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arXiv:2606.22284

Pairing-induced Bloch oscillations in an interacting Kitaev chain

E. S. Ma, Z. Song

Published Jun 21, 2026• 0 citations
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Abstract

We study the peculiar dynamics of the Kitaev chain induced by nearest-neighbor (NN) interaction. We show that a strong NN interaction suppresses single-particle hopping but enhances pairing, resulting in a Wannier-Stark ladder. Based on the spin-fermion correspondence at the symmetry point, the model maps to a transverse field Ising model on a zigzag lattice, providing a clear physical picture and guiding experimental verification. The Wannier-Stark state corresponds to a localized domain wall between ferromagnetic and antiferromagnetic phases. It exhibits Bloch oscillation even in the absence of a longitudinal field, in contrast to previous works. Numerical simulations of time-dependent observables verify these conclusions. Our findings provide an example demonstrating emergent Stark many-body localization.

DOI
10.48550/arxiv.2606.22284

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We study the peculiar dynamics of the Kitaev chain induced by nearest-neighbor (NN) interaction. We show that a strong NN interaction suppresses single-particle hopping but enhances pairing, resulting in a Wannier-Stark ladder. Based on the spin-fermion correspondence at the symmetry point, the model maps to a transverse field Ising model on a zigzag lattice, providing a clear physical picture and guiding experimental verification. The Wannier-Stark state corresponds to a localized domain wall between ferromagnetic and antiferromagnetic phases. It exhibits Bloch oscillation even in the absence of a longitudinal field, in contrast to previous works. Numerical simulations of time-dependent observables verify these conclusions. Our findings provide an example demonstrating emergent Stark many-body localization.
Bloch oscillations typically arise in periodic systems subjected to a constant force generated by a potential gradient. Here, we study domain-wall dynamics in coupled Ising layers under asymmetric longitudinal fields. The interlayer coupling is of Heisenberg type and acts as an effective transverse coupling in the emergent pseudospin representation. We show that the rung pseudospin structure gives rise to kinetic constraints, restricting the many-body dynamics to an emergent one-dimensional quasiparticle subspace within the original two-dimensional system. Furthermore, the imbalance between the longitudinal fields of the two layers induces an effective linear potential for the emergent domain-wall excitations, leading to their confinement between two oppositely polarized ferromagnetic domains. Remarkably, the resulting Wannier--Stark ladder of domain-wall excitations gives rise to Bloch oscillations in the absence of a conventional tilted potential, revealing a distinct mechanism for coherent quantum dynamics. Numerical simulations of time-dependent observables confirm the analytical predictions.
We investigate the impacts of an imaginary transverse field on the dynamics of magnetic domain walls in a quantum Ising chain. We show that an imaginary field plays a similar role as a real transverse field in forming a low-lying Wannier-Stark ladder. However, analytical and numerical calculations of the time evolutions in both systems show that the corresponding Bloch oscillations exhibit totally different patterns for the same initial states. These findings reveal the nontrivial effect of non-Hermiticity on quantum spin dynamics.
We investigate the Bose-Hubbard chain in the presence of nearest-neighbor pairing. The pairing term gives rise to an unusual gapped Z2{\mathbb{Z}}_{2}Z2​ Ising phase that has number fluctuation but no off-diagonal long range order. This phase has a strongly correlated many-body doubly degenerate ground state which is effectively a gap-protected macroscopic qubit. In the strongly interacting limit, the system can be mapped onto an anisotropic transverse spin chain, which in turn can be mapped to the better-known fermionic sister of the paired Bose-Hubbard chain: the Kitaev chain which hosts zero-energy Majorana bound states. While corresponding phases in the fermionic and bosonic systems have starkly different wave functions, they share identical energy spectra. We describe a possible cold-atom realization of the paired Bose-Hubbard model in a biased zigzag optical lattice with reservoir-induced pairing, opening a possible route towards experimental Kitaev chain spectroscopy.
We study spinless fermions on a finite chain with nearest-neighbor repulsion and in the presence of a Wannier-Stark (WS) linearly varying electric field potential. In the absence of the interaction, the eigenstates are localized for system's sizes larger than the localization length. We present several analytical expressions for the localization length, which in all cases is proportional to the inverse of the electric field. Using the density matrix renormalization group numerical technique, we observe that the ground state exhibits a decrease of the occupation on the chain sites from the 'bulk', with occupation 1, to the vacuum, with occupation 0. The width of this intermediate 'edge' region is also inversely proportional to the electric field, increasing linearly with the strength of the nearest-neighbor repulsion. For strong interactions, the occupations in the intermediate region exhibit a charge density wave. We also present the local density of states for sites in the intermediate 'domain wall' region. For the non-interacting case, the spectrum shows an increasing energy-localized structure as the field is increased, which is a consequence of the uniform energy distribution of the localized states (WS ladder). This structure survives for small interactions, and it smears out in the strongly interacting limit. Experimental variations of the slope of the potential (the electric field) on cold atom chains may test these predictions.
We consider spinless fermions on a finite one-dimensional lattice, interacting via nearest-neighbor repulsion and subject to a strong electric field. In the noninteracting case, due to Wannier-Stark localization, the single-particle wave functions are exponentially localized even though the model has no quenched disorder. We show that this system remains localized in the presence of interactions and exhibits physics analogous to models of conventional many-body localization (MBL). In particular, the entanglement entropy grows logarithmically with time after a quench, albeit with a slightly different functional form from the MBL case, and the level statistics of the many-body energy spectrum are Poissonian. We moreover predict that a quench experiment starting from a charge-density wave state would show results similar to those of Schreiber et al. [Science 349, 842 (2015)SCIEAS0036-807510.1126/science.aaa7432].
Stimulated by the experimental realization of spin-dependent tunneling via a gradient magnetic field [C. J. Kennedy et al., Phys. Rev. Lett. 111, 225301 (2013); M. Aidelsburger et al., Phys. Rev. Lett. 111, 185301 (2013)], we investigate the dynamics of Bloch oscillations and Landau-Zener tunneling of single spin-half particles in a periodic potential under the influence of a spin-dependent constant force. In analogy to the Wannier-Stark system, we call our system the Wannier-Zeeman system. If there is no coupling between the two spin states, the system can be described by two crossing Wannier-Stark ladders with opposite tilts. The spatial crossing between two Wannier-Stark ladders becomes a spatial anticrossing if the two spin states are coupled by external fields. For a wave packet away from the spatial anticrossing, due to the spin-dependent constant force, it will undergo spatial Landau-Zener transitions assisted by the intrinsic intraband Bloch oscillations, which we call the Bloch-Landau-Zener dynamics. If the interspin coupling is sufficiently strong, the system undergoes adiabatic Bloch-Landau-Zener dynamics, in which the spin dynamics follows the local dressed states. Otherwise, for nonstrong interspin couplings, the system undergoes nonadiabatic Bloch-Landau-Zener dynamics.