Polynomially restricted operator growth in dynamically integrable models

• URL: http://arxiv.org/abs/2406.13026v2
• Date: Mon, 21 Oct 2024 15:31:41 GMT
• Title: Polynomially restricted operator growth in dynamically integrable models
• Authors: Igor Ermakov, Tim Byrnes, Oleg Lychkovskiy,
• Abstract summary: We show that each Hamiltonian defines an equivalence relation, causing the operator space to be partitioned into equivalence classes. We provide a method to determine the dimension of the equivalence classes and evaluate it for various models, such as the $ XY $ chain and Kitaev model on trees. Our methods are used to reveal several new cases of simulable quantum dynamics, including a $XY$-$ZZ$ model which cannot be reduced to free fermions.
• Score: 0.0
• License:
• Abstract: We provide a framework to determine the upper bound to the complexity of a computing a given observable with respect to a Hamiltonian. By considering the Heisenberg evolution of the observable, we show that each Hamiltonian defines an equivalence relation, causing the operator space to be partitioned into equivalence classes. Any operator within a specific class never leaves its equivalence class during the evolution. We provide a method to determine the dimension of the equivalence classes and evaluate it for various models, such as the $ XY $ chain and Kitaev model on trees. Our findings reveal that the complexity of operator evolution in the $XY$ model grows from the edge to the bulk, which is physically manifested as suppressed relaxation of qubits near the boundary. Our methods are used to reveal several new cases of simulable quantum dynamics, including a $XY$-$ZZ$ model which cannot be reduced to free fermions.

Related papers

• Notes on solvable models of many-body quantum chaos [15.617052284991203]
  We study a class of many body chaotic models related to the Brownian Sachdev-Ye-Kitaev model. An emergent symmetry maps the quantum dynamics into a classical process.
  arXiv  Detail & Related papers  (2024-08-20T18:24:52Z)
• Classifying two-body Hamiltonians for Quantum Darwinism [0.0]
  We consider a generic model of an arbitrary finite-dimensional system interacting with an environment formed from an arbitrary collection of finite-dimensional degrees of freedom. We show that such models support quantum Darwinism if the set of operators acting on the system which enter the Hamiltonian satisfy a set of commutation relations with a pointer observable and with one other.
  arXiv  Detail & Related papers  (2024-05-01T18:42:43Z)
• Geometric Neural Diffusion Processes [55.891428654434634]
  We extend the framework of diffusion models to incorporate a series of geometric priors in infinite-dimension modelling. We show that with these conditions, the generative functional model admits the same symmetry.
  arXiv  Detail & Related papers  (2023-07-11T16:51:38Z)
• Emergent Spacetime in Quantum Lattice Models [0.0]
  Many quantum lattice models have an emergent relativistic description in their continuum limit. In this thesis, we investigate novel features of this relativistic description for a range of quantum lattice models. We show how to generate emergent curved spacetimes and identify observables at the lattice level which reveal this emergent behaviour.
  arXiv  Detail & Related papers  (2022-12-23T19:00:04Z)
• Fermionic approach to variational quantum simulation of Kitaev spin models [50.92854230325576]
  Kitaev spin models are well known for being exactly solvable in a certain parameter regime via a mapping to free fermions. We use classical simulations to explore a novel variational ansatz that takes advantage of this fermionic representation. We also comment on the implications of our results for simulating non-Abelian anyons on quantum computers.
  arXiv  Detail & Related papers  (2022-04-11T18:00:01Z)
• Numerically Probing the Universal Operator Growth Hypothesis [0.0]
  We numerically test this hypothesis for a variety of exemplary systems. The onset of the hypothesized universal behavior could not be observed in the attainable numerical data for the Heisenberg model.
  arXiv  Detail & Related papers  (2022-03-01T15:15:47Z)
• Low-Rank Constraints for Fast Inference in Structured Models [110.38427965904266]
  This work demonstrates a simple approach to reduce the computational and memory complexity of a large class of structured models. Experiments with neural parameterized structured models for language modeling, polyphonic music modeling, unsupervised grammar induction, and video modeling show that our approach matches the accuracy of standard models at large state spaces.
  arXiv  Detail & Related papers  (2022-01-08T00:47:50Z)
• Topological study of a Bogoliubov-de Gennes system of pseudo spin-$1/2$ bosons with conserved magnetization in a honeycomb lattice [0.0]
  We consider a non-Hermitian Hamiltonian with pseudo-Hermiticity for a system of bosons in a honeycomb lattice. Such a system is capable of acting as a topological amplifier, under time-reversal symmetry. We construct a convenient analytical description for the edge modes of the Haldane model in semi-infinite planes.
  arXiv  Detail & Related papers  (2021-10-07T02:00:12Z)
• Learning Neural Generative Dynamics for Molecular Conformation Generation [89.03173504444415]
  We study how to generate molecule conformations (textiti.e., 3D structures) from a molecular graph. We propose a novel probabilistic framework to generate valid and diverse conformations given a molecular graph.
  arXiv  Detail & Related papers  (2021-02-20T03:17:58Z)
• Sub-bosonic (deformed) ladder operators [62.997667081978825]
  We present a class of deformed creation and annihilation operators that originates from a rigorous notion of fuzziness. This leads to deformed, sub-bosonic commutation relations inducing a simple algebraic structure with modified eigenenergies and Fock states. In addition, we investigate possible consequences of the introduced formalism in quantum field theories, as for instance, deviations from linearity in the dispersion relation for free quasibosons.
  arXiv  Detail & Related papers  (2020-09-10T20:53:58Z)
• 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.