Dimerized Kitaev Chain Models

• Dimerized Kitaev chain is a one-dimensional spinless p-wave superconducting model with alternating bond strengths, interpolating between SSH and Kitaev physics.
• It exhibits distinct trivial, Kitaev-like, and SSH-like topological phases, characterized by varied Majorana edge modes and many-body diagnostics.
• Exact-solvable interacting regimes and extensions, including Floquet and quasiperiodic generalizations, offer deep insights into topological transitions and transport phenomena.

The dimerized Kitaev chain is a family of one-dimensional spinless $p$-wave superconducting lattice models with an explicit two-site unit cell and alternating bond strengths. In the standard fermionic usage, dimerization alternates intracell and intercell couplings in the SSH sense while retaining Kitaev pairing, so the model interpolates among the uniform Kitaev chain, the SSH chain, and interacting dimerized topological superconductors. Its clean limit already supports distinct trivial, Kitaev-like, and SSH-like topological sectors, while interacting, disordered, quasiperiodic, and Floquet generalizations produce exact-solvable lines, many-body Majorana phases, topological Anderson regimes, and parameter-space pumping phenomena (Ezawa, 2017, Li et al., 2018, Ma et al., 2024).

1. Canonical formulation and model variants

A standard interacting formulation uses a two-sublattice unit cell $(A,B)$ and a dimerization parameter $\eta$ that weights intracell bonds by $1+\eta$ and intercell bonds by $1-\eta$. A representative Hamiltonian is

$$\begin{aligned} H&=\sum_{j} \Big\{-t\big[(1+\eta)c_{j,A}^{\dagger}c_{j,B}+(1-\eta)c_{j,B}^{\dagger}c_{j+1,A}+h.c. \big] \ &\qquad - \Delta \big[(1+\eta)c_{j,A}^{\dagger}c_{j,B}^{\dagger}+(1-\eta)c_{j,B}^{\dagger}c_{j+1,A}^{\dagger}+h.c. \big] \ &\qquad + 4U \Big[ \Big(n_{j,A}-\frac{1}{2}\Big)\Big(n_{j,B}-\frac{1}{2}\Big) + \Big(n_{j,B}-\frac{1}{2}\Big)\Big(n_{j+1,A}-\frac{1}{2}\Big) \Big] \Big\} \ &\qquad -\mu\sum_{j} \left(c_{j,A}^{\dagger}c_{j,A}+c_{j,B}^{\dagger}c_{j,B}\right). \end{aligned}$$

In this form, dimerization modulates hopping, pairing, and interaction in the same SSH-like pattern. The limits are immediate: $\eta=0$ gives the uniform Kitaev chain, $\Delta=0$ gives an interacting SSH-type model, and $U=0$ gives the noninteracting dimerized Kitaev chain (Wang et al., 2017).

This canonical structure is not unique. Some works study a modified dimerized Kitaev chain in which hopping and pairing are alternated in opposite ways,

$$\begin{aligned} H &= -t \sum_{j} \Big[(1+\lambda)c^\dagger_{j,A}c_{j,B} + (1-\lambda)c^\dagger_{j,B}c_{j+1,A}+H.c.\Big] \ &\quad - \Delta \sum_{j}\Big[(1-\lambda)c^{\dagger}_{j,A}c^{\dagger}_{j,B}+ (1+\lambda)c^\dagger_{j,B}c^\dagger_{j+1,A} +H.c.\Big] + \mu \sum_{j}(c^\dagger_{j,A}c_{j,A}+c^\dagger_{j,B}c_{j,B}), \end{aligned}$$

which changes the edge-mode structure without removing the SSH-Kitaev interpolation (Wang et al., 2017). Other extensions add extra intercell hopping and pairing terms $(A,B)$0 and $(A,B)$1, producing a ladder-like effective geometry and new superconducting phases beyond the nearest-neighbor dimerized chain (Li et al., 2020). The common defining feature across these formulations is explicit bond alternation in a fermionic $(A,B)$2-wave chain rather than merely a bond-dependent sign structure.

