Effective field theory of the quantum skyrmion Hall effect

• URL: http://arxiv.org/abs/2412.19565v3
• Date: Thu, 16 Jan 2025 15:21:53 GMT
• Title: Effective field theory of the quantum skyrmion Hall effect
• Authors: Vinay Patil, Rafael Flores-Calderón, Ashley M. Cook,
• Abstract summary: We introduce effective field theories (EFTs) for the quantum skyrmion Hall effect (QSkHE) We employ a single, unifying generalisation for this purpose. We identify gauge theories with extra fuzzy dimensions generalised to retain dependence upon gauge fields over fuzzy coset spaces.
• Score: 0.0
• License:
• Abstract: Motivated by phenomenology of myriad recently-identified topologically non-trivial phases of matter, we introduce effective field theories (EFTs) for the quantum skyrmion Hall effect (QSkHE). We employ a single, unifying generalisation for this purpose: in essence, a lowest Landau level projection defining a non-commutative, fuzzy sphere with position coordinates proportional to SU(2) generators of matrix representation size $N\times N$, may host an intrinsically 2+1 dimensional, topologically non-trivial many-body state for small $N$ as well as large $N$. That is, isospin degrees of freedom associated with a matrix Lie algebra with $N \times N$ generators potentially encode some finite number of spatial dimensions for $N\ge 2$, a regime in which isospin has previously been treated as a label. This statement extends to more general $p$-branes subjected to severe fuzzification as well as membranes. As a consequence of this generalisation, systems with $d$ Cartesian spatial coordinates and isospin degrees of freedom encoding an additional $\delta$ fuzzy coset space coordinates can realise topologically non-trivial states of intrinsic dimensionality up to $d$+$\delta$+1. We therefore identify gauge theories with extra fuzzy dimensions generalised to retain dependence upon gauge fields over fuzzy coset spaces even for severe fuzzification (small $N$), as EFTs for the QSkHE. We furthermore generalise these EFTs to space manifolds with local product structure exploiting the dimensional hierarchy of (fuzzy) spheres. For this purpose, we introduce methods of anisotropic fuzzification and propose formulating topological invariants on fuzzy coset spaces as artifacts of projecting matrix Lie algebras to occupied subspaces. Importantly, we focus on phenomenology indicating the 2+1 D SU(2) gauge theory should be generalised using this machinery, and serves as a minimal EFT of the QSkHE.

Related papers

• Quantum Simulation of non-Abelian Lattice Gauge Theories: a variational approach to $\mathbb{D}_8$ [0.0]
  We show a procedure that removes the matter and improves the efficiency of the hardware resources. We map the lattice gauge theory onto qudit systems with local interactions. This can serve as a way of simulating lattice gauge theories in high spatial dimensions.
  arXiv  Detail & Related papers  (2025-01-29T18:59:59Z)
• Geometry of degenerate quantum states, configurations of $m$-planes and invariants on complex Grassmannians [55.2480439325792]
  We show how to reduce the geometry of degenerate states to the non-abelian connection $A$. We find independent invariants associated with each triple of subspaces. Some of them generalize the Berry-Pancharatnam phase, and some do not have analogues for 1-dimensional subspaces.
  arXiv  Detail & Related papers  (2024-04-04T06:39:28Z)
• Gaussian Entanglement Measure: Applications to Multipartite Entanglement of Graph States and Bosonic Field Theory [50.24983453990065]
  An entanglement measure based on the Fubini-Study metric has been recently introduced by Cocchiarella and co-workers. We present the Gaussian Entanglement Measure (GEM), a generalization of geometric entanglement measure for multimode Gaussian states. By providing a computable multipartite entanglement measure for systems with a large number of degrees of freedom, we show that our definition can be used to obtain insights into a free bosonic field theory.
  arXiv  Detail & Related papers  (2024-01-31T15:50:50Z)
• Estimating gate complexities for the site-by-site preparation of fermionic vacua [0.0]
  We study the ground state overlap as a function of the number of sites for a range of quadratic fermionic Hamiltonians. For one-dimensional systems, we find that two $N/2$-site ground states also share a large overlap with the $N$-site ground state everywhere except a region near the phase boundary.
  arXiv  Detail & Related papers  (2022-07-04T19:45:14Z)
• From locality to irregularity: Introducing local quenches in massive scalar field theory [68.8204255655161]
  We consider the dynamics of excited local states in massive scalar field theory in an arbitrary spacetime dimension. We identify different regimes of their evolution depending on the values of the field mass and the quench regularization parameter. We also investigate the local quenches in massive scalar field theory on a cylinder and show that they cause an erratic and chaotic-like evolution of observables.
  arXiv  Detail & Related papers  (2022-05-24T18:00:07Z)
• Threshold size for the emergence of a classical-like behaviour [68.8204255655161]
  We design a procedure to estimate the minimum size beyond which a system is amenable to a classical-like description. The specific case of a magnetic system is considered, with details of a gedanken experiment presented and thoroughly commented.
  arXiv  Detail & Related papers  (2022-03-25T11:31:14Z)
• Entanglement Entropy and Phase Space Density: Lowest Landau Levels and 1/2 BPS states [0.0]
  We consider the entanglement entropy of an arbitrary subregion in a system of $N$ non-relativistic fermions in $2+1$ dimensions. We show that the leading term in the entanglement entropy is a perimeter law with a shape independent coefficient.
  arXiv  Detail & Related papers  (2022-01-20T17:56:56Z)
• Quantum double aspects of surface code models [77.34726150561087]
  We revisit the Kitaev model for fault tolerant quantum computing on a square lattice with underlying quantum double $D(G)$ symmetry. We show how our constructions generalise to $D(H)$ models based on a finite-dimensional Hopf algebra $H$.
  arXiv  Detail & Related papers  (2021-06-25T17:03:38Z)
• Many Body Quantum Chaos and Dual Unitarity Round-a-Face [0.0]
  We propose a new type of locally interacting quantum circuits which are generated by unitary interactions round-a-face (IRF) We show how arbitrary dynamical correlation functions of local observables can be evaluated in terms of finite dimensional completely positive trace preserving unital maps. We provide additional data on dimensionality of the chiral extension of DUBG circuits with distinct local Hilbert spaces of dimensions $dneq d'$ residing at even/odd lattice sites.
  arXiv  Detail & Related papers  (2021-05-17T17:16:33Z)
• The Geometry of Time in Topological Quantum Gravity of the Ricci Flow [62.997667081978825]
  We continue the study of nonrelativistic quantum gravity associated with a family of Ricci flow equations. This topological gravity is of the cohomological type, and it exhibits an $cal N=2$ extended BRST symmetry. We demonstrate a standard one-step BRST gauge-fixing of a theory whose fields are $g_ij$, $ni$ and $n$, and whose gauge symmetries consist of (i) the topological deformations of $g_ij$, and (ii) the ultralocal nonrelativistic limit of space
  arXiv  Detail & Related papers  (2020-11-12T06:57:10Z)
• Reduced Phase Space Approach to the $U(1)^3$ model for Euclidean Quantum Gravity [0.0]
  A consistent model captures significant structure of the Ashtekar-Barbero $SU(2)$ gauge theory of Euclidean gravity. A non trivial realisation of the hypersurface deformation algebra makes it an interesting testing ground for quantum gravity.
  arXiv  Detail & Related papers  (2020-10-30T16:16:14Z)

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.