Fracton phases of matter

Abstract

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.

Subdiffusion in strongly tilted lattice systems

“…Note that this is different from the low-dimensional models [15][16][17][18] which show transitions between ergodic and nonergodic phases. Very recently, subdiffusion behavior is also observed in a specific circuit model that conserves the dipole momentum [19], where both symmetries are imposed from the beginning [20] and in more sophisticated fracton models [21,22]. To further support our analysis, we construct a solvable model by adding strong tilted potential to the quadratically coupled Sachdev-Ye-Kitaev model (SYK) [23][24][25][26].…”

Subsystem symmetry enriched topological order in three dimensions

“…A new paradigm in the classification of gapped phases of matter has recently begun thanks to the discovery of models with novel subdimensional physics. This includes the fracton topological phases [1][2][3][4][5][6][7][8][9][10][11][12], in which topological quasiparticles are either immobile or confined to move only within subsystem such as lines or planes, as well as models with subsystem symmetries, which are symmetries that act nontrivially only on rigid subsystems of the entire system [7,8,[13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29]. These two types of models are dual since gauging subsystem symmetries can result in fracton topological order, analogous to how topological order can be obtained by gauging a global symmetry [7,8,15].…”

“…Interplay between symmetries, symmetry defects, and symmetry charges in |SSPT , as revealed by Eqs (10). and(12). (a) Acting with a Z sub 1/2 2 symmetry on the linelike Z glob 2 flux creates Z sub 2/1 2 charges on neighboring planes.…”

Systematic construction of gapped nonliquid states

“…However, the classification of gapped nonliquid phases is still unclear (for a review, see Ref. [41]). In this paper, we are going to propose a very systematic construction of 3 + 1D gapped nonliquid phases for bosonic and fermionic systems with possible symmetry.…”