2. Bulk topology and edge structure

In chiral-symmetric formulations, the dimerized Kitaev chain is typically analyzed in class BDI, with an integer winding number. For the SSH-like dimerized model at $(A,B)$3, the noninteracting classification quoted in the Green’s-function analysis is

• $(A,B)$4 for $(A,B)$5 with $(A,B)$6,
• $(A,B)$7 for $(A,B)$8,
• $(A,B)$9 for $\eta$0 with $\eta$1, so the same dimerized superconducting chain realizes a trivial phase, a Kitaev-like topological phase, and an SSH-like topological phase (Li et al., 2018). In this language, $\eta$2 corresponds to one Majorana mode per edge, whereas $\eta$3 corresponds to two Majoranas per edge, equivalently one Dirac edge fermion at each end.

For the modified inverse-dimerization model, the bulk phase boundaries occur at

$\eta$4

and the same bulk invariant takes the values $\eta$5. The phase regions are explicitly given as trivial, topological superconductor, and SSH-like topological sectors (Wang et al., 2017). A notable refinement is that the $\eta$6 sector splits into two distinct edge-coupling patterns, labeled $\eta$7 and $\eta$8, which are not separated by the bulk invariant alone but are distinguished by edge Majorana correlation functions

$\eta$9

In the thermodynamic limit, both vanish in the trivial phase, exactly one is nonzero in a Kitaev-like phase, and both are nonzero in the SSH-like phase (Wang et al., 2017).

This separation between bulk winding and edge structure is one of the dimerized chain’s defining peculiarities. The uniform Kitaev chain has a single Majorana channel, whereas dimerization yields two competing bond sectors and therefore richer boundary phenomenology. In open chains, this is visible as either a single exponentially localized Majorana per end, two Majoranas per end, or finite-size hybridization patterns that depend on the detailed dimerization architecture.

3. Exact-solvable interacting regimes

At the symmetric point

$1+\eta$0

the interacting dimerized Kitaev chain becomes exactly solvable by a sequence of a Jordan–Wigner transformation, a $1+\eta$1 spin rotation, and a second Jordan–Wigner transformation. The fermionic model first maps to a dimerized $1+\eta$2 chain, then to a dimerized $1+\eta$3 chain, and finally to a quadratic fermion Hamiltonian

$1+\eta$4

This solvable line supports a seven-phase diagram in the $1+\eta$5 plane, including topological superconducting, charge-density-wave, Schrödinger-cat, single-electron-dimer, and superconducting-dimer phases, with tetra-critical points at

$1+\eta$6

The topological criterion is not the mere existence of a zero mode in the transformed quadratic problem, but specifically the existence of a type-I fermionic many-body Majorana edge state in the original interacting fermions (Ezawa, 2017).

The same solvable point under open boundary conditions yields an exact phase diagram organized more coarsely into trivial, topological superconducting, and SSH-like topological sectors. The exact transition lines are

$1+\eta$7

and the topological superconducting region is the small-$1+\eta$8 regime satisfying

$1+\eta$9

For negative dimerization, an SSH-like topological phase appears in an intermediate interaction window and carries two Majoranas per edge, while sufficiently strong coupling drives the system into trivial regimes such as CDW or CAT states (Wang et al., 2017).

The strong-dimerization limits clarify the topology. At $1-\eta$0, the chain splits into isolated dimers and the resulting dimer phases are trivial. At $1-\eta$1, a semi-infinite geometry leaves an unpaired edge site, reproducing the SSH-like topological mechanism (Ezawa, 2017). This explicit contrast between positive and negative dimerization survives in many descendants of the model.

4. Many-body diagnostics: Green’s functions and string order

A central interacting diagnostic is the zero-frequency Green’s-function winding number. For the dimerized Nambu basis, the invariant is written as

$1-\eta$2

with $1-\eta$3 after chiral block off-diagonalization (Li et al., 2018). This construction is essential in the interacting dimerized chain because fermion parity distinguishes only odd from even many-body sectors, whereas the Green’s-function invariant distinguishes the full set $1-\eta$4. In particular, the interacting $1-\eta$5 and $1-\eta$6 phases both have even fermion parity, so parity alone cannot separate trivial and SSH-like even-parity phases (Li et al., 2018).

