Fracton Topological Phases from Strongly Coupled Spin Chains

Abstract

We provide a new perspective on fracton topological phases, a class of three-dimensional topologically ordered phases with unconventional fractionalized excitations that are either completely immobile or only mobile along particular lines or planes. We demonstrate that a wide range of these fracton phases can be constructed by strongly coupling mutually intersecting spin chains and explain via a concrete example how such a coupled-spinchain construction illuminates the generic properties of a fracton phase. In particular, we describe a systematic translation from each coupled-spin-chain construction into a parton construction where the partons correspond to the excitations that are mobile along lines. Remarkably, our construction of fracton phases is inherently based on spin models involving only two-spin interactions and thus brings us closer to their experimental realization.One of the most striking features of topologically ordered phases in two dimensions is the existence of quasiparticle excitations with fractional quantum numbers and fractional exchange statistics [1]. In three dimensions, this fractionalization attains an even more exotic character and has proven to be a vast and exciting frontier. For example, there are loop-like excitations in addition to point-like excitations, and the intricate braiding patterns exhibited by these loop-like excitations are essential for characterizing the topological order [2,3].Fracton topological phases are topologically ordered phases in three dimensions with a particularly extreme form of fractionalization [4][5][6][7][8][9]. In these phases, there are point-like excitations that are either completely immobile or only mobile in a lower-dimensional subsystem, such as an appropriate line or plane. Remarkably, the restricted mobility of excitations has a purely topological origin and appears in translation-invariant systems without any disorder. In addition to being of fundamental interest from the perspective of topological phases, and providing an exciting disorder-free alternative to many-body localization [10,11], this phenomenology has important implications for quantum-information storage. Indeed, the immobility of excitations makes encoded quantum information more stable at finite temperature than in conventional topologically ordered phases [12,13].In recent years, several different viewpoints have been presented on fracton topological phases. From a purely conceptual perspective, fracton phases can be understood by gauging classical spin models with particular subsystem symmetries [14,15] or in terms of generalized parton constructions with overlapping directional gauge constraints and/or interacting parton Hamiltonians [16]. While these approaches can be used to understand the generic properties of fracton phases, the concrete spin models they provide are far from realistic as they involve interactions between many spins at the same time. From a more practical perspective, fracton phases can be constructed by coupling orthogonal stacks of two-dimensional to...

Absence of finite temperature phase transitions in the X-Cube model and its Zp generalization

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Ergodicity Breaking Arising from Hilbert Space Fragmentation in Dipole-Conserving Hamiltonians

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