Emergent phases of fractonic matter

Abstract

Fractons are emergent particles which are immobile in isolation, but which can move together in dipolar pairs or other small clusters. These exotic excitations naturally occur in certain quantum phases of matter described by tensor gauge theories. Previous research has focused on the properties of small numbers of fractons and their interactions, effectively mapping out the "Standard Model" of fractons. In the present work, however, we consider systems with a finite density of either fractons or their dipolar bound states, with a focus on the U (1) fracton models. We study some of the phases in which emergent fractonic matter can exist, thereby initiating the study of the "condensed matter" of fractons. We begin by considering a system with a finite density of fractons, which we show can exhibit microemulsion physics, in which fractons form small-scale clusters emulsed in a phase dominated by long-range repulsion. We then move on to study systems with a finite density of mobile dipoles, which have phases analogous to many conventional condensed matter phases. We focus on two major examples: Fermi liquids and quantum Hall phases. A finite density of fermionic dipoles will form a Fermi surface and enter a Fermi liquid phase. Interestingly, this dipolar Fermi liquid exhibits a finite-temperature phase transition, corresponding to an unbinding transition of fractons. Finally, we study chiral two-dimensional phases corresponding to dipoles in "quantum Hall" states of their emergent magnetic field. We study numerous aspects of these generalized quantum Hall systems, such as their edge theories and ground state degeneracies. arXiv:1709.09673v2 [cond-mat.str-el]

Anisotropic layer construction of anisotropic fracton models

“…(35) the parameters of the original Kitaev honeycomb model must be appropriately tuned such that only the terms remaining in Eq. (35) are dominant. On the other hand, the couplings between adjacent layers are not restrictive to the form in Eq.…”

Gauging permutation symmetries as a route to non-Abelian fractons

“…These peculiar particles have attracted significant recent interest, thereby revealing intriguing connections to quantum information processing [9][10][11][12], topological order [13][14][15][16][17][18][19][20][21][22], sub-system symmetries [23][24][25][26][27][28][29][30], and slow quantum dynamics [1,3,[31][32][33]. Much of the phenomenology of fractons can also be realized in tensor gauge theories [34][35][36][37][38][39][40][41][42][43][44] with higher moment conservation laws, unveiling further connections of fractons with elasticity [45][46][47][48][49] and even gravity [50][51][52]. For a recent review of fractonic physics, we refer the reader to Ref.…”

Crystal-to-fracton tensor gauge theory dualities

“…[1][2][3][4][5][6][7][8] It was later realized that these new particles have a natural theoretical description in the language of tensor gauge theories, which exhibit restricted mobility due to an unusual set of higher moment charge conservation laws, such as conservation of dipole moment. [9][10][11][12] Rapid recent progress in the field has established connections with numerous other areas of physics, such as localization [13][14][15] , gravity 16 , holography 17,18 , quantum Hall systems 19,20 , hole-doped antiferromagnets 21 , and deconfined quantum criticality 22 , among many other theoretical developments. We refer the reader to Reference 48 for a review of fracton physics.…”