The same Green’s-function formalism explains a subtler point: even the uniform interacting Kitaev chain requires an enlarged dimerized Nambu basis in its CDW phase because the ground state spontaneously acquires a two-sublattice structure. This observation foreshadows the correct treatment of the explicitly dimerized chain, for which the enlarged sublattice-resolved $1-\eta$7 Green’s function is natural from the outset (Li et al., 2018).

A complementary exact perspective uses local and nonlocal order parameters at the symmetric point $1-\eta$8. The topological superconducting order parameter is a Majorana string order $1-\eta$9, the interaction-dominated CDW and CAT phases are diagnosed by a local density order parameter $$\begin{aligned} H&=\sum_{j} \Big\{-t\big[(1+\eta)c_{j,A}^{\dagger}c_{j,B}+(1-\eta)c_{j,B}^{\dagger}c_{j+1,A}+h.c. \big] \ &\qquad - \Delta \big[(1+\eta)c_{j,A}^{\dagger}c_{j,B}^{\dagger}+(1-\eta)c_{j,B}^{\dagger}c_{j+1,A}^{\dagger}+h.c. \big] \ &\qquad + 4U \Big[ \Big(n_{j,A}-\frac{1}{2}\Big)\Big(n_{j,B}-\frac{1}{2}\Big) + \Big(n_{j,B}-\frac{1}{2}\Big)\Big(n_{j+1,A}-\frac{1}{2}\Big) \Big] \Big\} \ &\qquad -\mu\sum_{j} \left(c_{j,A}^{\dagger}c_{j,A}+c_{j,B}^{\dagger}c_{j,B}\right). \end{aligned}$$0, and dimerization resolves the uniform string order into two rarefied string order parameters $$\begin{aligned} H&=\sum_{j} \Big\{-t\big[(1+\eta)c_{j,A}^{\dagger}c_{j,B}+(1-\eta)c_{j,B}^{\dagger}c_{j+1,A}+h.c. \big] \ &\qquad - \Delta \big[(1+\eta)c_{j,A}^{\dagger}c_{j,B}^{\dagger}+(1-\eta)c_{j,B}^{\dagger}c_{j+1,A}^{\dagger}+h.c. \big] \ &\qquad + 4U \Big[ \Big(n_{j,A}-\frac{1}{2}\Big)\Big(n_{j,B}-\frac{1}{2}\Big) + \Big(n_{j,B}-\frac{1}{2}\Big)\Big(n_{j+1,A}-\frac{1}{2}\Big) \Big] \Big\} \ &\qquad -\mu\sum_{j} \left(c_{j,A}^{\dagger}c_{j,A}+c_{j,B}^{\dagger}c_{j,B}\right). \end{aligned}$$1 and $$\begin{aligned} H&=\sum_{j} \Big\{-t\big[(1+\eta)c_{j,A}^{\dagger}c_{j,B}+(1-\eta)c_{j,B}^{\dagger}c_{j+1,A}+h.c. \big] \ &\qquad - \Delta \big[(1+\eta)c_{j,A}^{\dagger}c_{j,B}^{\dagger}+(1-\eta)c_{j,B}^{\dagger}c_{j+1,A}^{\dagger}+h.c. \big] \ &\qquad + 4U \Big[ \Big(n_{j,A}-\frac{1}{2}\Big)\Big(n_{j,B}-\frac{1}{2}\Big) + \Big(n_{j,B}-\frac{1}{2}\Big)\Big(n_{j+1,A}-\frac{1}{2}\Big) \Big] \Big\} \ &\qquad -\mu\sum_{j} \left(c_{j,A}^{\dagger}c_{j,A}+c_{j,B}^{\dagger}c_{j,B}\right). \end{aligned}$$2 defined on alternating bond sublattices. The exact factorization

