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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2019

Fractional excitations in foliated fracton phases

Fractional excitations in fracton models exhibit novel features not present in conventional topological phases: their mobility is constrained, there are an infinitude of types, and they bear an exotic sense of ‘braiding’. Hence, they require a new framework for proper characterization. Based on our definition of foliated fracton phases in which equivalence between models includes the possibility of adding layers of gapped 2D states, we propose to characterize fractional excitations in these phases up to the addition of quasiparticles with 2D mobility. That is, two quasiparticles differing by a set of quasiparticles that move along 2D planes are considered to be equivalent; likewise, ‘braiding’ statistics are measured in a way that is insensitive to the attachment of 2D quasiparticles. The fractional excitation types and statistics defined in this way provide a universal characterization of the underlying foliated fracton order which can subsequently be used to establish phase relations. We demonstrate as an example the equivalence between the X-cube model and the semionic X-cube model both in terms of fractional excitations and through an exact mapping.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Effective fractonic behavior in a two-dimensional exactly solvable spin liquid

In this work we propose a \mathbb{Z}_N ℤ N clock model which is exactly solvable on the lattice. We find exotic properties for the low-energy physics, such as UV/IR mixing and excitations with restricted mobility, that resemble fractonic physics from higher dimensional models. We then study the continuum descriptions for the lattice system in two distinct regimes and find two qualitative distinct field theories for each one of them. A characteristic time scale that grows exponentially fast with N^2 N 2 (and diverges rapidly as function of system parameters) separates these two regimes. For times below this scale, the system is described by an effective fractonic Chern-Simons-like action, where higher-form symmetries prevent quasiparticles from hopping. In this regime, the system behaves effectively as a fracton as isolated particles, in practice, never leave their original position. Beyond the large characteristic time scale, the excitations are mobile and the effective field theory is given by a pure mutual Chern-Simons action. In this regime, the UV/IR properties of the system is captured by a peculiar realization of the translation group.

Delfino, Guilherme↗
DOE OSTI2020

Fracton phases via exotic higher-form symmetry-breaking

We study p-string condensation mechanisms for fracton phases from the viewpoint of higher-form symmetry, focusing on the examples of the X-cube model and the rank-two symmetric-tensor scalar charge theory. This work is motivated by questions of the relationship between fracton phases and continuum quantum field theories, and also provides general principles to describe p-string condensation independent of specific lattice model constructions. We give a perspective on higher-form symmetry in lattice models in terms of cellular homology. Applying this perspective to the coupled-layer construction of the X-cube model, we identify a foliated 1-form symmetry that is broken in the X-cube phase, but preserved in the phase of decoupled toric code layers. Similar considerations for the scalar charge theory lead to a framed 1-form symmetry. These symmetries are distinct from standard 1-form symmetries that arise, for instance, in relativistic quantum field theory. Here, we also give a general discussion on interpreting p-string condensation, and related constructions involving gauging of symmetry, in terms of higher-form symmetry.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

fcc lattice, checkerboards, fractons, and quantum field theory

In this work, we consider XY-spin degrees of freedom on an FCC lattice, such that the system respects some subsystem global symmetry. We then gauge this global symmetry and study the corresponding $U(1)$ gauge theory on the FCC lattice. Surprisingly, this $U(1)$ gauge theory is dual to the original spin system. We also analyze a similar $\mathbb{Z}_N$ gauge theory on that lattice. All these systems are fractonic. The $U(1)$ theories are gapless and the $\mathbb{Z}_N$ theories are gapped. We analyze the continuum limits of all these systems and present free continuum Lagrangians for their low-energy physics. Our $\mathbb{Z}_2$ FCC gauge theory is the continuum limit of the well known checkerboard model of fractons. Our continuum analysis leads to a straightforward proof of the known fact that this theory is dual to two copies of the $\mathbb{Z}_2$ X-cube model. We find new models and new relations between known models. The $\mathbb{Z}_N$ FCC gauge theory can be realized by coupling three copies of an anisotropic model of lineons and planons to a certain exotic $\mathbb{Z}_2$ gauge theory. Also, although for $N=2$ this model is dual to two copies of the $\mathbb{Z}_2$ X-cube model, a similar statement is not true for higher $N$.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Global dipole symmetry, compact Lifshitz theory, tensor gauge theory, and fractons

