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.
We use infinite matrix-product-state techniques to study the time evolution of the charge-density-wave (CDW) order after a quench or a light pulse in a fundamental fermion-boson model. The motion of fermions in the model is linked to the creation of bosonic excitations, which counteracts the melting of the CDW order. For low-energy quenches corresponding to a change of the boson relaxation rate, we find behavior similar to that in an effective t−V model. When the boson energy is quenched instead or a light pulse is applied to the system, the transient dynamics are more complex, with the CDW order first quickly decreasing to an intermediate value while the density-wave-like order of the bosons rises. In the case of pulse irradiation, the subsequent time evolution of the CDW order depends strongly on the photon frequency. For frequencies slightly below the boson energy, we observe a temporary increase of the CDW order parameter. Our results reveal the complex physics of driven Mott insulators in low-dimensional systems with strong correlations. Published by the American Physical Society 2024
We study correlations in space and time after a quantum quench in the Bose Hubbard model. We obtain a two particle irreducible effective action within the Schwinger-Keldysh formalism that allows us to study dynamics in both the superfluid and Mott insulating phases. We derive equations of motion for both the superfluid order parameter and two-point correlation functions. We discuss the numerical solutions of these equations and calculate the quasimomentum distribution for quenches in the Mott phase. We demonstrate light-cone like spreading of correlations in the Mott phase in both one and two dimensions and calculate the propagation velocity in each dimension.
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 investigate field-induced excitation production from the unit-filled Mott background of a one-dimensional dipole-conserving Bose--Hubbard chain driven by a periodic quadratic potential, realizing a time-dependent rank-two electric field. Unlike protocols that manipulate pre-existing dipolar or fractonic excitations, we address their production from an initially Mott-like state without prepared dipolar or fractonic excitations. A single correlated hop directly nucleates the compact
∣030⟩ configuration at the atomic energy
3U, while a lower manifold derived from
2U contains spatially resolved dipole--antidipole configurations. Exact diagonalization shows that finite hopping turns this lower manifold into a dispersive band whose finite-chain edge lies substantially below the compact
3U scale. Despite this lower energetic edge, its normalized odd-harmonic spectral weight is perturbatively suppressed as
(J/U)2, reflecting virtual hybridization of the initial and final eigenstates. A consistent second-order treatment of the
∣1111⟩↔∣0220⟩ channel includes diagonal self-energy shifts and predicts a weak-field resonance displacement confirmed by exact time evolution. Extended-chain dynamics shows genuine dipole--antidipole separation together with redistribution into higher-energy many-body sectors. The resulting mechanism provides a condensed-matter analogue of multiphoton dynamical Schwinger production in which exact dipole conservation replaces mobile opposite charges by mobile opposite dipoles, while isolated fractonic charges remain immobile.
We employ a projection operator technique to study the equilibrium phases and the non-equilibrium quench and ramp dynamics of ultracold bosons described by a two-dimensional (2D) Bose-Hubbard model coupled to a high-finesse cavity with competing local short-range and cavity-mediated long-range interactions. Our analysis relies on a systematic elimination of high-energy virtual hopping processes; this enables us to capture the effects of short-range quantum fluctuations on the phase diagram of the model while treating the cavity-induced long-range interaction within mean-field theory. We find that the phase boundaries between the superfluid (SF), supersolid (SS), charge-density-wave (CDW) and Mott insulating (MI) phases are significantly modified by the presence of these fluctuations. We use this approach to study the dynamics of bosons following a quench/ramp from the CDW to the SS and SF phases; our analysis indicates the presence of oscillatory dynamics characterized by a single frequency due to a quench which takes the system near the critical point. In contrast, for a quench deep inside the SF phase, the dynamics involves multiple frequencies. An explicit comparison with Gutzwiller mean-field theory shows the importance of quantum fluctuations in shaping such post-quench dynamics; this feature may be tested experimentally as we discuss. We also study the ramp dynamics of these bosons and identify a bound on the ramp rate above which the present method is expected to produce accurate results.