$$\begin{aligned} H&=\sum_{j} \Big\{-t\big[(1+\eta)c_{j,A}^{\dagger}c_{j,B}+(1-\eta)c_{j,B}^{\dagger}c_{j+1,A}+h.c. \big] \ &\qquad - \Delta \big[(1+\eta)c_{j,A}^{\dagger}c_{j,B}^{\dagger}+(1-\eta)c_{j,B}^{\dagger}c_{j+1,A}^{\dagger}+h.c. \big] \ &\qquad + 4U \Big[ \Big(n_{j,A}-\frac{1}{2}\Big)\Big(n_{j,B}-\frac{1}{2}\Big) + \Big(n_{j,B}-\frac{1}{2}\Big)\Big(n_{j+1,A}-\frac{1}{2}\Big) \Big] \Big\} \ &\qquad -\mu\sum_{j} \left(c_{j,A}^{\dagger}c_{j,A}+c_{j,B}^{\dagger}c_{j,B}\right). \end{aligned}$$3

shows that dimerization can produce phases in which only one rarefied component condenses, yielding sublattice-selective topological regions absent in the uniform chain (Chitov, 2017). At this solvable point, the critical exponents satisfy

$$\begin{aligned} H&=\sum_{j} \Big\{-t\big[(1+\eta)c_{j,A}^{\dagger}c_{j,B}+(1-\eta)c_{j,B}^{\dagger}c_{j+1,A}+h.c. \big] \ &\qquad - \Delta \big[(1+\eta)c_{j,A}^{\dagger}c_{j,B}^{\dagger}+(1-\eta)c_{j,B}^{\dagger}c_{j+1,A}^{\dagger}+h.c. \big] \ &\qquad + 4U \Big[ \Big(n_{j,A}-\frac{1}{2}\Big)\Big(n_{j,B}-\frac{1}{2}\Big) + \Big(n_{j,B}-\frac{1}{2}\Big)\Big(n_{j+1,A}-\frac{1}{2}\Big) \Big] \Big\} \ &\qquad -\mu\sum_{j} \left(c_{j,A}^{\dagger}c_{j,A}+c_{j,B}^{\dagger}c_{j,B}\right). \end{aligned}$$4

and the transitions fall in the 2D Ising universality class (Chitov, 2017).

5. Disorder, quasiperiodicity, and Floquet generalizations

With Anderson-type onsite disorder,

$$\begin{aligned} H&=\sum_{j} \Big\{-t\big[(1+\eta)c_{j,A}^{\dagger}c_{j,B}+(1-\eta)c_{j,B}^{\dagger}c_{j+1,A}+h.c. \big] \ &\qquad - \Delta \big[(1+\eta)c_{j,A}^{\dagger}c_{j,B}^{\dagger}+(1-\eta)c_{j,B}^{\dagger}c_{j+1,A}^{\dagger}+h.c. \big] \ &\qquad + 4U \Big[ \Big(n_{j,A}-\frac{1}{2}\Big)\Big(n_{j,B}-\frac{1}{2}\Big) + \Big(n_{j,B}-\frac{1}{2}\Big)\Big(n_{j+1,A}-\frac{1}{2}\Big) \Big] \Big\} \ &\qquad -\mu\sum_{j} \left(c_{j,A}^{\dagger}c_{j,A}+c_{j,B}^{\dagger}c_{j,B}\right). \end{aligned}$$5

the clean dimerized Kitaev superconductor at $$\begin{aligned} H&=\sum_{j} \Big\{-t\big[(1+\eta)c_{j,A}^{\dagger}c_{j,B}+(1-\eta)c_{j,B}^{\dagger}c_{j+1,A}+h.c. \big] \ &\qquad - \Delta \big[(1+\eta)c_{j,A}^{\dagger}c_{j,B}^{\dagger}+(1-\eta)c_{j,B}^{\dagger}c_{j+1,A}^{\dagger}+h.c. \big] \ &\qquad + 4U \Big[ \Big(n_{j,A}-\frac{1}{2}\Big)\Big(n_{j,B}-\frac{1}{2}\Big) + \Big(n_{j,B}-\frac{1}{2}\Big)\Big(n_{j+1,A}-\frac{1}{2}\Big) \Big] \Big\} \ &\qquad -\mu\sum_{j} \left(c_{j,A}^{\dagger}c_{j,A}+c_{j,B}^{\dagger}c_{j,B}\right). \end{aligned}$$6 has the phase boundary

