Quantum many-body systems with fractonic excitations can realize fascinating phases of matter. Here, we study the low-energy excitations of a constrained Bose-Hubbard model in one dimension, which conserves the center of mass or, equivalently, the dipole moment in addition to the particle number. This model is known to realize fractonic phases, including a dipole Mott insulator, a dipole Luttinger liquid, and a metastable dipole supersolid. We use tensor network methods to compute spectral functions from the dynamical response of the system and verify predictions from low-energy field theories of the corresponding ground-state phases. We demonstrate the existence of gapped excitations compatible with strong coupling results in a dipole Mott insulator, linear sound modes characteristic of a Luttinger liquid of dipoles, and soft quadratic modes at both zero and finite momenta in a supersolid state with charge density wave order and phase coherence at noninteger filling.
Fractonic constraints can lead to exotic properties of quantum many-body systems. Here, we investigate the dynamics of fracton excitations on top of the ground states of a one-dimensional, dipole-conserving Bose-Hubbard model. We show that nearby fractons undergo a collective motion mediated by exchanging virtual dipole excitations, which provides a powerful dynamical tool to characterize the underlying ground-state phases. We find that, in the gapped Mott insulating phase, fractons are confined to each other as motion requires the exchange of massive dipoles. When crossing the phase transition into a gapless Luttinger liquid of dipoles, fractons deconfine. Their transient deconfinement dynamics scales diffusively and exhibits strong but subleading contributions described by a quantum Lifshitz model. We examine prospects for the experimental realization in tilted Bose-Hubbard chains by numerically simulating the adiabatic state preparation and subsequent time evolution and find clear signatures of the low-energy fracton dynamics.
When particles move through a crystal or optical lattice, their motion can sometimes become frozen by strong external forces -- yet collective motion may still emerge through subtle many-body effects. In this work, we explore such constrained dynamics by realizing a dipole-conserving Bose-Hubbard model, where single atoms are immobile but pairs of particles can move cooperatively while preserving the system's center of mass, i.e. the overall dipole moment of the particle distribution. Starting from a one-dimensional chain of ultracold bosonic atoms in an optical lattice, we generate localized dipole excitations consisting of a hole and a doublon using site-resolved optical potentials and characterize their quantum walks and scattering dynamics. Our study provides a bottom-up investigation of a Hamiltonian with kinetic constraints, and paves the way for exploring low-energy phases of fractonic matter in existing experimental platforms.
We study the entanglement and bipartite fluctuations of fractonic phases in a one-dimensional dipole-conserving Bose-Hubbard chain using the density matrix renormalization group method. We demonstrate that bipartite charge fluctuations fail to detect quantum phase transitions in fractonic systems. Instead, we introduce bipartite dipole fluctuations,
Fd, which exhibit scaling laws identical to the entanglement entropy
S. For example, at integer filling
n=2, both
Fd and
S show logarithmic scaling in dipole Luttinger liquids and area-law scaling in dipole Mott insulators. Interestingly, in the dipole supersolid phase at noninteger filling
n=3/2, we reveal that
Fd and
S obey area laws despite the phase being compressible and hosting long-range dipole-dipole order. Moreover, we identify another phase at
n=3/2, previously called the fractional Mott insulator phase, as a dipole-conserving charge density wave state. In this phase,
Fd and
S follow area laws, but
Fd exhibits an additional period-2 oscillation. These findings provide insights into the interplay between dipole conservation, quantum fluctuations, and entanglement in the fractonic phases.
We consider the concept of fractons as particles or quasiparticles which obey a specific fractal statistics in connection with a one-dimensional Luttinger liquid theory. We obtain a dual statistics parameter = ν + 1 which is identified with the controlling parameter e -2φ of the Luttinger model. In this way, a bosonic system characterized by a fractal index i f [ h ] = i f [2] = 1 is considered in a conformal field theory with central charge c [ν = 0] = 1 = i f [2] with a compactified radius R = 1/ 1/2 = 1. Thus, we have a mapping of a bosonic theory to a fermionic one and vice versa, i.e. the duality symmetry = 3- h of the universal class h of fractons defined in the interval 1< h <2 is satisfied.