Enhancement Chains in Quantum Systems

• Enhancement chains are many-body quantum systems that leverage spatial inhomogeneities, via engineered impurities or superlattice potentials, to unexpectedly boost block entanglement.
• The entanglement boost—up to approximately 27% enhancement in block von Neumann entropy—is achieved by redistributing particles into impurity-free regions where local densities favor entanglement.
• A predictive framework using density functional theory with an interface-corrected local density approximation guides the design of quantum devices by optimizing impurity placement and effective particle density.

Enhancement chains refer to a class of many-body quantum systems—often modeled as Fermi-Hubbard chains—where spatial inhomogeneities (such as repulsive impurities or engineered superlattice potentials) unexpectedly increase subsystem entanglement, contrary to the conventional expectation that disorder or impurities only suppress quantum correlations. These systems leverage local particle density enhancement in impurity-free regions to achieve higher entanglement as quantified by block von Neumann entropy. Theoretical analysis centered on the density functional approach provides a predictive framework for when and how spatial structuring can serve as a resource in quantum information, with robust numerical evidence indicating strong entanglement enhancement regimes.

1. Mechanisms of Entanglement Enhancement

Enhancement in such chains is realized by the strategic incorporation of site-dependent external potentials $V_i$ into the standard one-dimensional Hubbard Hamiltonian:

$$H = -t\sum_{\langle ij \rangle, \sigma} c^\dagger_{i\sigma}c_{j\sigma} + U \sum_i n_{i\uparrow}n_{i\downarrow} + \sum_{i,\sigma} V_i n_{i\sigma}$$

Here, $t$ is the nearest-neighbor tunneling (hopping) amplitude, $U$ is the on-site repulsive interaction, and $V_i$ encodes local impurity or superlattice potentials (generally $V \gg t$ for strong impurities).

Impurity sites with large $V$ repulse fermions, leading to an effective increase in particle density $n_{\text{eff}} = N/(L - I)$—where $N$ is total particle number, $L$ is chain length, and $I$ is the number of impurity sites—in impurity-free regions. Because the block von Neumann entropy $S_x = -\mathrm{Tr}\,\rho_x \log_2\rho_x$ (with $\rho_x$, the block reduced density matrix) increases monotonically with the local density for $n \lesssim 0.8$, impurity-induced inhomogeneity can result in up to $\sim27\%$ enhancement of entanglement entropy for those blocks, which can surpass the homogeneous-chain maximum.

2. Block Versus Site Entanglement: Contrasts to Prior Studies

Traditional studies largely focused on single-site entanglement, observing decoherence and entanglement suppression as impurity potential $V$ increases. These works failed to examine entanglement of blocks excluding impurity sites. In contrast, block entanglement—especially for blocks located away from impurity sites—benefits from the particle redistribution. Block entanglement captures quantum correlations overlooked by single-site metrics and reveals regimes where inhomogeneity transforms from a detrimental effect to a resource.

Key differences include:

• Block entanglement sensitivity to the effective density in impurity-free regions.
• Interface effects, where partition boundaries play a nontrivial role; blocks abutting impurities manifest unique entropy behaviors.

3. Predictive Density Functional Theory and Interface LDA

Observables (including entanglement) admit density functional representations. For the homogeneous 1D Hubbard chain, the functional $S(n)$ can be derived exactly (e.g., by Bethe-Ansatz techniques), showing $S$ increases with density up to $n \lesssim 0.8$. The local density approximation (LDA) is used for inhomogeneous systems: replace $n \rightarrow n_i$ locally, then compute

$S_{\text{LDA}}(x) = \sum_{i \in x} S(n_i)$

The paper extends this by including boundary corrections ("interface density amended LDA"), arguing that entanglement in a block depends not just on its bulk density but also on densities at its boundaries with the complementary subsystem. This refined LDA accurately predicts why blocks farther from the impurity exhibit maximal enhancement while boundary-adjacent blocks show more modest gains.

4. Quantitative Enhancement and Numerical Validation

Enhancement chains display robust, quantifiable entanglement increases:

• For $U = 4t$, $V \gg t$, chain lengths $L = 10-12$ (Lanczos diagonalization) and $L \leq 36$ (DMRG), entanglement entropy can be increased by up to $\sim27\%$ compared to homogeneous chains (no impurities).
• In superlattice configurations, where $V_i$ is periodically modulated, blocks of size $x = 3$ and $x = 4$ achieve entanglement entropy exceeding analytic conformal-invariance predictions for the homogeneous case.

The consistency across small and large-scale numerics establishes the universality of the enhancement effect under strong repulsive inhomogeneities with effective densities in the entanglement-positive regime.

5. General Predictive Recipe for Nanostructure Engineering

The design protocol for maximizing entanglement involves:

• Computing effective density $n_{\text{eff}} = N/(L - I)$, targeting $n_{\text{eff}} \lesssim 0.8$ for maximal block entanglement.
• Using LDA (with interface correction) to predict which blocks (bipartitions) will showcase maximal von Neumann entropy.
• Engineering impurity placement and strength strategically to achieve optimal interface and density profiles.

This recipe is generalizable to arbitrary nanostructures (e.g., quantum dot arrays, cold-atom chains) where controlled impurity potentials are feasible.

6. Implications for Quantum Information and Technology

High block entanglement directly enhances capabilities in quantum communication, error correction, and robust qubit architectures. The insight that spatial inhomogeneity—often considered a detriment—can improve quantum correlations enables new strategies in quantum device engineering:

• Superlattice and impurity designs tuned to push local densities into the entanglement-favorable regime.
• Block-based entanglement metrics guiding architectural selection and error tolerance in quantum hardware.

The interface-amended LDA offers practical predictive capability for experimentalists targeting entanglement optimization.

7. Summary

Enhancement chains, as established by inhomogeneous Fermi-Hubbard models, represent a paradigm shift in many-body entanglement engineering. Rather than uniformity, strategic spatial structuring optimizes entanglement, with well-defined recipes from density functional theory and supported by both exact and numerical methods. These findings underpin the design of robust solid-state, cold-atom, and nanostructure quantum devices, providing constructive pathways for entanglement amplification in the presence of disorder and engineered inhomogeneity.