Type-II Scars in Rydberg Arrays

• Type-II scars are a class of quantum many-body scars characterized by a pinned sublattice that remains inert while the other sublattices exhibit coherent, SU(2)-like oscillations.
• They are defined via a precise three-sublattice partition (A, B, and C) with strict graph-theoretic criteria that exploit frustration to create a low-dimensional nonthermal sector.
• Experimental relevance is highlighted by the use of Rydberg blockade models and state-resolved fluorescence imaging to observe long-lived revival dynamics and nonthermal trajectories.

Searching arXiv for the primary paper and closely related usage of “Type-II scars.” Attempting arXiv search for the cited identifiers. Type-II scars are a class of quantum many-body scars in frustrated Rydberg arrays in which strong frustration pins part of the lattice while the complementary degrees of freedom undergo coherent, approximately $SU(2)$-like oscillations (Desaules et al., 6 May 2026). In this usage, the mechanism is not a perturbative repair of frustration but an exploitation of it: a “dead” sublattice remains nearly inert, and the remaining active sublattices realize a low-dimensional nonthermal sector with long-lived revivals. The phrase is not uniform across the scars literature. In other settings it has been used, or can be naturally interpreted, for non-ergodic multifractal sectors, finite exact embedded sectors, or scarred dynamics coexisting with volume-law entanglement (Mondal et al., 2021, Dai, 2024, Zhao et al., 2021). The graph-theoretic Rydberg construction provides the sharpest explicit definition.

1. Definition in frustrated Rydberg arrays

In the constrained Rydberg setting, Type-II scars arise in strongly frustrated PXP models on graphs $G(V,E)$ for which the vertex set can be partitioned into three disjoint sublattices,

$$V=A\cup B\cup C,\qquad A\cap B=A\cap C=B\cap C=\emptyset.$$

The sublattices $A$ and $B$ are the active sublattices that host coherent oscillations, whereas $C$ is a dead or pinned sublattice whose dynamics is strongly suppressed by frustration and local constraints (Desaules et al., 6 May 2026).

The physical picture is that excitations are kinematically or effectively energetically disfavored on $C$. When $C$ stays near a simple configuration, typically the all-down state, it serves as a static buffer enforcing blockade constraints while $A$ and $B$ remain almost unconstrained and can oscillate. This distinguishes Type-II scars from the Type-I mechanism introduced in the same work. Type-I scars use a clique cover and locally entangled building blocks such as dimer or triangle $G(V,E)$0-states to map a mildly frustrated lattice onto an effective bipartite lattice. Type-II scars instead sacrifice part of the Hilbert space by freezing $G(V,E)$1, thereby creating an emergent scarred subspace for the remaining spins.

The construction is motivated by the failure of conventional Néel-like scarring on non-bipartite lattices composed largely of triangles or tetrahedra. On bipartite lattices such as the chain, square, or honeycomb lattices, standard PXP scarring is associated with approximate bipartite structure. On triangular, kagome, quasi-2D asanoha, and pyrochlore-like geometries, the blockade constraints are strongly frustrated, and Type-II scarring is designed precisely for that regime.

2. Constrained Hamiltonian and graph-theoretic $G(V,E)$2 construction

The underlying model is the deep-blockade Rydberg Hamiltonian,

$G(V,E)$3

with

$G(V,E)$4

Each spin flip is therefore allowed only when all neighbors of site $G(V,E)$5 are in $G(V,E)$6, implementing the Rydberg blockade (Desaules et al., 6 May 2026).

The graph-theoretic construction introduces

$G(V,E)$7

together with

$G(V,E)$8

and

$G(V,E)$9

The commutator $$V=A\cup B\cup C,\qquad A\cap B=A\cap C=B\cap C=\emptyset.$$0 is then used to approximate an $$V=A\cup B\cup C,\qquad A\cap B=A\cap C=B\cap C=\emptyset.$$1 algebra in a scarred subspace. If this algebra approximately closes, and the system is prepared in a lowest-weight state of $$V=A\cup B\cup C,\qquad A\cap B=A\cap C=B\cap C=\emptyset.$$2, the evolution under $$V=A\cup B\cup C,\qquad A\cap B=A\cap C=B\cap C=\emptyset.$$3 resembles precession of a large spin.

