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arXiv:2310.16084 · Physical review. B./Physical review. B

Dynamical spectral response of fractonic quantum matter

Philip Zechmann, Julian Boesl, Johannes Feldmeier, Michael Knap

Published Mar 21, 2024• 10 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevb.109.125137

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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.
We investigate the quench dynamics in the dipolar Bose-Hubbard model (DBHM) in one dimension. The boson hopping is constrained by dipole conservation and shows fractonic dynamics. The ground states at large Hubbard interaction U are Mott insulators at integer filling and a period-2 charge density wave (CDW) at half-integer filling. We focus on Mott-to-Mott and CDW-to-CDW quenches and find that dipole correlation spreading shows the light-cone behavior with the Lieb-Robinson (LR) velocity proportional to the dipole kinetic energy J and the square of the density in the case of Mott quench at integer filling. An effective model for postquench dynamics is constructed under the dilute-dipole approximation and fits the numerical results well. For the CDW quench, we observe a much reduced LR velocity of order J 2 / U and additional periodic features in the time direction. The emergence of a CDW ground state and the reduced LR velocity at half-integer filling can both be understood by careful application of the second-order perturbation theory. The oscillatory behavior arises from quantum scars in the quadrupole sector of the spectrum and is captured by a PXP-like model that we derive by projecting the DBHM to the quadrupolar sector of the Hilbert space. Published by the American Physical Society 2024
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{\mathcal{F}}^{d}Fd, which exhibit scaling laws identical to the entanglement entropy SSS. For example, at integer filling n=2n=2n=2, both Fd{\mathcal{F}}^{d}Fd and SSS 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=3/2n=3/2n=3/2, we reveal that Fd{\mathcal{F}}^{d}Fd and SSS obey area laws despite the phase being compressible and hosting long-range dipole-dipole order. Moreover, we identify another phase at n=3/2n=3/2n=3/2, previously called the fractional Mott insulator phase, as a dipole-conserving charge density wave state. In this phase, Fd{\mathcal{F}}^{d}Fd and SSS follow area laws, but Fd{\mathcal{F}}^{d}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.
Fractons are emergent particles which are immobile in isolation, but which can move together in dipolar pairs or other small clusters. These exotic excitations naturally occur in certain quantum phases of matter described by tensor gauge theories. Previous research has focused on the properties of small numbers of fractons and their interactions, effectively mapping out the ``standard model'' of fractons. In the present work, however, we consider systems with a finite density of either fractons or their dipolar bound states, with a focus on the U(1)U(1)U(1) fracton models. We study some of the phases in which emergent fractonic matter can exist, thereby initiating the study of the ``condensed matter'' of fractons. We begin by considering a system with a finite density of fractons, which we show can exhibit microemulsion physics, in which fractons form small-scale clusters emulsed in a phase dominated by long-range repulsion. We then move on to study systems with a finite density of mobile dipoles, which have phases analogous to many conventional condensed matter phases. We focus on two major examples: Fermi liquids and quantum Hall phases. A finite density of fermionic dipoles will form a Fermi surface and enter a Fermi liquid phase. Interestingly, this dipolar Fermi liquid exhibits a finite-temperature phase transition, corresponding to an unbinding transition of fractons. Finally, we study chiral two-dimensional phases corresponding to dipoles in ``quantum Hall'' states of their emergent magnetic field. We study numerous aspects of these generalized quantum Hall systems, such as their edge theories and ground state degeneracies.