$$\begin{aligned} H&=\sum_{j} \Big\{-t\big[(1+\eta)c_{j,A}^{\dagger}c_{j,B}+(1-\eta)c_{j,B}^{\dagger}c_{j+1,A}+h.c. \big] \ &\qquad - \Delta \big[(1+\eta)c_{j,A}^{\dagger}c_{j,B}^{\dagger}+(1-\eta)c_{j,B}^{\dagger}c_{j+1,A}^{\dagger}+h.c. \big] \ &\qquad + 4U \Big[ \Big(n_{j,A}-\frac{1}{2}\Big)\Big(n_{j,B}-\frac{1}{2}\Big) + \Big(n_{j,B}-\frac{1}{2}\Big)\Big(n_{j+1,A}-\frac{1}{2}\Big) \Big] \Big\} \ &\qquad -\mu\sum_{j} \left(c_{j,A}^{\dagger}c_{j,A}+c_{j,B}^{\dagger}c_{j,B}\right). \end{aligned}$$7

Disorder can then induce a topological superconducting phase with Majorana zero modes in a region that is trivial in the clean limit. A representative case is $$\begin{aligned} H&=\sum_{j} \Big\{-t\big[(1+\eta)c_{j,A}^{\dagger}c_{j,B}+(1-\eta)c_{j,B}^{\dagger}c_{j+1,A}+h.c. \big] \ &\qquad - \Delta \big[(1+\eta)c_{j,A}^{\dagger}c_{j,B}^{\dagger}+(1-\eta)c_{j,B}^{\dagger}c_{j+1,A}^{\dagger}+h.c. \big] \ &\qquad + 4U \Big[ \Big(n_{j,A}-\frac{1}{2}\Big)\Big(n_{j,B}-\frac{1}{2}\Big) + \Big(n_{j,B}-\frac{1}{2}\Big)\Big(n_{j+1,A}-\frac{1}{2}\Big) \Big] \Big\} \ &\qquad -\mu\sum_{j} \left(c_{j,A}^{\dagger}c_{j,A}+c_{j,B}^{\dagger}c_{j,B}\right). \end{aligned}$$8, where the system is clean-trivial but becomes topological for

$$\begin{aligned} H&=\sum_{j} \Big\{-t\big[(1+\eta)c_{j,A}^{\dagger}c_{j,B}+(1-\eta)c_{j,B}^{\dagger}c_{j+1,A}+h.c. \big] \ &\qquad - \Delta \big[(1+\eta)c_{j,A}^{\dagger}c_{j,B}^{\dagger}+(1-\eta)c_{j,B}^{\dagger}c_{j+1,A}^{\dagger}+h.c. \big] \ &\qquad + 4U \Big[ \Big(n_{j,A}-\frac{1}{2}\Big)\Big(n_{j,B}-\frac{1}{2}\Big) + \Big(n_{j,B}-\frac{1}{2}\Big)\Big(n_{j+1,A}-\frac{1}{2}\Big) \Big] \Big\} \ &\qquad -\mu\sum_{j} \left(c_{j,A}^{\dagger}c_{j,A}+c_{j,B}^{\dagger}c_{j,B}\right). \end{aligned}$$9

as diagnosed by a real-space winding number $\eta=0$0 and a zero-bias conductance plateau at $\eta=0$1 (Hua et al., 2019). Dimerization is therefore a control parameter for disorder-induced Majorana physics rather than a mere perturbation of the uniform chain.

Replacing random disorder by a staggered quasiperiodic potential produces an equally rich static problem. In the quasiperiodic dimerized Kitaev chain with $\eta=0$2, the combined action of dimerization and quasiperiodicity yields extended, critical, and localized phases, together with two distinct mobility edges. For the representative case $\eta=0$3, the chain exhibits a sequence

$\eta=0$4

as $\eta=0$5 increases, with a first topological transition near $\eta=0$6 and a second near $\eta=0$7 (Roy et al., 2022). The same model also displays a broad multifractal regime, identified by $\eta=0$8, and thus departs strongly from the simpler Aubry–André paradigm.