For Type-II scars, the partition $$V=A\cup B\cup C,\qquad A\cap B=A\cap C=B\cap C=\emptyset.$$4 is required to satisfy three graph-theoretic criteria:

$$V=A\cup B\cup C,\qquad A\cap B=A\cap C=B\cap C=\emptyset.$$5

$$V=A\cup B\cup C,\qquad A\cap B=A\cap C=B\cap C=\emptyset.$$6

$$V=A\cup B\cup C,\qquad A\cap B=A\cap C=B\cap C=\emptyset.$$7

$$V=A\cup B\cup C,\qquad A\cap B=A\cap C=B\cap C=\emptyset.$$8

$$V=A\cup B\cup C,\qquad A\cap B=A\cap C=B\cap C=\emptyset.$$9

Condition (I) forbids $A$0–$A$1, $A$2–$A$3, and $A$4–$A$5 edges, so any edge touching $A$6 or $A$7 must terminate on $A$8. Condition (II) ensures that every $A$9-site is watched by both active sublattices. Condition (III) enforces strong frustration within $B$0 or sufficiently strong coupling of $B$1 to $B$2, which is the ingredient that actually pins $B$3. When this last condition is violated, the reported behavior is typically only short-lived oscillation rather than robust scarring.

3. Pinned sublattice mechanism and natural initial states

Under conditions (I)–(III), the dynamics separates into a nearly inert pinned sector and an active oscillating sector (Desaules et al., 6 May 2026). For $B$4, the occupation

$B$5

remains close to zero for long times when the initial state has $B$6 fully down. The sites in $B$7 are constrained both by their internal connectivity and by the requirement that neighboring $B$8 and $B$9 sites remain compatible with blockade.

By contrast, $C$0 and $C$1 do not directly blockade each other. Since the relevant constraints are mediated through $C$2, and $C$3 remains almost unexcited, the active sites behave approximately as two interpenetrating sets of non-interacting spins subject to the global $C$4-like structure. The crucial operator $C$5 has commuting local terms for Type-II partitions, because the dressed $C$6 on $C$7 share no overlapping support on neighbors once condition (I) is imposed.

This yields an especially simple initial state: the ground state of $C$8,

$C$9

with $C$0. This state is a product state, has low entanglement, and is described as experimentally easy to prepare via a single site-dependent global pulse along the $C$1 axis. Under $C$2, it evolves approximately as an $C$3 coherent state and produces sinusoidal oscillations of observables closely related to $C$4, notably the sublattice occupations

$C$5

A useful complementary state is $C$6, the ground state of $C$7, which is generally entangled but lies close to the same scarred sector. In weaker-pinning geometries, deformations of these states improve revivals. The quasi-2D pyrochlore analysis introduces product states $C$8, with $C$9 reproducing $C$0, and an entangled $C$1 that penalizes excitations in $C$2.

4. Lattice realizations and dynamical diagnostics

The explicit Type-II realizations highlighted are the asanoha lattice and a quasi-2D pyrochlore lattice, both built from tetrahedral motifs (Desaules et al., 6 May 2026). The asanoha lattice is described as a triangular lattice in which each triangle is thickened into a tetrahedron, alternating up and down tetrahedra. This geometry is more frustrated than the pure two-dimensional triangular lattice, and the partition $C$3 can be chosen so that the tetrahedral connectivity enforces all three Type-II criteria.

In the asanoha case, starting from $C$4, the return fidelity

$C$5

shows pronounced revivals. The local and sublattice occupations exhibit the characteristic Type-II pattern: $C$6 remains very small for $C$7, while $C$8 and $C$9 oscillate with large amplitude and almost out of phase.

The quasi-2D pyrochlore lattice implements the same three-sublattice logic but with weaker pinning, because each $A$0-site has fewer neighbors in $A$1 than in the asanoha construction. The resulting revivals are clear but not perfect, and $A$2 exhibits some residual oscillation. In that setting, deforming the initial state materially improves the scarring. For an optimized $A$3, the $A$4 family gives much better revivals than $A$5, and $A$6 with $A$7 has overlap $A$8 with $A$9; $B$0 yields nearly perfect revivals together with $B$1.

The principal diagnostics are return fidelity and the sublattice averages

$B$2

Type-II scarring is characterized by $B$3 for all times and large-amplitude periodic motion of $B$4 and $B$5.

5. Spectral interpretation and nonthermal trajectories

The full PXP Hamiltonian remains nonintegrable and chaotic in the full Hilbert space, with eigenstates obeying ETH and Wigner–Dyson level statistics, but the scarred behavior is attributed to a small set of atypical eigenstates with enhanced overlap on $B$6-like initial states, lower entanglement entropy than typical states at the same energy, and an approximate $B$7 ladder or band in energy space (Desaules et al., 6 May 2026). For Type-II scars, that special band is associated primarily with excitations on $B$8, while $B$9 stays pinned.

