess the impact of quantum fluctuations on these patterns by numerically investigating the spin S=1/2 quantum version of a classical spin model on the octahedral lattice featuring exact realizations of multifold and quadratic pinch points, as well as an unusual pinch line singularity. Based on large scale pseudofermion and pseudo-Majorana functional renormalization group calculations, we take the intactness of these spectroscopic signatures as a measure for the stability of the corresponding fracton phases. We find that in all three cases, quantum fluctuations significantly modify the shape of pinch points or lines by smearing them out and shifting signal away from the singularities in contrast to effects of pure thermal fluctuations. This indicates possible fragility of these phases and allows us to identify characteristic fingerprints of their remnants.
Recently, a new class of three-dimensional spin liquid models have been theoretically discovered, which feature generalized Coulomb phases of emergent symmetric tensor U(1)U(1)U(1) gauge theories. These ``higher rank'' tensor models are particularly intriguing due to the presence of quasiparticles with restricted mobility, such as fractons. We investigate universal experimental signatures of tensor Coulomb phases. Most notably, we show that tensor Coulomb spin liquids (both quantum and classical) feature characteristic pinch point singularities in their spin-spin correlation functions, accessible via neutron scattering, which can be readily distinguished from pinch points in conventional U(1)U(1)U(1) spin liquids. These pinch points can thus serve as a crisp experimental diagnostic for such phases. We also tabulate the low-temperature heat capacity of various tensor Coulomb phases, which serves as a useful additional diagnostic in certain cases.
Gapless fracton quantum spin liquids are exotic phases of matter described by higher-rank U(1) gauge theories, which host gapped and immobile fracton matter excitations as well as gapless photons. Despite well-known field theories, no spin models beyond purely classical systems have been identified to realize these phases. Using error-controlled Green function Monte Carlo, here we investigate a square lattice spin-1 model that shows precise signatures of a fracton quantum spin liquid without indications of conventional ordering. Specifically, the magnetic response exhibits characteristic patterns of suppressed pinch points that accurately match the prediction of a rank-2 U(1) field theory and reveals the existence of emergent photon excitations in 2+1 spacetime dimensions. Remarkably, this type of fracton quantum spin liquid is not only identified in the system's ground state but also in generic low-energy sectors of a strongly fragmented Hilbert space.
We explain how gapped quantum spin liquids, both conventional and "fractonic," may be unambiguously diagnosed experimentally using the technique of multidimensional coherent spectroscopy."Conventional" nonchiral gapped quantum spin liquids (e.g., Z 2 spin liquid) do not have sharp signatures in linear response, but they do have clear fingerprints in nonlinear response, accessible through the already existing experimental technique of two-dimensional coherent spectroscopy.Type I fracton phases (e.g., X-cube) are (surprisingly) even easier to distinguish, with strongly suggestive features even in linear response, and unambiguous signatures in nonlinear response.Type II fracton systems, like Haah's code, are most subtle, and they may require consideration of high-order nonlinear response for unambiguous diagnosis.
Strongly correlated many-body systems provide a platform for novel phases of matter where constituent particles organize themselves in a variety of ways. At low temperature, these particles interact quantum mechanically and generate entanglement building up exotic quantum phases, such as topologcial order, where there can be emergent excitations which cannot be created locally. Such excitations, if gapped, are also called topological excitations.Fracton is one of such gapped point-like topological excitation in three dimensional system. Different from conventional topological excitation, it is immobile and was firstly discovered in exact solvable models exhibiting fracton topological order. This new order has sub-extensive topological ground-state degeneracy and generically also possesses other mobile excitations restricted to move in sub-dimensional spaces. Also, it has been noticed that the charges of symmetric-tensor U(1) gauge theories can be fractons. Its immobility is due to the existence of multiple conservation laws.In this thesis, I will present the relation among the gapped fracton topological order, gapless fracton phase described by U(1) symmetric tensor gauge theories, and ordinary topological ordered phases. Particularly, the fracton topological order exhibited in an exact solvable model called X- cube model can be constructed by coupling toric code layers. The mechanism leads to fracton topological orders is dubbed “p-string condensation” or “p-membrane condensation,” in which strings or membranes built up from particle excitations from layers of topological orders condense. This allows the fusion properties, braiding statistics, and ground-state degeneracy of the resulting fracton order to be easily understood in terms of more familiar degrees of freedom. And the fracton topological order in the X-cube model can also be obtained from a particular rank-2 symmetric tensor gauge theory called scalar charge theory by a partial confinement transition followed by Higgs mechanism removing the gapless photon modes.