We study field theories with global dipole symmetries and gauge dipole symmetries. The famous Lifshitz theory is an example of a theory with a global dipole symmetry. We study in detail its 1+1d version with a compact field. When this global symmetry is promoted to a $U(1)$ dipole gauge symmetry, the corresponding gauge field is a tensor gauge field. This theory is known to lead to fractons. In order to resolve various subtleties in the precise meaning of these global or gauge symmetries, we place these 1+1d theories on a lattice and then take the continuum limit. Interestingly, the continuum limit is not unique. Different limits lead to different continuum theories, whose operators, defects, global symmetries, etc. are different. We also consider a lattice gauge theory with a $\mathbb Z_N$ dipole gauge group. Surprisingly, several physical observables, such as the ground state degeneracy and the mobility of defects depend sensitively on the number of sites in the lattice. Our analysis forces us to think carefully about global symmetries that do not act on the standard Hilbert space of the theory, but only on the Hilbert space in the presence of defects. We refer to them as time-like global symmetries and discuss them in detail. Furthermore, these time-like global symmetries allow us to phrase the mobility restrictions of defects (including those of fractons) as a consequence of a global symmetry.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

(2+1)-dimensional compact Lifshitz theory, tensor gauge theory, and fractons

The (2+1)-dimensional continuum Lifshitz theory of a free compact scalar field plays a prominent role in a variety of quantum systems in condensed matter physics and high energy physics. It is known that in compact space, it has an infinite ground-state degeneracy. In order to understand this theory better, we consider two candidate lattice regularizations of it using the modified Villain formalism. We show that these two lattice theories have significantly different global symmetries (including a dipole global symmetry), anomalies, ground-state degeneracies, and dualities. In particular, one of them is self-dual. Given these theories and their global symmetries, we can couple them to corresponding gauge theories. Here, these are two different U(1) tensor gauge theories. The resulting models have excitations with restricted mobility, i.e., fractons. Finally, we give an exact lattice realization of the fracton and lineon-elasticity dualities for the Lifshitz theory, and scalar and vector charge gauge theories.

2-dimensional systems↗
DOE OSTI2022

Field Theories for type-II fractons

We derive an effective field theory for a type-II fracton starting from the Haah code on the lattice. The effective topological theory is not given exclusively in terms of an action; it must be supplemented with a condition that selects physical states. Without the constraint, the action only describes a type-I fracton. The constraint emerges from a condition that cube operators multiply to the identity, and it cannot be consistently implemented in the continuum theory at the operator level, but only in a weaker form, in terms of matrix elements of physical states. Informed by these studies and starting from the opposite end, i.e., the continuum, we discuss a Chern-Simons-like theory that does not need a constraint or projector, and yet has no mobile excitations. Whether this continuum theory admits a lattice counterpart remains unanswered.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

Gauging nexus between topological and fracton phases

Coupled layer constructions are a valuable tool for capturing the universal properties of certain interacting quantum phases of matter in terms of the simpler data that characterizes the underlying layers. In the study of fracton phases, the X-Cube model in 3+1D can be realized via such a construction by starting with a stack of 2+1D Toric Codes and turning on a coupling which condenses a composite "particle-string" object. In a recent work [Phys. Rev. B 112, 125124 (2025)], we have demonstrated that in fact, the particle-string can be viewed as a symmetry defect of a topological 1-form symmetry. In this paper, we study the result of gauging this symmetry in depth. We unveil a rich gauging web relating the X-Cube model to symmetry protected topological (SPT) phases protected by a mix of subsystem and higher-form symmetries, subsystem symmetry fractionalization in the 3+1D Toric Code, and non-trivial extensions of topological symmetries by subsystem symmetries. Here, our work emphasizes the importance of topological symmetries in non-topological, geometric phases of matter.

