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Ayumi Ukai

Publications and source records attributed to Ayumi Ukai.

3 recordsLinked to original sources
arXiv2026

Volume-Independent Spectral Stability of Energy-Truncated Effective Hamiltonians in Quantum Spin Systems

We prove a volume-uniform effective-Hamiltonian theorem for bounded finite-range quantum spin systems on possibly infinite lattices. For any finite target region, we construct an energy-truncated Hamiltonian and prove a volume-uniform spectral-overlap bound controlling the leakage of its low-energy spectral subspace into the high-energy spectral subspace of the original Hamiltonian. The bound may contain non-exponential spectral-window terms, but its cutoff-dependent remainder decays exponentially in the cutoff. In finite volume, this yields stability of low-lying eigenvalues, with eigenvalue errors controlled by the exponentially small cutoff-dependent remainder. In infinite volume, we prove the corresponding spectral-overlap estimate in the GNS representation of an infinite-volume ground state. Thus, for bounded finite-range interactions, we extend and strengthen the effective-Hamiltonian mechanism of Arad, Kuwahara, and Landau by replacing the finite-volume operator-norm formulation with a volume-uniform spectral-overlap formulation applicable in the thermodynamic limit.

math-ph↗
arXiv2025

Spectral Small-Incremental-Entangling: Breaking Quasi-Polynomial Complexity Barriers in Long-Range Interacting Systems

How the detailed structure of quantum complexity emerges from quantum dynamics remains a fundamental challenge highlighted by advances in quantum simulators and information processing. The celebrated Small-Incremental-Entangling (SIE) theorem provides a universal constraint on the rate of entanglement generation, yet it leaves open the problem of fully characterizing fine entanglement structures. Here we introduce the concept of Spectral-Entangling strength, which captures the structural entangling power of an operator, and establish a spectral SIE theorem: a universal speed limit for R'enyi entanglement growth at $α\ge 1/2$, revealing a robust $1/s^2$ decay threshold in the entanglement spectrum. Remarkably, our bound at $α=1/2$ is both qualitatively and quantitatively optimal, defining the universal threshold beyond which entanglement growth becomes unbounded. This exposes the detailed structure of Schmidt coefficients and enables rigorous truncation-based error control, linking entanglement structure to computational complexity. Building on this, we derive a generalized entanglement area law under an adiabatic-path condition, extending a central principle of quantum many-body physics to general interactions. As a concrete application, we show that one-dimensional long-range interacting systems admit polynomial bond-dimension approximations for ground, time-evolved, and thermal states, thereby closing the long-standing quasi-polynomial gap and demonstrating that such systems can be simulated efficiently with tensor-network methods. By explicitly controlling R'enyi entanglement, we obtain a rigorous, a priori error guarantee for the time-dependent density-matrix renormalization-group algorithm. Overall, our results extend the SIE theorem to the spectral domain and establish a unified framework that unveils the detailed and universal structure underlying quantum complexity.

quant-ph↗