Emergent fractons and algebraic quantum liquid from plaquette melting transitions

Abstract

Paramagnetic spin systems with spontaneously broken spatial symmetries, such as valence bond solid (VBS) phases, can host topological defects carrying non-trivial quantum numbers, which enables the paradigm of deconfined quantum criticality. In this work, we study the properties of topological defects in valence plaquette solid (VPS) phases on square and cubic lattices. We show that the defects of the VPS order parameter, in addition to possessing non-trivial quantum numbers, have fracton mobility constraints deep in the VPS phase, which has been overlooked previously. The spinon inside a single vortex cannot move freely in any direction, while a dipolar pair of vortices with spinon pairs can only move perpendicular to its dipole moment. These mobility constraints, while they persist, can potentially inhibit the condensation of vortices and preclude a continuous transition from the VPS to the Néel antiferromagnet. Instead, the VPS melting transition can be driven by proliferation of spinon dipoles. For example, we argue that a 2d VPS can melt into a stable gapless phase in the form of an algebraic bond liquid with algebraic correlations and long range entanglement. Such a bond liquid phase yields a concrete example of the elusive 2d Bose metal with symmetry fractionalization. We also study 3d valence plaquette and valence cube ordered phase, and demonstrate that the topological defects therein also have fractonic dynamics. Possible nearby phases after melting the valence plaquettes or cubes are also discussed.

Tunable deconfined quantum criticality and interplay of different valence-bond solid phases*

“…Here we note that some of the prerequisites for fractons outlined in Ref. [41] in the context of the pVBS has analogies in the sVBS, and the latter may be a more likely host of fractons under realistic conditions. Though we do not have quantitative results from QMC simulations, we will here argue that fracton-like excitation are generically pos- sible in sVBS states.…”

“…Even if the spinon vortex is realized, unlike the case of the cVBS the dimer pattern will only allow local fluctuations enabling the spinon to propagate in specific directions (in an extreme case of only short dimers). The spinons may then be regarded as a type of fracton-an excitation with constrained mobilityas argued recently for spinons in a plaquette VBS (pVBS) [41]. Though in the case of the pVBS the fracton property may only be realized in practice in extreme cases where the four-spin singlets can be refarded as rigid objects, as pointed out in Ref.…”

“…Considering the possibility of fractontype spinons and their propensity to nucleate AFM order (in analogy with Ref. [41]), it is, however, not even clear if very strong quantum fluctuations of the sVBS can be achieved before a first-order transition takes place.…”

Fracton phases of matter

“…However, in the absence of a constant energy input to sustain this particle creation, an individual fracton will remain immobile. These unusual new particles were first encountered in certain exactly-solvable three-dimensional spin and Majorana models [1-4, 6-8], but have since been shown to arise in contexts ranging from topological crystalline defects [9] to plaquette-ordered paramagnets [10] (see also precursor work in Ref. [11]).…”

“…This includes both artificially engineered fractons, for example built from Majorana islands [48], and realizations of fractons in familiar condensed matter settings, such as plaquette paramagnets [10] and hole-doped antiferromagnets [49]. Finally, in Section IX, we conclude with some open questions and an outlook on the field of fractons.…”