Anyons↗
DOE OSTI2021

Higher-rank tensor field theory of non-abelian fracton and embeddon

We formulate a new class of tensor gauge field theories in any dimension that is a hybrid class between symmetric higher-rank tensor gauge theory (i.e., higher-spin gauge theory) and anti-symmetric tensor topological field theory. Our theory describes a mixed unitary phase interplaying between gapless and gapped topological order phases (which can live with or without Euclidean, Poincaré, or anisotropic symmetry, at least in ultraviolet high or intermediate energy field theory, but not yet to a lattice cutoff scale). The “gauge structure” can be compact, continuous, abelian or non-abelian. Our theory sits outside the paradigm of Maxwell electromagnetic theory in 1865 and Yang–Mills isospin/color theory in 1954. We discuss its local gauge transformation in terms of the ungauged vector-like or tensor-like higher-moment global symmetry. The non-abelian gauge structure is caused by gauging the non-commutative symmetries: a higher-moment symmetry and a charge conjugation (particle–hole) symmetry. Vector global symmetries along time direction may exhibit time crystals. We explore the relation of these long-range entangled matters to a non-abelian generalization of Fracton order in condensed matter, a field theory formulation of foliation, the spacetime embedding and Embeddon that we newly introduce, and possible fundamental physics applications to dark matter or dark energy.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Fractonic gauge theory of smectics

Motivated by striped correlated quantum matter, and the recently developed duality between elasticity of a two-dimensional (2D) crystal and a gauge theory, we derive a dual coupled U(1) vector gauge theory for a two-dimensional (2D) quantum smectic, where the disclination is mapped onto the fractonic charge, that we demonstrate can only move transversely to smectic layers. This smectic gauge theory dual also emerges from a gauge dual of a quantum crystal through a Higgs transition corresponding to a single flavor of its dipole condensation, an anisotropic quantum melting via dislocation proliferation. A condensation of the second flavor of dislocations a corresponds to another Higgs transition describing the smectic-to-nematic melting. We also utilize the electrostatic limit of this duality to formulate a melting of a 2D classical smectic in terms of a higher derivative sine–Gordon model, demonstrating its instability to a nematic at any nonzero temperature. Generalizing this classical duality to a 3D smectic, gives formulation of a 3D nematic-to-smectic transition in terms of an anisotropic Abelian-Higgs model.

36 MATERIALS SCIENCE↗
DOE OSTI2021

A modified Villain formulation of fractons and other exotic theories

We reformulate known exotic theories (including theories of fractons) on a Euclidean spacetime lattice. We write them using the Villain approach and then we modify them to a convenient range of parameters. The new lattice models are closer to the continuum limit than the original lattice versions. In particular, they exhibit many of the recently found properties of the continuum theories including emergent global symmetries and surprising dualities. Also, these new models provide a clear and rigorous formulation to the continuum models and their singularities. In appendices, we use this approach to review well-studied lattice models and their continuum limits. These include the XY-model, the $\mathbb{Z}_N$ clock-model, and various gauge theories in diverse dimensions. Here, this presentation clarifies the relation between the condensed-matter and the high-energy views of these systems. It emphasizes the role of symmetries associated with the topology of field space, duality, and various anomalies.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Fracton-elasticity duality in twisted moiré superlattices

We formulate a fracton-elasticity duality for twisted moiré superlattices, taking into account that they are incommensurate crystals with dissipative phason dynamics. From a dual tensor-gauge formulation, as compared to standard crystals, we identify twice the number of conserved charges that describe topological lattice defects, namely, disclinations and another type of defects that we dub discompressions. Furthermore, the key implication of these conservation laws is that both glide and climb motions of lattice dislocations are suppressed, indicating that dislocation networks may become exceptionally stable. We also generalize our results to other planar incommensurate crystals and quasicrystals.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Gapped lineon and fracton models on graphs

We introduce a $\mathbb{Z}_N$ stabilizer code that can be defined on any spatial lattice of the form $\Gamma\times C_{L_z}$, where $\Gamma$ is a general graph. We also present the low-energy limit of this stabilizer code as a Euclidean lattice action, which we refer to as the anisotropic $\mathbb{Z}_N$ Laplacian model. It is gapped, robust (i.e., stable under small deformations), and has lineons. Its ground state degeneracy (GSD) is expressed in terms of a "mod $N$-reduction" of the Jacobian group of the graph $\Gamma$. In the special case when space is an $L\times L\times L_z$ cubic lattice, the logarithm of the GSD depends on $L$ in an erratic way and grows no faster than $O(L)$. Furthermore, we also discuss another gapped model, the $\mathbb{Z}_N$ Laplacian model, which can be defined on any graph. It has fractons and a similarly strange GSD.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Fracton superfluid hydrodynamics

