Fractals and spontaneous symmetry breaking with type-B Goldstone modes: a perspective from entanglement
- URL: http://arxiv.org/abs/2407.17925v1
- Date: Thu, 25 Jul 2024 10:24:11 GMT
- Title: Fractals and spontaneous symmetry breaking with type-B Goldstone modes: a perspective from entanglement
- Authors: Huan-Qiang Zhou, Qian-Qian Shi, John O. Fjærestad, Ian P. McCulloch,
- Abstract summary: The one-dimensional spin-$s$ $rm SU(2)$ ferromagnetic Heisenberg model, as a paradigmatic example for spontaneous symmetry breaking ( SSB) with type-B Goldstone modes (GMs), is expected to exhibit an abstract fractal underlying the ground state subspace.
This intrinsic abstract fractal is here revealed from a systematic investigation into the entanglement entropy for a linear combination of factorized (unentangled) ground states on a fractal decomposable into a set of the Cantor sets.
Our argument may be extended to any quantum many-body systems undergoing SSB with type-B GM
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: The one-dimensional spin-$s$ ${\rm SU}(2)$ ferromagnetic Heisenberg model, as a paradigmatic example for spontaneous symmetry breaking (SSB) with type-B Goldstone modes (GMs), is expected to exhibit an abstract fractal underlying the ground state subspace. This intrinsic abstract fractal is here revealed from a systematic investigation into the entanglement entropy for a linear combination of factorized (unentangled) ground states on a fractal decomposable into a set of the Cantor sets. The entanglement entropy scales logarithmically with the block size, with the prefactor being half the fractal dimension of a fractal, as long as the norm for the linear combination scales as the square root of the number of the self-similar building blocks kept at each step $k$ for a fractal, under an assumption that the maximum absolute value of the coefficients in the linear combination is chosen to be around one, and the coefficients in the linear combination are almost constants within the building blocks. Actually, the set of the fractal dimensions for all the Cantor sets forms a {\it dense} subset in the interval $[0,1]$. As a consequence, the ground state subspace is separated into a disjoint union of countably infinitely many regions, each of which is labeled by a decomposable fractal. Hence, the interpretation of the prefactor as half the fractal dimension is valid for any support beyond a fractal, which in turn leads to the identification of the fractal dimension with the number of type-B GMs for the orthonormal basis states. Our argument may be extended to any quantum many-body systems undergoing SSB with type-B GMs.
Related papers
- 1D self-similar fractals with centro-symmetric Jacobians: asymptotics
and modular data [0.0]
We establishs of growing one dimensional self-similar fractal graphs, they are networks that allow multiple edges weighted between nodes.
An additional structure is endowed with the repeating units of centro-symmetric Jacobians in the adjacency of a linear graph creating a self-similar fractal.
arXiv Detail & Related papers (2024-01-27T22:07:58Z) - The signaling dimension in generalized probabilistic theories [48.99818550820575]
The signaling dimension of a given physical system quantifies the minimum dimension of a classical system required to reproduce all input/output correlations of the given system.
We show that it suffices to consider extremal measurements with rayextremal effects, and we bound the number of elements of any such measurement in terms of the linear dimension.
For systems with a finite number of extremal effects, we recast the problem of characterizing the extremal measurements with ray-extremal effects.
arXiv Detail & Related papers (2023-11-22T02:09:16Z) - Quantum Entanglement on Fractal Landscapes [9.254741613227333]
We explore the interplay of fractal geometry and quantum entanglement by analyzing the von Neumann entropy and the entanglement contour in the scaling limit.
For gapless ground states exhibiting a finite density of states at the chemical potential, we reveal a super-area law characterized by the presence of a logarithmic divergence in the entanglement entropy.
Remarkably, this pattern bears resemblance to intricate Chinese paper-cutting designs.
arXiv Detail & Related papers (2023-11-02T12:50:27Z) - Learning Fractals by Gradient Descent [19.93434604598185]
Recent works in visual recognition have leveraged this property to create random fractal images for model pre-training.
We propose a novel approach that learns the parameters underlying a fractal image via gradient descent.
We show that our approach can find fractal parameters of high visual quality and be compatible with different loss functions.
arXiv Detail & Related papers (2023-03-14T17:20:25Z) - Spectral embedding and the latent geometry of multipartite networks [67.56499794542228]
Many networks are multipartite, meaning their nodes can be divided into partitions and nodes of the same partition are never connected.
This paper demonstrates that the node representations obtained via spectral embedding live near partition-specific low-dimensional subspaces of a higher-dimensional ambient space.
We propose a follow-on step after spectral embedding, to recover node representations in their intrinsic rather than ambient dimension.
arXiv Detail & Related papers (2022-02-08T15:52:03Z) - Topological Random Fractals [0.0]
topological random fractals exhibit a robust mobility gap, support quantized conductance and represent a well-defined thermodynamic phase of matter.
Our results establish topological random fractals as the most complex systems known to support nontrivial band topology with their distinct unique properties.
arXiv Detail & Related papers (2021-12-16T12:11:19Z) - Stochastic Fractal and Noether's Theorem [0.0]
We consider the binary fragmentation problem in which, at any breakup event, one of the daughter segments survives with probability $p$ or disappears with probability $1!!p$.
For a fractal dimension $d_f$, we find that the $d_f$-th moment $M_d_f$ is a conserved quantity, independent of $p$ and $alpha$.
In an attempt to connect the symmetry with the conserved quantity, we reinterpret the continuity equation of a Euclidean quantum-mechanical system.
arXiv Detail & Related papers (2020-10-15T18:00:21Z) - Shining Light on Quantum Transport in Fractal Networks [6.067025327033905]
We experimentally investigate quantum transport in fractal networks by performing continuous-time quantum walks in fractal photonic lattices.
We observe anomalous transport governed solely by the fractal dimension.
Our experiment allows the verification of physical laws in a quantitative manner and reveals the transport dynamics with unprecedented detail.
arXiv Detail & Related papers (2020-05-27T14:28:28Z) - Dynamical solitons and boson fractionalization in cold-atom topological
insulators [110.83289076967895]
We study the $mathbbZ$ Bose-Hubbard model at incommensurate densities.
We show how defects in the $mathbbZ$ field can appear in the ground state, connecting different sectors.
Using a pumping argument, we show that it survives also for finite interactions.
arXiv Detail & Related papers (2020-03-24T17:31:34Z) - 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) - Distributed, partially collapsed MCMC for Bayesian Nonparametrics [68.5279360794418]
We exploit the fact that completely random measures, which commonly used models like the Dirichlet process and the beta-Bernoulli process can be expressed as, are decomposable into independent sub-measures.
We use this decomposition to partition the latent measure into a finite measure containing only instantiated components, and an infinite measure containing all other components.
The resulting hybrid algorithm can be applied to allow scalable inference without sacrificing convergence guarantees.
arXiv Detail & Related papers (2020-01-15T23:10:13Z)
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.