Tunable information insulation induced by constraint mismatch

Abstract

We study a composite model of two $1D$ $PXP$ chains with dual constraints, forming a junction that acts as an infinite kinematic barrier to quantum information exchange. Moreover, the hard wall at the junction which acts as a perfect reflector, preventing any quantum information leakage between the two sides of the composite chain, can be made permeable by relaxing the constraint at the junction sites. Multiple frozen junctions shatter the Hilbert space into disjoint Krylov fragments, the number of which increases exponentially with the engineered defects. Furthermore, the energy level statistics in each symmetry-resolved sector are strictly Poissonian, demonstrating that the tensor sum of the disjoint Hamiltonians results in a pure superposition of the chaotic spectra of the sub- $PXP$ chains. We also find that a chirally protected zero-energy mode can exist which has local peaks at the physical edges and within the bulk near the junction sites. This state is protected from hybridization with bulk states induced by any chirality preserving disorder. Due to the tensor product structure of the eigenfunctions, the non-zero energy scar states also multiply in number. Finally, we introduce novel Fock states with spatially tunable thermal and athermal regions. This architecture can be readily realized in programmable Rydberg atom platforms using optical tweezers, addressing beams and facilitation techniques.

Figures (4)

• Figure 1: Panel $(a)$ shows an open $PXP-d$-$PXP-PXP-d$-$PXP$ chain of length, $L=16$ with three junctions each of which does not allow $00$ and $11$. Panel $(b)$ shows all the Hilbert space fragments of varying Hilbert space dimensions ($HSD$) for the chain in panel (a). Panel $(c)$ shows that the level statistics of a $PXP-d$-$PXP$ chain of length $L=22$ in the $S=+1$ sector of the $01$ fragment is Poissonian in contrast with the $WD$ statistics of a pure $PXP$ chain of length $L=20$ in the $R=+1$ sector, which is shown in the inset. Panel $(d)$ shows how the number of zero modes $N_z$ scale with the system size in the $PXP-d$-$PXP$ chain as well as in the $PXP$ chain. The scaling of the accidental and product modes for the $PXP-d$-$PXP$ chain is shown in the inset.
• Figure 2: Panel (a) shows the density profile $\langle n_l^{i} \rangle$ on the left half of the chain and $\langle n_r^{i} \rangle$ on the right half of the chain for the tensor product state $|0_l\rangle|01\rangle|0_r\rangle$. The blue curve corresponds to the chirally protected zero mode, obtained by introducing a random $PXP$ disorder into the individual sub-chains ($L_{\text{sub}}=14$) with amplitudes $\epsilon_j$ drawn from a uniform distribution $\epsilon_j \in [0, 10^{-5}]$. The red curve shows the tensor product of the least entangled zero modes (LEZM) of the respective sub-chains, obtained via an entanglement minimization algorithm in the pristine limit. Panel (b) shows the bipartite Von Neumann entanglement entropy $S_E$ for the $01$ sector of the composite PXP-$d$-PXP chain ($L=22$), utilizing a two-cut bipartition at $j=5$ and $j=15$. The LEZM for this composite model, isolated via the SVD minimization technique, is additionally highlighted.
• Figure 3: Panel $(a)$ shows that the $OTOC$, $C_{ij}$ for a $PXP-d$-$PXP$ chain of length, $L=22$ in the initial state $|00..00|01|11..10\rangle$ with site $i=21$, is confined to $j>11$ under unitary time evolution. In panel $(b)$ we show the same when the $00$ constraint is lifted for $L=20$. In panel $(c)$, we show the caging effect of quantum information between two junctions in the initial state $|000|10|10101101_{i}1010|10|000\rangle$($L=22$). Panel $(d)$ shows the late time average of the entanglement entropy, $\bar{S}_{\infty}(x)$ as a function of cuts along the chain where cuts, $x$ are made on the different bonds, for a $PXP-d$-$PXP$ chain in it's vacuum state, $|00..0|01|1..11\rangle$$(L=20)$. Here, the blue curve shows the case when both $00$ and $11$ are not allowed at the junction and the red curve shows the same when the junction becomes permeable and allows only $00$.
• Figure 4: Panel $(a)$ shows the dynamics of the onsite density $\langle n_{r,l}^{j}(t)\rangle$ for two representative points, $j=8$ and $j=18$ in the two regions separated by the junction for a $PXP-d$-$PXP$ chain in the initial state $|01..01|01|11..11\rangle (L=22)$. Here, as usual, no $00$ or $11$ are allowed at the junction. Panel $(b)$ shows the late time average of the entanglement entropy, $\bar{S}_{\infty}(x)$ as a function of cuts along the chain where the cuts, $x$ are made on different bonds. Time variation of $S_{j}(t)$ is shown in the inset for the same sites as in panel $(a)$.