We examine the hydrodynamics of systems with spontaneously broken multipolar symmetries using a systematic effective field theory. We focus on the simplest nontrivial setting: a system with charge and dipole symmetry, but without momentum conservation. When no symmetries are broken, our formalism reproduces the quartic subdiffusion (ω ~ –ik 4 ) characteristic of “fracton hydrodynamics” with conserved dipole moment. Our formalism also captures spontaneous breaking of charge and/or dipole symmetry. When charge symmetry is spontaneously broken, the hydrodynamic modes are quadratically propagating and quartically relaxing (ω ~ ±k 2 – ik 4 ). When the dipole symmetry is spontaneously broken but the charge symmetry is preserved, then we find quadratically relaxing (diffusive) transverse modes, plus another mode which, depending on parameters, may be either purely diffusive (ω ~ – ik 2 ) or quadratically propagating and quadratically relaxing (ω ~ ± k 2 – ik 2 ). Furthermore, our work provides concrete predictions that may be tested in near-term cold atom experiments, and also lays out a general framework that may be applied to study systems with spontaneously broken multipolar symmetries.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Fractonic coset construction for spontaneously broken translations

We study the homogeneous breaking of spatial translation symmetry concomitantly with the spontaneous breaking of other internal and spacetime symmetries, including dilations. We use the symmetry-breaking pattern as the only input to derive, via the coset construction, general effective field theories for the symmetry-originated modes associated with Goldstone’s theorem, namely the Nambu-Goldstone candidates. Through explicit computations, we show that integrating out the explicit massive Nambu-Goldstone candidates or imposing symmetric constraints, namely the inverse Higgs constraints, to express massive modes in terms of the massless ones leads to physically distinct effective field theories. This sensitivity to the chosen method can be traced back to the homogeneous breaking of translations, the homogeneous aspect of the breaking induces a mixing between internal and spacetime symmetries at the level of the Lie algebra. This, in turn, leads to subtle discussions about the inverse Higgs constraints, in particular that they lead to a loss of generality in our specific examples. The derived general effective field theories also give rise to a broad class of theories exhibiting emergent enhanced shift symmetries, which constrain the mobility of the modes. The latter are referred to as fractonic modes. Published by the American Physical Society 2025

Chavda, Ameya (ORCID:0000000211731605)↗
DOE OSTI2024

Large N Fractons

We consider theories of N -component fields with exotic spacetime symmetries, including a conserved dipole moment. Microscopic charges are immobile by symmetry, and so resemble fractons. Using collective fields we solve these models to leading order in large N . The large N solution reveals that these models are strongly correlated, and that interactions dress the microscopic charges so that they become mobile, long-lived quasiparticles. Dipole symmetry is spontaneously broken throughout the phase diagram of these models, leading to a low-energy Goldstone description. Published by the American Physical Society 2024

Physics↗
DOE OSTI2021

Exotic $\mathbb{Z}_N$ symmetries, duality, and fractons in 3+1-dimensional quantum field theory

Following our earlier analyses of nonstandard continuum quantum field theories, we study here gapped systems in 3+1 dimensions, which exhibit fractonic behavior. In particular, we present three dual field theory descriptions of the low-energy physics of the X-cube model. A key aspect of our constructions is the use of discontinuous fields in the continuum field theory. Spacetime is continuous, but the fields are not.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Exotic symmetries, duality, and fractons in 2+1-dimensional quantum field theory

We discuss nonstandard continuum quantum field theories in 2+1 dimensions. They exhibit exotic global symmetries, a subtle spectrum of charged excitations, and dualities similar to dualities of systems in 1+1 dimensions. These continuum models represent the low-energy limits of certain known lattice systems. One key aspect of these continuum field theories is the important role played by discontinuous field configurations. In two companion papers, we will present 3+1-dimensional versions of these systems. In particular, we will discuss continuum quantum field theories of some models of fractons.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