Periodic driving enriches the quasiperiodic dimerized chain further by introducing independent zero- and $\eta=0$9-quasienergy topological sectors. In the kicked model, the Floquet invariants are

$\Delta=0$0

and the intermediate-frequency regime supports extended, critical, and localized bulk phases. In the zero-mode sector, the driven chain can undergo a sequence trivial $\Delta=0$1 topological $\Delta=0$2 Anderson localized, while the $\Delta=0$3-mode sector supports a Floquet topological Anderson phase in which both bulk and edge states are localized but the $\Delta=0$4-gap remains topological (Roy et al., 2023). This gives the dimerized Kitaev chain a genuine Floquet topology not reducible to static SSH-Kitaev physics.

6. Pumping, transport, longer-range couplings, and spectroscopy

A dimerized Kitaev chain with spatially modulated chemical potential can host parameter-space nodal loops and topological charge pumping. In the special case $\Delta=0$5, a partial particle-hole transformation maps the model to the Rice–Mele Hamiltonian,

$\Delta=0$6

which exposes a hidden Thouless-pump structure despite the absence of particle-number conservation. The pumped charge is $\Delta=0$7 for quasiadiabatic loops inside the nodal loop and $\Delta=0$8 for loops enclosing it (Ma et al., 2024). In this setting, dimerization is not only a static topological ingredient but part of a two-parameter control space carrying a Chern number.

Transport in engineered mesoscopic versions of the dimerized chain reveals an additional layer of structure. In a superconducting SSH chain realized with semiconducting quantum dots coupled by superconducting segments, the Majorana representation splits the system into two effective coupled chains. The nonlocal conductance

$\Delta=0$9

then measures interference between Majorana edge modes from the two sectors, and the sign of the response depends on a parity effect in the number of unit cells $U=0$0 (Medina et al., 12 Sep 2025). This parity-controlled CAR-versus-EC interference is a specifically dimerized phenomenon; it is absent in the ordinary one-channel Kitaev chain.

Extended couplings produce yet another hierarchy of phases. Adding extra intercell hopping and pairing $U=0$1 generates a new “degenerated Kitaev-like” phase with

$U=0$2

interpreted as two Majorana zero modes per edge and a $U=0$3 zero-bias Andreev conductance (Li et al., 2020). More recently, high-harmonic studies of a dimerized Kitaev chain with hopping modulation $U=0$4 showed that the bond-alternating structure generates a four-band BdG spectrum with Majorana bound states and finite-energy mid-gap states; for $U=0$5 the mid-gap states remain isolated from the bulk, whereas for $U=0$6 they hybridize with it, strongly modifying harmonic-emission plateaus (R. et al., 5 Jun 2025). In both cases, dimerization reorganizes not only the ground-state topology but also the accessible dynamical and spectroscopic channels.

7. Terminology and related but distinct usages

The phrase “dimerized Kitaev chain” is not universal across subfields. In the fermionic literature summarized above, it denotes an explicitly bond-alternating spinless $U=0$7-wave superconducting chain. In the spin-chain literature, however, “Kitaev chain” can instead mean a one-dimensional bond-directional spin model, which is a different object.

