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arXiv:2607.12484

Solitary waves of attracting SU(N) fermions

Aysha Alsubaihi, Wayne Jordan Chetcuti, Frédéric Chevy, Juan Polo, Luigi Amico A

Published Jul 14, 2026• 0 citations
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Abstract

We study the formation, dynamics, and disorder robustness of bound states in attractively interacting SU(N) fermions on a one-dimensional ring lattice. Using exact diagonalization in fixed-momentum sectors and Bethe ansatz exact results as a guide, we resolve the many-body spectrum into bands related to the possible partitions of the particles into bound composites, and characterize their internal structure also through density-density and N-body correlations. A pinning quench protocol reveals a transition from dispersive spreading to dynamical localization as the attractive interaction increases relative to the single-particle hopping. We find that the bound state dynamics for one-particle per component occurs as a many-body quantum walk similar to that of a single particle with a re-normalized effective mass. Such a property, that is the quantum version of the shape-preserving motion of classical solitons, can provide the dynamical signature of the fermionic solitary waves. We probe the robustness of the fermionic bound-state dynamics under on-site disorder.

DOI
10.48550/arxiv.2607.12484

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We study the formation, dynamics, and disorder robustness of bound states in attractively interacting SU(N) fermions on a one-dimensional ring lattice. Using exact diagonalization in fixed-momentum sectors and Bethe ansatz exact results as a guide, we resolve the many-body spectrum into bands related to the possible partitions of the particles into bound composites, and characterize their internal structure also through density-density and N-body correlations. A pinning quench protocol reveals a transition from dispersive spreading to dynamical localization as the attractive interaction increases relative to the single-particle hopping. We find that the bound state dynamics for one-particle per component occurs as a many-body quantum walk similar to that of a single particle with a re-normalized effective mass. Such a property, that is the quantum version of the shape-preserving motion of classical solitons, can provide the dynamical signature of the fermionic solitary waves. We probe the robustness of the fermionic bound-state dynamics under on-site disorder.
We study the dynamics and thermalization of strongly correlated fermions in finite one-dimensional lattices after a quantum quench. Our calculations are performed using exact diagonalization. We focus on one- and two-body observables such as the momentum distribution function [n(k)][n(k)][n(k)] and the density-density structure factor [N(k)][N(k)][N(k)], respectively, and study the effects of approaching an integrable point. We show that while the relaxation dynamics and thermalization of N(k)N(k)N(k) for fermions is very similar to the one of hardcore bosons, the behavior of n(k)n(k)n(k) is distinctively different. The latter observable exhibits a slower relaxation dynamics in fermionic systems. We identify the origin of this behavior, which is related to the off-diagonal matrix elements of n(k)n(k)n(k) in the basis of the eigenstates of the Hamiltonian. More generally, we find that thermalization occurs far away from integrability and that it breaks down as one approaches the integrable point.
We use the coordinate Bethe ansatz to study the Lieb–Liniger model of a one-dimensional gas of bosons on a finite-sized ring interacting via an attractive delta-function potential. We calculate zero-temperature correlation functions for seven particles in the vicinity of the crossover to a localized solitonic state and study the dynamics of a system of four particles quenched to attractive interactions from the ideal-gas ground state. We determine the time evolution of correlation functions, as well as their temporal averages, and discuss the role of bound states in shaping the postquench correlations and relaxation dynamics.
Eigenstates of Bose particles with repulsive contact interactions in one-dimensional space with periodic boundary conditions can be found with the help of the Bethe ansatz. The type II excitation spectrum identified by E. H. Lieb, reproduces the dispersion relation of dark solitons in the mean-field approach. The corresponding eigenstates possess translational symmetry which can be broken in measurements of positions of particles. We analyze emergence of single and double solitons in the course of the measurements and investigate dynamics of the system. In the weak interaction limit, the system follows the mean-field prediction for a short period of time. Long time evolution reveals many-body effects that are related to an increasing uncertainty of soliton positions. In the strong interaction regime particles behave like impenetrable bosons. Then, the probability densities in the configuration space become identical to the probabilities of noninteracting fermions but the wave functions themselves remember the original Bose statistics. Especially, the phase flips that are key signatures of the solitons in the weak interaction limit, can be observed in the time evolution of the strongly interacting bosons.
Employing the Bethe ansatz approach and numerical simulations of measurements of particles' positions we investigate a post-quench many-body dynamics of attractively interacting bosons on a ring, which in the mean-field approach corresponds to the so-called breather solution. Despite the fact that the initial many-body ground state is translationally invariant, the measurements reveal breather dynamics if quantum fluctuations of the center of mass of the system are extracted. Moreover, the analysis of the many-body evolution shows signatures of dissociation of the solitons that form the breather.
We study an ultracold atomic gas with attractive interactions in a one-dimensional optical lattice. We find that its excitation spectrum displays a quantum soliton band, corresponding to N-particle bound states, and a continuum band of other, mostly extended, states. For a system of a finite size, the two branches are degenerate in energy for weak interactions, while a gap opens above a threshold value of the interaction strength. We find that the interplay between degenerate extended and bound states has important consequences for both static and dynamical properties of the system. In particular, the solitonic states turn out to be protected from spatial perturbations and random disorder. We discuss how such dynamics implies that our system effectively provides an example of a quantum many-body system that, with the variation of the bosonic lattice filling, crosses over from integrable nonergodic to nonintegrable ergodic dynamics, through nonintegrable-nonergodic regimes.
An impurity coupled to a bath is a paradigmatic problem of many-body physics and relevant for various systems. In this work, we study the dynamics due to impurities in one-dimensional lattice systems using the numerical time-evolving block decimation method and analytic calculations. We consider both noninteracting and interacting fermions as the bath, in particular fermions in a singlet superfluid state due to attractive on-site interactions, and baths with a periodic or nearly periodic structure due to nearest-neighbor repulsion. Previous theoretical and experimental research mainly considers homogeneous baths with contact interactions. We find novel phenomena when the bath is probed with energies above its characteristic energyscale. In publication I, a driven perturbation with velocity above the speed of sound of the interacting fermions retains the ground-state power-law decay of singlet superfluid correlations. In publication III, we study the decoherence of an impurity in terms of the purity of its density matrix. The impurity and the bath fermions have different masses, and we find the fastest decoherence for a light impurity in a heavy bath, whereas the fastest dissipation of energy occurs for equal masses. In publications II and IV, we consider a bath of fermions with repulsive nearest-neighbor interactions. In a half-filled lattice, the bath is in the Mott insulator state with a particle every two sites. A filling above one half leads to solitons seen as domain walls in the arrangement of the particles. We find that within a resonance region of interactions, the impurity can create an additional soliton-antisoliton pair in the bath. These two excitations have very different dynamics: The antisoliton can form a bound state with the impurity while the soliton excitation propagates. When the ground state of the bath contains solitons, the antisoliton excitation is confined close to its origin. These phenomena are explained by energy conservation, since processes with an energy change larger than the bandwidth are suppressed. Recent developments in experiments with ultracold gases in optical lattices offer possibilities for testing the theoretical predictions of this work. Long-range interactions in lattice models have been observed in experiments with magnetic atoms and dipolar molecules. Furthermore, single-site addressing techniques allow to create localized impurities and track their motion, and to measure the purity of many-body states.