Generalized electromagnetism of subdimensional particles: A spin liquid story

Abstract

It has recently been shown that there exists a class of stable gapless spin liquids in 3+1 dimensions described by higher rank tensor U (1) gauge fields, giving rise to an emergent tensor electromagnetism. The tensor gauge field of these theories couples naturally to subdimensional particles (such as fractons), which are restricted by gauge invariance to move only along lower-dimensional subspaces of the system. We here work out some of the basic generalized electromagnetic properties of subdimensional particles coupled to tensor electromagnetism, such as generalized electrostatic fields, potential formulations, Lorentz forces, Maxwell equations, and Biot-Savart laws. Some concepts from conventional electromagnetism will carry over directly, while others require significant modification. arXiv:1606.08857v2 [cond-mat.str-el]

Finite-temperature screening of U (1) fractons

“…We expect the same qualitative physics should hold for any U (1) model with these basic characteristics. The model we will work with has been studied in some detail in previous literature [1][2][3]16 . We will review the most important features of this phase here, though we refer the reader to these previous works for more details.…”

“…Recent work has established the stability of threedimensional spin liquid phases described by higher rank tensor gauge theories, such as the U (1) higher spin gauge theories [1][2][3] and the "generalized lattice gauge theories" of Vijay, Haah, and Fu 4,5 , which are the natural discrete analogue. The most exotic feature of these higher-rank phases is the fact that the emergent tensor gauge field must be coupled to excitations with subdimensional behavior.…”

“…Such an immobile excitation is called a fracton, or a 0-dimensional particle. Theoretical evidence for these immobile particles has been seen for more than a decade [6][7][8][9][10][11] , but interest in the topic has particularly surged just in the last few years [2][3][4][5][12][13][14][15][16][17][18][19] , establishing the subject as a new subfield of condensed matter physics.…”

“…Previous work on this topic [1][2][3] has already established many of the properties of these fractons, such as their conservation laws and their interactions with the tensor gauge field. This earlier work focused on the zero-temperature behavior of these phases, analyzing the physics of isolated particles.…”

Emergent gravity of fractons: Mach’s principle revisited

“…For many years, all consistent interacting theories basically fell into two classes: gravity (the spin-2 case) and variants of Vasiliev theory, which involves an infinite tower of all possible higher spin fields [9]. However, recent work has shown that it is actually possible to consistently formulate an interacting theory of any higher spin gauge field in (3 þ 1) dimensions, but that it requires the existence of particles restricted to motion along certain lower-dimensional subspaces [10][11][12]. This same phenomenon of restricted mobility had earlier found concrete realization in a condensed matter setting, first in work due to Chamon [13] and in several other models [14][15][16], including Haah's code [17,18].…”