Excited states from local effective Hamiltonians of matrix product states and their entanglement spectrum transition

• URL: http://arxiv.org/abs/2511.16746v1
• Date: Thu, 20 Nov 2025 19:00:38 GMT
• Title: Excited states from local effective Hamiltonians of matrix product states and their entanglement spectrum transition
• Authors: Denise Cocchiarella, Mingru Yang, Yueshui Zhang, Mari Carmen Bañuls, Hong-Hao Tu, Yuhan Liu,
• Abstract summary: We provide a conformal field theory perspective that helps elucidate this connection.<n>We predict an entanglement-spectrum transition of excited states as the ratio of the subsystem size to the total system size is varied.<n>Our numerical results support this picture and demonstrate a reorganization of the entanglement spectrum into distinct conformal towers as this ratio changes.
• Score: 18.458863288479844
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Solving excited states is a challenging task for interacting systems. For one-dimensional critical systems, however, excited states can be directly accessed from the eigenvectors of the local effective Hamiltonian that is constructed from the ground state obtained by variational matrix product state (MPS) optimization. Despite its numerical success, the theoretical mechanism underlying this method has remained largely unexplored. In this work, we provide a conformal field theory (CFT) perspective that helps elucidate this connection. The key insight is that this construction effectively uses a truncated basis of ground-state Schmidt vectors to represent excited states, where the contribution of each Schmidt vector can be expressed as a CFT correlation function and shown to decay with increasing Schmidt index. The CFT analysis further predicts an entanglement-spectrum transition of excited states as the ratio of the subsystem size to the total system size is varied. Our numerical results support this picture and demonstrate a reorganization of the entanglement spectrum into distinct conformal towers as this ratio changes.

Related papers

• SIGMA: Scalable Spectral Insights for LLM Collapse [51.863164847253366]
  We introduce SIGMA (Spectral Inequalities for Gram Matrix Analysis), a unified framework for model collapse.<n>By utilizing benchmarks that deriving and deterministic bounds on the matrix's spectrum, SIGMA provides a mathematically grounded metric to track the contraction of the representation space.<n>We demonstrate that SIGMA effectively captures the transition towards states, offering both theoretical insights into the mechanics of collapse.
  arXiv  Detail & Related papers  (2026-01-06T19:47:11Z)
• Squeezed Coherent States in Supersymmetric Quantum Mechanics with Position-Dependent Mass [0.0]
  We construct and analyze a class of squeezed coherent states within the framework of supersymmetric quantum mechanics.<n>The resulting states exhibit non-classical features, such as squeezing, coherence, and modified uncertainty relations.
  arXiv  Detail & Related papers  (2025-08-10T08:13:15Z)
• Grassmann Variational Monte Carlo with neural wave functions [45.935798913942904]
  We formalize the framework introduced by Pfau et al.citepfau2024accurate in terms of Grassmann geometry of the Hilbert space.<n>We validate our approach on the Heisenberg quantum spin model on the square lattice, achieving highly accurate energies and physical observables for a large number of excited states.
  arXiv  Detail & Related papers  (2025-07-14T13:53:13Z)
• An application of the theta operator in generalized hypergeometric coherent states formalism [0.0]
  We examine one of the multiple applications of theta operator xd/dx in quantum mechanics, namely, in the formalism of generalized hypergeometric coherent states (GHG CSs) A series of new results were obtained and some already known ones were found / confirmed. To support the theoretical considerations presented above, we examined, as example, the quantum systems with a linear energy spectrum.
  arXiv  Detail & Related papers  (2024-04-19T18:07:59Z)
• Magic in generalized Rokhsar-Kivelson wavefunctions [0.0]
  We study magic, as quantified by the stabilizer Renyi entropy, in a class of models known as generalized Rokhsar-Kive systems. We find that the maximum of the SRE generically occurs at a cusp away from the quantum critical point, where the derivative suddenly changes sign.
  arXiv  Detail & Related papers  (2023-11-14T19:00:05Z)
• Enhanced Entanglement in the Measurement-Altered Quantum Ising Chain [43.80709028066351]
  Local quantum measurements do not simply disentangle degrees of freedom, but may actually strengthen the entanglement in the system.<n>This paper explores how a finite density of local measurement modifies a given state's entanglement structure.
  arXiv  Detail & Related papers  (2023-10-04T09:51:00Z)
• Message-Passing Neural Quantum States for the Homogeneous Electron Gas [41.94295877935867]
  We introduce a message-passing-neural-network-based wave function Ansatz to simulate extended, strongly interacting fermions in continuous space. We demonstrate its accuracy by simulating the ground state of the homogeneous electron gas in three spatial dimensions.
  arXiv  Detail & Related papers  (2023-05-12T04:12:04Z)
• Three-fold way of entanglement dynamics in monitored quantum circuits [68.8204255655161]
  We investigate the measurement-induced entanglement transition in quantum circuits built upon Dyson's three circular ensembles. We obtain insights into the interplay between the local entanglement generation by the gates and the entanglement reduction by the measurements.
  arXiv  Detail & Related papers  (2022-01-28T17:21:15Z)
• Excited states from eigenvector continuation: the anharmonic oscillator [58.720142291102135]
  Eigenvector continuation (EC) has attracted a lot attention in nuclear structure and reactions as a variational resummation tool for many-body expansions. This work is dedicated to a detailed understanding of the emergence of excited states from the eigenvector continuation approach.
  arXiv  Detail & Related papers  (2021-08-05T19:28:25Z)
• Emergent statistical mechanics from properties of disordered random matrix product states [1.3075880857448061]
  We introduce a picture of generic states within the trivial phase of matter with respect to their non-equilibrium and entropic properties. We prove that disordered random matrix product states equilibrate exponentially well with overwhelming probability under the time evolution of Hamiltonians. We also prove two results about the entanglement Renyi entropy.
  arXiv  Detail & Related papers  (2021-03-03T19:05:26Z)
• Variational optimization of continuous matrix product states [0.0]
  We show how to optimize continuous matrix product states for systems with inhomogeneous external potentials. We show how both the energy and its backwards derivative can be calculated exactly and at a cost that scales as the cube of the bond dimension. We illustrate this by finding ground states of interacting bosons in external potentials, and by calculating boundary or Casimir energy corrections of continuous many-body systems.
  arXiv  Detail & Related papers  (2020-06-02T17:35:41Z)
• Gaussian Process States: A data-driven representation of quantum many-body physics [59.7232780552418]
  We present a novel, non-parametric form for compactly representing entangled many-body quantum states. The state is found to be highly compact, systematically improvable and efficient to sample. It is also proven to be a universal approximator' for quantum states, able to capture any entangled many-body state with increasing data set size.
  arXiv  Detail & Related papers  (2020-02-27T15:54:44Z)

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.