Spontaneously broken subsystem symmetries

Abstract

We investigate the spontaneous breaking of subsystem symmetries directly in the context of continuum field theories by calculating the correlation function of charged operators. Our methods confirm the lack of spontaneous symmetry breaking in some of the existing continuum field theories with subsystem symmetries, as had previously been established based on a careful analysis of the spectrum. We present some novel continuum field theory constructions that do exhibit spontaneous symmetry breaking whenever allowed by general principles. These interesting patterns of symmetry breaking occur despite the fact that all the theories we study are non-interacting.

Large $N$ fractons

“…With this low energy description in hand we may assess whether or not the dipole symmetry is restored by infrared fluctuations. We refer the reader to the discussion in [30] for more detail. By the same methods used there, we find that long-wavelength fluctuations of the Ψ i restore dipole symmetry at finite temperature in d ≤ 2, but not in d > 2.…”

“…Products of charges and anticharges can be arranged to carry vanishing net charge but nonzero dipole number. To assess whether long-wavelength fluctuations restore the U (1) and dipole symmetries, we can use the methods of [30] to find that the symmetry is restored at finite temperature in d ≤ 4. These fluctuations are a 1/N effect, and so are invisible in our large N analysis.…”

Fractionalization of subsystem symmetries in two dimensions

“…Symmetries that act nontrivially on rigid submanifolds of space-subsystem symmetries-are a generalization of global symmetries, which have recently come to prominence in a number of diverse settings. For example, generalized gauge theories based on subsystem symmetries lead to exotic fracton topological order [1][2][3], quantum dynamics with subsystem symmetries can lead to glassy behavior and anomalous subdiffusive spreading of information [4][5][6][7], and field theories having subsystem symmetries display mixing between long range and short range physics (UV/IR mixing) [8][9][10][11]. On the quantum information side, certain phases of matter protected by subsystem symmetries, such as cluster states, can be used as resources for universal measurement-based quantum computation (MBQC) [12][13][14][15][16].…”

Fractionalization of subsystem symmetries in two dimensions

“…Symmetries that act non-trivially on rigid submanifolds of space-subsystem symmetries-are a generalization of global symmetries which have recently come to prominence in a number of diverse settings. For example, generalized gauge theories based on subsystem symmetries lead to exotic fracton topological order [1][2][3], quantum dynamics with subsystem symmetries can lead to glassy behaviour and anomalous subdiffusive spreading of information [4][5][6][7], and field theories having subsystem symmetries display mixing between long range and short range physics (UV/IR mixing) [8][9][10][11]. On the quantum information side, certain phases of matter protected by subsystem symmetries, such as cluster states, can be used as resources for universal measurement-based quantum computation (MBQC) [12][13][14][15][16].…”