Scaling limits of lattice quantum fields by wavelets
- URL: http://arxiv.org/abs/2010.11121v2
- Date: Tue, 26 Oct 2021 14:18:07 GMT
- Title: Scaling limits of lattice quantum fields by wavelets
- Authors: Vincenzo Morinelli, Gerardo Morsella, Alexander Stottmeister, Yoh
Tanimoto
- Abstract summary: The renormalization group is considered as an inductive system of scaling maps between lattice field algebras.
We show that the inductive limit of free lattice ground states exists and the limit state extends to the familiar massive continuum free field.
- Score: 62.997667081978825
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We present a rigorous renormalization group scheme for lattice quantum field
theories in terms of operator algebras. The renormalization group is considered
as an inductive system of scaling maps between lattice field algebras. We
construct scaling maps for scalar lattice fields using Daubechies' wavelets,
and show that the inductive limit of free lattice ground states exists and the
limit state extends to the familiar massive continuum free field, with the
continuum action of spacetime translations. In particular, lattice fields are
identified with the continuum field smeared with Daubechies' scaling functions.
We compare our scaling maps with other renormalization schemes and their
features, such as the momentum shell method or block-spin transformations.
Related papers
- Finite time path field theory perturbative methods for local quantum spin chain quenches [0.0]
We discuss local magnetic field quenches using perturbative methods of finite time path field theory.
We show how to: i) calculate the basic "bubble" diagram in the Loschmidt echo of a quenched chain to any order in the perturbation; ii) resum the generalized Schwinger-Dyson equation for the fermion two point retarded functions in the "bubble" diagram.
arXiv Detail & Related papers (2024-09-05T18:00:08Z) - Curvature from multipartite entanglement in quantum gravity states [0.0]
We investigate the multipartite entanglement of a uniformly curved quantum 3D space region with boundary.
We find three entanglement regimes depending on the ratio between the number of tags (curvature) and the area of the dual surface at the boundary.
arXiv Detail & Related papers (2023-05-04T09:27:33Z) - Quantum Reference Frames at the Boundary of Spacetime [0.0]
An analysis is given of the local phase space of gravity coupled to matter to second order in perturbation theory.
The boundary modes take the role of reference frames for both diffeomorphisms and internal Lorentz rotations.
A multi-fingered Schr"odinger equation determines the relational evolution of the quantum states in the bulk.
arXiv Detail & Related papers (2023-02-22T20:10:03Z) - Continuous percolation in a Hilbert space for a large system of qubits [58.720142291102135]
The percolation transition is defined through the appearance of the infinite cluster.
We show that the exponentially increasing dimensionality of the Hilbert space makes its covering by finite-size hyperspheres inefficient.
Our approach to the percolation transition in compact metric spaces may prove useful for its rigorous treatment in other contexts.
arXiv Detail & Related papers (2022-10-15T13:53:21Z) - Holographic properties of superposed quantum geometries [0.0]
We study the holographic properties of a class of quantum geometry states characterized by a superposition of discrete geometric data.
This class includes spin networks, the kinematic states of lattice gauge theory and discrete quantum gravity.
arXiv Detail & Related papers (2022-07-15T17:37:47Z) - Conformal field theory from lattice fermions [77.34726150561087]
We provide a rigorous lattice approximation of conformal field theories given in terms of lattice fermions in 1+1-dimensions.
We show how these results lead to explicit error estimates pertaining to the quantum simulation of conformal field theories.
arXiv Detail & Related papers (2021-07-29T08:54:07Z) - Radiative topological biphoton states in modulated qubit arrays [105.54048699217668]
We study topological properties of bound pairs of photons in spatially-modulated qubit arrays coupled to a waveguide.
For open boundary condition, we find exotic topological bound-pair edge states with radiative losses.
By joining two structures with different spatial modulations, we find long-lived interface states which may have applications in storage and quantum information processing.
arXiv Detail & Related papers (2020-02-24T04:44:12Z) - Operator-algebraic renormalization and wavelets [62.997667081978825]
We construct the continuum free field as the scaling limit of Hamiltonian lattice systems using wavelet theory.
A renormalization group step is determined by the scaling equation identifying lattice observables with the continuum field smeared by compactly supported wavelets.
arXiv Detail & Related papers (2020-02-04T18:04:51Z) - From stochastic spin chains to quantum Kardar-Parisi-Zhang dynamics [68.8204255655161]
We introduce the asymmetric extension of the Quantum Symmetric Simple Exclusion Process.
We show that the time-integrated current of fermions defines a height field which exhibits a quantum non-linear dynamics.
arXiv Detail & Related papers (2020-01-13T14:30:36Z)
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.