Efficient search for excitable zero-modes in constrained systems

• URL: http://arxiv.org/abs/2608.31165v1
• Date: Mon, 31 Aug 2026 17:59:12 GMT
• Title: Efficient search for excitable zero-modes in constrained systems
• Abstract summary: I present an efficient protocol for finding analytical expressions for translation-in-variant EZMs in constrained systems.<n>I demonstrate the power of this method on a decorated Rydberg chain.<n>I then show how the physical structure of the manifold, which is tied to the local eigenbasis, also allows one to derive analytical expressions for ZMs at non-zero momentum.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Kinetically constrained systems, such as those representing Rydberg atom arrays in the blockade regime, have gathered considerable attention due to the presence of atypical eigenstates in their spectrum. The latter manifests itself through the presence of quantum many-body scars as well as unusually large zero-mode (ZM) subspaces which contain analytically tractable eigenstates with various entanglement scalings. In particular, some of the latter are excitable zero-modes (EZMs), meaning that they can be promoted to a non-zero energy for open boundary conditions. In this work, I present an efficient protocol for finding analytical expressions for translation-invariant EZMs in constrained systems, based on the eigendecomposition of the local unconstrained Hamiltonian. I demonstrate the power of this method on a decorated Rydberg chain. In that model, my protocol directly produces a continuous matrix-product-state manifold located entirely in the zero-energy eigenspace for periodic boundary conditions. The span of that manifold grows exponentially with the system, and for odd system sizes it covers the entire zero-momentum eigenspace with zero energy. I then show how the physical structure of the manifold, which is tied to the local eigenbasis, also allows one to derive analytical expressions for ZMs at non-zero momentum and for a polynomial number of exact scars at $E=\pm\sqrt{3}$.

Related papers

• Modular-Annihilator Parent Hamiltonians for Purified Gibbs States: Spectral Design and Controlled Approximation [0.0]
  We study the exact finite sum-of-squares (SoS) construction of their parent Hamiltonians and the associated Lindbladian based on modular annihilators.<n>The purified Gibbs state remains a common zero mode while the freedom to choose and combine the generators can be used to optimize the spectral properties of the parent Hamiltonian.
  arXiv  Detail & Related papers  (2026-08-31T05:33:17Z)
• Quantum Chaos with a Macroscopic Zero-Mode Sector [36.947315248138345]
  Chaotic many-body spectra are expected to densely fill their energy window.<n>We show that constrained spin chains with chiral symmetry evade this expectation by hosting an exponentially large manifold of symmetry-protected exact zero modes.
  arXiv  Detail & Related papers  (2026-07-10T15:17:05Z)
• Unitary discretization of the Koopman-von Neumann equation for quantum simulation of fluid and plasma dynamics [45.88028371034407]
  KvN framework embeds the Liouville equation into a Hilbert space with norm-preserving, unitary evolution.<n>Weyl-ordered KvN generator is derived as the unique anti-Hermitian operator symmetrization for real velocity fields.
  arXiv  Detail & Related papers  (2026-05-18T23:27:02Z)
• Ergodicity breaking in matrix-product-state effective Hamiltonians [0.0]
  We show that the density-matrix renormalization group (DMRG) effective Hamiltonian encodes detailed information about the dynamics far from equilibrium.<n>In the random-field XXZ spin chain, the spectrum of the effective Hamiltonian is shown to capture the transition from thermal to many-body localized regimes.
  arXiv  Detail & Related papers  (2026-03-27T18:00:01Z)
• Efficient Eigenstate Preparation in an Integrable Model with Hilbert Space Fragmentation [39.49473274097833]
  We consider the preparation of all the eigenstates of spin chains using quantum circuits.<n>We showivities of the growth is also achievable for interacting models where the interaction between the particles is sufficiently simple.
  arXiv  Detail & Related papers  (2024-11-22T18:57:08Z)
• Exact dynamics of quantum dissipative $XX$ models: Wannier-Stark localization in the fragmented operator space [49.1574468325115]
  We find an exceptional point at a critical dissipation strength that separates oscillating and non-oscillating decay. We also describe a different type of dissipation that leads to a single decay mode in the whole operator subspace.
  arXiv  Detail & Related papers  (2024-05-27T16:11:39Z)
• Diagnosing non-Hermitian Many-Body Localization and Quantum Chaos via Singular Value Decomposition [0.0]
  Strong local disorder in interacting quantum spin chains can turn delocalized eigenmodes into localized eigenstates. This is accompanied by distinct spectral statistics: chaotic for the delocalized phase and integrable for the localized phase. We ask whether random dissipation (without random disorder) can induce chaotic or localized behavior in an otherwise integrable system.
  arXiv  Detail & Related papers  (2023-11-27T19:00:01Z)
• Duality between open systems and closed bilayer systems, and thermofield double states as quantum many-body scars [49.1574468325115]
  We find a duality between open many-body systems governed by the Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) equation. Under this duality, the identity operator on the open system side maps to the thermofield double state. We identify broad classes of many-body open systems with nontrivial explicit eigen operators $Q$ of the Lindbladian superoperator.
  arXiv  Detail & Related papers  (2023-04-06T15:38:53Z)
• Localization in the random XXZ quantum spin chain [55.2480439325792]
  We study the many-body localization (MBL) properties of the Heisenberg XXZ spin-$frac12$ chain in a random magnetic field. We prove that the system exhibits localization in any given energy interval at the bottom of the spectrum in a nontrivial region of the parameter space.
  arXiv  Detail & Related papers  (2022-10-26T17:25:13Z)
• Area-law entangled eigenstates from nullspaces of local Hamiltonians [0.0]
  Eigenstate thermalization in quantum many-body systems implies that eigenstates at high energy are similar to random vectors. We show that interacting quantum models that have a nullspace provide a route to non-thermal eigenstates.
  arXiv  Detail & Related papers  (2021-02-26T18:17:18Z)
• Spectral statistics in constrained many-body quantum chaotic systems [0.0]
  We study the spectral statistics of spatially-extended many-body quantum systems with on-site Abelian symmetries or local constraints. In particular, we analytically argue that in a system of length $L$ that conserves the $mth$ multipole moment, $t_mathrmTh$ scales subdiffusively as $L2(m+1)$.
  arXiv  Detail & Related papers  (2020-09-24T17:59:57Z)
• Models of zero-range interaction for the bosonic trimer at unitarity [91.3755431537592]
  We present the construction of quantum Hamiltonians for a three-body system consisting of identical bosons mutually coupled by a two-body interaction of zero range. For a large part of the presentation, infinite scattering length will be considered.
  arXiv  Detail & Related papers  (2020-06-03T17:54:43Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.