arXiv:2506.09818

Anomalous slow-down of the bound state dynamics in a non-locally coupled quantum circuit

Paul, Biswajit, Suman Mondal, Tapan Mishra

Published Jun 11, 2025• 0 citations

Abstract

Additional hopping channels in a tight-binding lattice is known to introduce faster dynamics of a quantum mechanical particle. However, we show that in the case of a repulsively bound state, the dynamics becomes abnormally slow when next-nearest neighbor (NNN) hopping is allowed for the particles. We show that such slowing down occurs for some magic strength of the NNN hopping at which the bound state band exhibits a quasi-flatband feature. We reveal this anomalous dynamical behavior by analyzing the quench dynamics of two nearest neighbor (NN) spin excitations (magnons) on a ferromagnetic chain by allowing both NN and NNN couplings. By implementing digital quantum computing simulations on a NISQ device, we obtain such non-trivial signatures and complement the results with exact numerical calculations. Moreover, through perturbative arguments, we reveal that the slowing down is due to the destructive interference between different paths associated to the bound state dynamics.

DOI: 10.48550/arxiv.2506.09818

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arXiv:2506.09818

Anomalous slow-down of the bound state dynamics in a non-locally coupled quantum circuit

Paul, Biswajit, Suman Mondal, Tapan Mishra

Published Jun 11, 2025• 0 citations

arXiv HTML PDF

Abstract

DOI: 10.48550/arxiv.2506.09818

Related papers

Two-dimensional Hubbard model with nearest- and next-nearest-neighbor hopping

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arXiv:2004.08435Physical review. B./Physical review. BAug 24, 202014 citations

We study the magnetic properties of the two-dimensional Hubbard model with nearest-neighbor (t) and next-nearest-neighbor (

{t}_{2}

) hopping and on-site repulsion U. We first calculate the mean-field phase diagram as a function of band filling and U. Because of the Van Hove singularity in the density of states, we find a ferromagnetic phase extending to zero U for certain band filling. For the half-filled band case, antiferromagnetism sets in at a finite value of U if

{t}_{2}

\ensuremath{\ne}0. We study the behavior of spin-spin correlation functions for small lattices of up to N=64 atoms using Monte Carlo simulations, as well as exact diagonalization for N=4. Our results show enhanced ferromagnetic correlations in some regions, but apparently no ferromagnetic long-range order. In the half-filled case, our numerical results are consistent with a nonzero critical U. For a non-half-filled band our results suggest that there is no long-range order.

n_i(t)

within the system and the growth of the total particle number

N(t)

in it. For case (i), we provide analytical insights into the dynamics of the nearest-neighbor model using an adiabatic approximation, which relies on assuming faster relaxation of coherences of the single particle density matrix. For case (ii), we perform numerical computations using the time-evolving block decimation (TEBD) algorithm and analyze the density profile and the growth exponent in

N(t)

. Our detailed study reveals an interesting interplay between Hamiltonian dynamics and various environmentally induced mechanisms in open quantum systems, such as local source and bulk dephasing. It brings out rich dynamics, including universal dynamical scaling and anomalous behavior across various time scales and is of relevance to various quantum simulation platforms.

We study the attractive (i.e., negative-U) Hubbard model with nearest (t) and next-nearest-neighbor (

{\mathit{t}}_{2}

) hopping on a square lattice. A spin-down particle-hole transformation maps the negative-U model at any band filling onto a repulsive model with a magnetic field and at zero chemical potential; the sign of the second-neighbor hopping constant in this model depends on the spin state. For large \ensuremath{\Vert}U\ensuremath{\Vert},

{\mathit{t}}_{2}

induces a coupling between spin operators in next-nearest-neighbor sites: antiferromagnetic between the z components and ferromagnetic along the transverse direction. The superconducting transition is investigated through Monte Carlo simulations on the attractive model. Fixing both U and the band filling, we find that the critical temperature increases steadily with

{\mathit{t}}_{2}

L

-edge resonant inelastic x-ray scattering (RIXS) intensity of the doped $t\text{\ensuremath{-}}t\ensuremath{'}\text{\ensuremath{-}}J$ model for a set of $t\ensuremath{'}$ values. We find evidence that the spin and charge degrees of freedom of the doped holes are not strictly separated anymore as $|t\ensuremath{'}|$ increases and identify the consequences of this in the dynamical response functions. The inclusion of NNN hopping couples the spinon and holon excitations, resulting in the formation of a spin polaron, where a ferromagnetic spin-polarization cloud dresses the doped carrier. The spin polaron manifests itself as additional spectral weight in the dynamical correlation functions, which appear simultaneously in the spin- and charge-sensitive channels. We also demonstrate that RIXS can provide a unique view of the spin polaron, due to its sensitivity to both the spin and charge degrees of freedom.