Fractons from Partons

TL;DR

The paper develops a unified parton-based framework to understand and construct fracton phases in three dimensions. By decomposing physical degrees of freedom into Majorana partons with directional or interacting constraints, it derives both a fermionic type-I fracton model and bosonic fracton phases including type-I and a novel type-II model with fractal logical operators; the type-II construction saturates an upper bound on encoded qubits for certain system sizes. The authors connect fracton phenomenology to invariant gauge groups, provide exact parent Hamiltonians via a topological bootstrap, and establish a variational route to realize fracton physics in more realistic settings beyond exactly solvable models. Together, these results broaden the landscape of fracton phases and offer new tools for exploring phase transitions, symmetry considerations, and potential experimental realizations.

Abstract

Fracton topological phases host fractionalized excitations that are either completely immobile or only mobile along certain lines or planes. We demonstrate how such phases can be understood in terms of two fundamentally different types of parton constructions, in which physical degrees of freedom are decomposed into clusters of "parton" degrees of freedom subject to emergent gauge constraints. First, we employ non-interacting partons subject to multiple overlapping constraints to describe a fermionic fracton model. Second, we demonstrate how interacting partons can be used to develop new models of bosonic fracton phases, both with string and membrane logical operators (type-I fracton phases) and with fractal logical operators (type-II fracton phases). In particular, we find a new type-II model which saturates a bound on its information storage capacity. Our parton approach is generic beyond exactly solvable models and provides a variational route to realizing fracton phases in more physically realistic systems.

Figures (6)

• Figure 1: Fermionic type-I fracton model from non-interacting partons. (a) Two physical Majorana fermions $\gamma_{A,B}$ at each site (blue sphere) are decomposed into six Majorana partons $\gamma_{1,...,6}$ (green spheres) subject to two constraints. (b) Parton state specified by imposing $i\gamma_j\gamma_k = 1$ for each link (green zigzag). (c) Eight-Majorana term of the parent Hamiltonian whose ground state is the projected parton state.
• Figure 2: Bosonic type-I fracton model from interacting partons. (a) Two spin-one-halves at each site (blue sphere) are decomposed into eight Majorana partons (green spheres) subject to two constraints. (b) Parton state specified by four constraints for each parton cube. (c) Independent eight-spin interactions of the parent Hamiltonian.
• Figure 3: Bosonic type-II fracton model from interacting partons. (a) Two spin-one-halves at each site (blue sphere) are decomposed into eight Majorana partons (green spheres) subject to two constraints. (b) Parton state specified by four constraints for each eight-Majorana unit cell. (c) Independent eight-spin interactions of the parent Hamiltonian.
• Figure 4: Fractal structure in our type-II fracton model. (a) For the model in Fig. 3(c), the single-site operator $\sigma^x \tau^y$ creates six excitations (red dots). (b) Six such operators in the given configuration create six defects with the same shape as in (a) but with doubled linear dimension.
• Figure 5: (a) The physical spin-1/2 at each site (blue sphere) is decomposed into four Majorana partons $\gamma_{1,2,3,4}$ (green spheres) subject to the constraint $\gamma_1 \gamma_2 \gamma_3 \gamma_4 = 1$. (b) The parton state for the Wen plaquette model is the product state of dimers formed by pairs of Majoranas on each link (green zigzag).