This picture clarifies a common source of confusion. The abstract of the Rydberg work emphasizes an exponential family of scarred trajectories on the hexagonal lattice that can encode information protected from thermalization, but that construction is explicitly Type-I, not Type-II. It relies on dimer Néel patterns on a bipartite lattice. The Type-II analogue is not an exponential set of dimer covers but a family of trajectories specified by valid partitions $G(V,E)$00 and by deformations such as $G(V,E)$01 and $G(V,E)$02. The same qualitative logic applies: as long as the dynamics remains confined to an approximate scarred subspace, local observables retain memory of initial conditions for times much longer than microscopic timescales, and relaxation to ETH expectations is delayed.

A plausible implication is that Type-II scars are best viewed not as isolated eigenstates alone but as dynamically selected sectors defined by a pinned buffer and an active oscillating subsystem. In this sense, the pinned sublattice is not a spectator. It is the structural ingredient that permits the approximate $G(V,E)$03 organization of the remaining degrees of freedom.

6. Broader uses of the term and taxonomic ambiguity

The phrase “Type-II scars” does not carry a single universal definition across the literature. The coupled-top model does not use the term explicitly, but it naturally supports a two-type reading in which orbit-pinned scars of unstable fixed points or periodic orbits form one class, while non-ergodic multifractal states form a distinct, “Type-II” sector not localized near a particular orbit (Mondal et al., 2021). In that setting, the relevant diagnostics are relative entanglement entropy, generalized multifractal dimensions $G(V,E)$04, and OTOC/FOTOC behavior rather than a pinned sublattice.

A different usage appears in orthogonal quantum many-body scars, where persistent oscillations coexist with rapid volume-law entanglement generation in a constrained orthogonal metal. There the Type-II intuition is that non-ergodicity need not coincide with low-entanglement eigenstates; the scarred sector can violate ETH dynamically while the physical half-chain entanglement grows extensively (Zhao et al., 2021). Exact valence-bond solid scars in the square-lattice Heisenberg model are also positioned as Type-II because they form a finite set of exact, area-law, symmetry-breaking eigenstates embedded in an otherwise thermal spectrum without an equally spaced tower (Dai, 2024).

Several other developments fit the same broader category. Floquet–Bloch scars are described as a symmetry-protected Floquet scar family with rigid quasienergy pairing and translation-invariant discrete time-crystal behavior (Huang et al., 2022). “Majorana Scars as Group Singlets” constructs a protected scar subspace as the $G(V,E)$05 singlet sector of a Majorana lattice model, with $G(V,E)$06 and $G(V,E)$07 families and logarithmic entanglement scaling (Sun et al., 2022). “Hidden $G(V,E)$08 subspace symmetry protection for quantum scars” analyzes a spin-1 XY tower as a Type-II scar sector protected by a hidden commutant symmetry and diagnosed by an LSM-type twist operator and QFI scaling (Sharma et al., 25 Feb 2026). “Enhanced many-body quantum scars from the non-Hermitian Fock skin effect” describes a non-Hermitian, constraint-driven scar mechanism whose protected sector is stabilized by directional pumping in Fock space (Shen et al., 2024). These usages are related but not interchangeable.

7. Experimental relevance and open problems

The Rydberg construction is explicitly framed for programmable atom arrays in the blockade regime, where lattice geometry is tunable and single-site addressing permits sublattice-dependent state preparation (Desaules et al., 6 May 2026). The natural Type-II initial state $G(V,E)$09 is a simple product state with sublattice-dependent phases, and the key observables—site occupations and sublattice averages—are directly measurable by state-resolved fluorescence imaging. The experimentally salient signature is the simultaneous observation of suppressed dynamics on $G(V,E)$10, large-amplitude oscillations on $G(V,E)$11 and $G(V,E)$12, and long-lived return-fidelity peaks.

Several open directions are explicit. One is robustness away from the ideal PXP limit, including finite detuning, long-range interactions, disorder, and decoherence. Another is coexistence of Type-I and Type-II scars on the same lattice and the possibility of hybrid mechanisms. A further problem is whether Type-II scarred states can act as a vacuum for nonthermal excitations and support anomalous transport. The graph-theoretic role of maximal independent sets also suggests extension beyond the standard Rydberg PXP model to broader constrained-spin settings.

Type-II scars therefore occupy two levels of meaning. In the narrow and currently sharp sense of frustrated Rydberg arrays, they are the nonthermal trajectories generated when strong frustration pins a buffer sublattice and leaves the rest of the lattice to precess coherently. In the broader scars literature, they designate a family resemblance among nonthermal sectors that are embedded, symmetry-protected, multifractal, or otherwise distinct from the conventional approximate-$G(V,E)$13 tower paradigm. The Rydberg formulation supplies one of the clearest microscopic realizations of that broader idea.