This distinction matters because some recent one-dimensional Kitaev materials papers are not about the fermionic dimerized $U=0$8-wave chain at all. “Transforming from Kitaev to Disguised Ising Chain: Application to CoNb$U=0$9O$$\begin{aligned} H &= -t \sum_{j} \Big[(1+\lambda)c^\dagger_{j,A}c_{j,B} + (1-\lambda)c^\dagger_{j,B}c_{j+1,A}+H.c.\Big] \ &\quad - \Delta \sum_{j}\Big[(1-\lambda)c^{\dagger}_{j,A}c^{\dagger}_{j,B}+ (1+\lambda)c^\dagger_{j,B}c^\dagger_{j+1,A} +H.c.\Big] + \mu \sum_{j}(c^\dagger_{j,A}c_{j,A}+c^\dagger_{j,B}c_{j,B}), \end{aligned}$$0” studies a spin-$$\begin{aligned} H &= -t \sum_{j} \Big[(1+\lambda)c^\dagger_{j,A}c_{j,B} + (1-\lambda)c^\dagger_{j,B}c_{j+1,A}+H.c.\Big] \ &\quad - \Delta \sum_{j}\Big[(1-\lambda)c^{\dagger}_{j,A}c^{\dagger}_{j,B}+ (1+\lambda)c^\dagger_{j,B}c^\dagger_{j+1,A} +H.c.\Big] + \mu \sum_{j}(c^\dagger_{j,A}c_{j,A}+c^\dagger_{j,B}c_{j,B}), \end{aligned}$$1 bond-dependent $$\begin{aligned} H &= -t \sum_{j} \Big[(1+\lambda)c^\dagger_{j,A}c_{j,B} + (1-\lambda)c^\dagger_{j,B}c_{j+1,A}+H.c.\Big] \ &\quad - \Delta \sum_{j}\Big[(1-\lambda)c^{\dagger}_{j,A}c^{\dagger}_{j,B}+ (1+\lambda)c^\dagger_{j,B}c^\dagger_{j+1,A} +H.c.\Big] + \mu \sum_{j}(c^\dagger_{j,A}c_{j,A}+c^\dagger_{j,B}c_{j,B}), \end{aligned}$$2 chain with alternating bond types and staggered anisotropic terms, but explicitly does not study either an explicitly dimerized fermionic Kitaev chain or the textbook Majorana-chain model (Churchill et al., 2024). Likewise, the spin-1 Kitaev-$$\begin{aligned} H &= -t \sum_{j} \Big[(1+\lambda)c^\dagger_{j,A}c_{j,B} + (1-\lambda)c^\dagger_{j,B}c_{j+1,A}+H.c.\Big] \ &\quad - \Delta \sum_{j}\Big[(1-\lambda)c^{\dagger}_{j,A}c^{\dagger}_{j,B}+ (1+\lambda)c^\dagger_{j,B}c^\dagger_{j+1,A} +H.c.\Big] + \mu \sum_{j}(c^\dagger_{j,A}c_{j,A}+c^\dagger_{j,B}c_{j,B}), \end{aligned}$$3 chain with single-ion anisotropy develops a spontaneously dimerized phase for sufficiently negative anisotropy, but that phase is an emergent translation-symmetry-broken state of an interacting spin chain rather than a chain with externally imposed SSH-like bond alternation in a fermionic Hamiltonian (Luo et al., 8 Jul 2026).

A related intermediate case is the dimerized Kitaev spin chain in a modulated transverse field, which maps by Jordan–Wigner transformation to a dimerized spinless $$\begin{aligned} H &= -t \sum_{j} \Big[(1+\lambda)c^\dagger_{j,A}c_{j,B} + (1-\lambda)c^\dagger_{j,B}c_{j+1,A}+H.c.\Big] \ &\quad - \Delta \sum_{j}\Big[(1-\lambda)c^{\dagger}_{j,A}c^{\dagger}_{j,B}+ (1+\lambda)c^\dagger_{j,B}c^\dagger_{j+1,A} +H.c.\Big] + \mu \sum_{j}(c^\dagger_{j,A}c_{j,A}+c^\dagger_{j,B}c_{j,B}), \end{aligned}$$4-wave superconducting chain and exhibits moiré coexistence of locally distinct regimes (Wang et al., 2019). This suggests a useful terminological rule: in fermionic topological-superconductor work, “dimerized Kitaev chain” usually means an SSH-Kitaev hybrid with explicit alternating couplings, whereas in quantum-magnet work it may refer either to bond-directional spin exchange with a two-bond motif or to spontaneous dimerization in a Kitaev-derived spin system. The shared name reflects a common one-dimensional, bond-structured heritage, but the microscopic degrees of freedom, symmetry class, and topological diagnostics are fundamentally different.