Bridging conformal field theory and parton approaches to SU(n)_k chiral spin liquids

• URL: http://arxiv.org/abs/2501.09567v1
• Date: Thu, 16 Jan 2025 14:42:00 GMT
• Title: Bridging conformal field theory and parton approaches to SU(n)_k chiral spin liquids
• Authors: Tong Liu, Ying-Hai Wu, Hong-Hao Tu, Tao Xiang,
• Abstract summary: We employ the SU(n)_k Wess-Zumino-Witten (WZW) model in conformal field theory to construct lattice wave functions in both one and two dimensions. In one dimension, these wave functions describe critical spin chains whose universality classes are in one-to-one correspondence with the WZW models used in the construction. In two dimensions, our constructions yield model wave functions for chiral spin liquids, and we show how to find all topological sectors of them in a systematic way.
• Score: 48.225436651971805
• License:
• Abstract: We employ the SU(n)_k Wess-Zumino-Witten (WZW) model in conformal field theory to construct lattice wave functions in both one and two dimensions. It is unveiled that these wave functions can be reinterpreted as parton states, which enables efficient conversion to matrix product states such that many physical properties can be evaluated directly. In one dimension, these wave functions describe critical spin chains whose universality classes are in one-to-one correspondence with the WZW models used in the construction. In two dimensions, our constructions yield model wave functions for chiral spin liquids, and we show how to find all topological sectors of them in a systematic way. Using the null vectors of Kac-Moody algebras, parent Hamiltonians of the SU(3)_k series are derived. The SU(3)_k chiral spin liquids are lattice analogs of non-Abelian spin-singlet fractional quantum Hall states, and the k = 2 member hosts Fibonacci anyons.

Related papers

• Towards the phase diagram of fermions coupled with $SO(3)$ quantum links in $(2+1)$-D [0.0]
  Quantum link models (QLMs) are generalizations of Wilson's lattice gauge theory formulated with finite-dimensional link Hilbert spaces. We extend the model to $(2+1)d$ dimensions for the first time, and report on our initial results.
  arXiv  Detail & Related papers  (2024-12-12T19:13:05Z)
• Phases of 2d massless QCD with qubit regularization [3.3963028001679065]
  continuum theory is described by N free fermions in the ultraviolet (UV) and a coset Wess-Zumino-Witten (WZW) model in the infrared (IR)
  arXiv  Detail & Related papers  (2023-12-29T18:41:39Z)
• Double-scale theory [77.34726150561087]
  We present a new interpretation of quantum mechanics, called the double-scale theory. It is based on the simultaneous existence of two wave functions in the laboratory reference frame. The external wave function corresponds to a field that pilots the center-of-mass of the quantum system. The internal wave function corresponds to the interpretation proposed by Edwin Schr"odinger.
  arXiv  Detail & Related papers  (2023-05-29T14:28:31Z)
• Third quantization of open quantum systems: new dissipative symmetries and connections to phase-space and Keldysh field theory formulations [77.34726150561087]
  We reformulate the technique of third quantization in a way that explicitly connects all three methods. We first show that our formulation reveals a fundamental dissipative symmetry present in all quadratic bosonic or fermionic Lindbladians. For bosons, we then show that the Wigner function and the characteristic function can be thought of as ''wavefunctions'' of the density matrix.
  arXiv  Detail & Related papers  (2023-02-27T18:56:40Z)
• Angular Momentum Eigenstates of the Isotropic 3-D Harmonic Oscillator: Phase-Space Distributions and Coalescence Probabilities [0.0]
  We compute the probabilities for coalescence of two distinguishable, non-relativistic particles into a bound state. We use a phase-space formulation and hence need the Wigner distribution functions of angular momentum eigenstates.
  arXiv  Detail & Related papers  (2021-12-22T23:16:44Z)
• Constructing tensor network wavefunction for a generic two-dimensional quantum phase transition via thermofield double states [2.416375474510521]
  Two-dimensional quantum Rokhsar-Kivelson (RK) type models can be mapped into the partition functions of two-dimensional statistical models. We introduce the universality of the thermofield double (TFD) state, which is a purification of the equilibrium density operator. By expressing the TFD state in terms of the projected entangled pair state, its $N$-order of R'enyi entropy results in a three-dimensional statistical model in Euclidian spacetime.
  arXiv  Detail & Related papers  (2020-12-28T09:05:55Z)
• Quantum trimer models and topological SU(3) spin liquids on the kagome lattice [0.0]
  We study quantum trimer models and resonating SU(3)-singlet models on the kagome lattice. We show that the quantum order ultimately displayed by the model depends on the relative weight assigned to different types of trimers.
  arXiv  Detail & Related papers  (2020-06-15T18:00:25Z)
• 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)
• External and internal wave functions: de Broglie's double-solution theory? [77.34726150561087]
  We propose an interpretative framework for quantum mechanics corresponding to the specifications of Louis de Broglie's double-solution theory. The principle is to decompose the evolution of a quantum system into two wave functions. For Schr"odinger, the particles are extended and the square of the module of the (internal) wave function of an electron corresponds to the density of its charge in space.
  arXiv  Detail & Related papers  (2020-01-13T13:41:24Z)
• SU$(3)_1$ Chiral Spin Liquid on the Square Lattice: a View from Symmetric PEPS [55.41644538483948]
  Quantum spin liquids can be faithfully represented and efficiently characterized within the framework of Projectedangled Pair States (PEPS) Characteristic features are revealed by the entanglement spectrum (ES) on an infinitely long cylinder. Special features in the ES are shown to be in correspondence with bulk anyonic correlations, indicating a fine structure in the holographic bulk-edge correspondence.
  arXiv  Detail & Related papers  (2019-12-31T16:30:25Z)

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.