We theoretically demonstrate that a type of robust two-particle bound state embedded in the continuum (BIC), which we call Floquet-Hubbard (FH) BIC, can be induced in a homogeneous (i.e., defect-free) Hubbard semilattice by an intense oscillating electric field. While single-particle BIC states are fragile states that exist solely for specially tailored potentials, FH BIC states are found in a wide range of parameter space, do not require fulfillment of resonance conditions, and are thresholdless. Analytical results are derived in the high-frequency limit of field modulation by a multiple-time-scale asymptotic analysis of the ac-driven Hubbard Hamiltonian in the two-particle sector. A FH BIC mode basically corresponds to a molecular state, in which the two particles bind together, undergoing correlated tunneling on the lattice. Localization of the molecular state is induced by the external oscillating field, which effectively attracts the molecular state at the edge of the semi-infinite lattice. Our results can pave the way for the study and interpretation of strong-field phenomena in correlated-particles physics.
A bound state in the continuum (BIC) is a spatially localized energy eigenstate embedded in a continuous spectrum of extended eigenstates. While diverse types of single-particle BICs have been reported in the literature, understanding how such localization persists in interacting many-body systems remains a fundamental problem. Here, we present numerical evidence and a perturbative analysis supporting the existence of many-body BICs in a one-dimensional Bose-Hubbard chain with an attractive impurity potential, a system previously known to host a BIC in the two-particle sector. Furthermore, we demonstrate that the Bethe-type construction of the known two-particle BIC breaks down already for three particles even for arbitrary finite superpositions of Bethe waves. The resulting BICs violate the eigenstate thermalization hypothesis for several local one- and two-body observables, leading to nonthermal dynamics from experimentally accessible initial states.
We investigate bound states in the one-dimensional two-particle Bose-Hubbard model with an attractive (
V>0) impurity potential. This is a one-dimensional, discrete analogy of the hydrogen negative ion (H${}^{\ensuremath{-}}$) problem. There are several different types of bound states in this system, each of which appears in a specific region. For given
V, there exists a (positive) critical value
Uc1 of
U (the on-site atom-atom interaction), below which the ground state is a bound state. Interestingly, close to the critical value ($U\ensuremath{\lesssim}{U}_{c1}$), the ground state can be described by the Chandrasekhar-type variational wave function, which was initially proposed for H${}^{\ensuremath{-}}$. For
U>Uc1, the ground state is no longer a bound state. However, there exists a second (larger) critical value
Uc2 of
U, above which a molecule-type bound state is established and stabilized by the repulsion. We have also tried to solve for the eigenstates of the model using the Bethe ansatz. The model possesses a global
Z2 symmetry (parity) which allows classification of all eigenstates into even and odd states. It is found that all states with odd parity have the Bethe form, but none of the states in the even-parity sector. This allows us to identify analytically two odd-parity bound states, which appear in the parameter regions $\ensuremath{-}2V<U<\ensuremath{-}V$ and $\ensuremath{-}V<U<0$, respectively. Remarkably, the latter one can be embedded in the continuum spectrum with appropriate parameters. Moreover, in part of these regions, there exists an even-parity bound state accompanying the corresponding odd-parity bound state with almost the same energy.
Abstract Bound states in the continuum (BICs), referring to spatially localized bound states with energies falling within the range of extended modes, have been extensively investigated in single-particle systems, leading to diverse applications in photonics, acoustics, and other classical-wave systems. Recently, there has been theoretical interest in exploring many-body BICs in interacting quantum systems, which necessitate the careful design of impurity potentials or spatial profiles of interaction. Here, we propose a type of many-body BICs localized at boundaries, which can be purely induced by the uniform onsite interaction without requiring any specific design of impurity potential or nonlocal interaction. We numerically show that three or more interacting bosons can concentrate on the boundary of a homogeneous one-dimensional lattice, which is absent at single- and two-particle counterparts. Moreover, the eigenenergy of multi-boson bound states can embed within the continuous energy spectra of extended scattering states, thereby giving rise to interaction-induced boundary many-body BICs. Furthermore, by mapping Fock states of three and four bosons to nonlinear circuit networks, we experimentally simulate boundary many-body BICs. Our findings enrich the comprehension of correlated BICs beyond the single-particle level, and have the potential to inspire future investigations on exploring many-body BICs.
We report a bound state of the one-dimensional two-particle (bosonic or fermionic) Hubbard model with an impurity potential. This state has the Bethe-ansatz form, although the model is nonintegrable. Moreover, for a wide region in parameter space, its energy is located in the continuum band. A remarkable advantage of this state with respect to similar states in other systems is the simple analytical form of the wave function and eigenvalue. This state can be tuned in and out of the continuum continuously.