Wegner's Ising gauge spins versus Kitaev's Majorana partons: Mapping and application to anisotropic confinement in spin-orbital liquids

• URL: http://arxiv.org/abs/2306.09405v3
• Date: Mon, 29 Apr 2024 09:52:10 GMT
• Title: Wegner's Ising gauge spins versus Kitaev's Majorana partons: Mapping and application to anisotropic confinement in spin-orbital liquids
• Authors: Urban F. P. Seifert, Sergej Moroz,
• Abstract summary: A common construction of $mathbbZ$ lattice gauge theories, first introduced by Wegner, involves Ising gauge spins placed on links. A common construction of $mathbbZ$ lattice gauge theories, first introduced by Wegner, involves Ising gauge spins placed on links.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Emergent gauge theories take a prominent role in the description of quantum matter, supporting deconfined phases with topological order and fractionalized excitations. A common construction of $\mathbb{Z}_2$ lattice gauge theories, first introduced by Wegner, involves Ising gauge spins placed on links and subject to a discrete $\mathbb{Z}_2$ Gauss law constraint. As shown by Kitaev, $\mathbb{Z}_2$ lattice gauge theories also emerge in the exact solution of certain spin systems with bond-dependent interactions. In this context, the $\mathbb{Z}_2$ gauge field is constructed from Majorana fermions, with gauge constraints given by the parity of Majorana fermions on each site. In this work, we provide an explicit Jordan-Wigner transformation that maps between these two formulations on the square lattice, where the Kitaev-type gauge theory emerges as the exact solution of a spin-orbital (Kugel-Khomskii) Hamiltonian. We then apply our mapping to study local perturbations to the spin-orbital Hamiltonian, which correspond to anisotropic interactions between electric-field variables in the $\mathbb{Z}_2$ gauge theory. These are shown to induce anisotropic confinement that is characterized by emergence of weakly-coupled one-dimensional spin chains. We study the nature of these phases and corresponding confinement transitions in both absence and presence of itinerant fermionic matter degrees of freedom. Finally, we discuss how our mapping can be applied to the Kitaev spin-1/2 model on the honeycomb lattice.

Related papers

• Fractional Wannier Orbitals and Tight-Binding Gauge Fields for Kitaev Honeycomb Superlattices with Flat Majorana Bands [0.19116784879310028]
  Fractional excitations offer vast potential for both fundamental physics and quantum technologies. Here, we investigate the evolution of low-energy Majorana dispersions across various crystalline phases of the pi-flux in the Kitaev spin model on a honeycomb lattice. We identify conditions under which this superexchange interaction acts as a Z2 gauge field, governing the tight-binding hopping of Majorana Wannier orbitals.
  arXiv  Detail & Related papers  (2024-07-17T13:44:39Z)
• $\mathbb{Z}_N$ lattice gauge theories with matter fields [0.0]
  We study fermions and bosons in $mathbb Z_N$ lattice gauge theories. We present analytical arguments for the most important phases and estimates for phase boundaries of the model.
  arXiv  Detail & Related papers  (2023-08-24T21:05:15Z)
• Quantum quenches in fractonic field theories [0.0]
  We study out-of-equilibrium dynamics caused by global quantum quenches in fractonic scalar field theories. We discuss a generalization to $mathbbZ_n$-symmetric field theories, and introduce a proper regularization.
  arXiv  Detail & Related papers  (2023-06-26T18:00:02Z)
• Measurement phase transitions in the no-click limit as quantum phase transitions of a non-hermitean vacuum [77.34726150561087]
  We study phase transitions occurring in the stationary state of the dynamics of integrable many-body non-Hermitian Hamiltonians. We observe that the entanglement phase transitions occurring in the stationary state have the same nature as that occurring in the vacuum of the non-hermitian Hamiltonian.
  arXiv  Detail & Related papers  (2023-01-18T09:26:02Z)
• Emergent $\mathbb{Z}_2$ gauge theories and topological excitations in Rydberg atom arrays [0.0]
  We show that the combination of Rydberg interactions and appropriate lattice geometries leads to emergent $mathbbZ$ gauge theories endowed with matter fields. We describe how Rydberg platforms could realize two distinct classes of topological $mathbbZ$ quantum spin liquids.
  arXiv  Detail & Related papers  (2022-04-01T18:00:00Z)
• Manipulating Generalized Dirac Cones In Quantum Metasurfaces [68.8204255655161]
  We consider a collection of single quantum emitters arranged in a honeycomb lattice with subwavelength periodicity. We show that introducing uniaxial anisotropy in the lattice results in modified dispersion relations.
  arXiv  Detail & Related papers  (2022-03-21T17:59:58Z)
• Phase diagram of Rydberg-dressed atoms on two-leg square ladders: Coupling supersymmetric conformal field theories on the lattice [52.77024349608834]
  We investigate the phase diagram of hard-core bosons in two-leg ladders in the presence of soft-shoulder potentials. We show how the competition between local and non-local terms gives rise to a phase diagram with liquid phases with dominant cluster, spin, and density-wave quasi-long-range ordering.
  arXiv  Detail & Related papers  (2021-12-20T09:46:08Z)
• 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)
• Spectrum of localized states in fermionic chains with defect and adiabatic charge pumping [68.8204255655161]
  We study the localized states of a generic quadratic fermionic chain with finite-range couplings. We analyze the robustness of the connection between bands against perturbations of the Hamiltonian.
  arXiv  Detail & Related papers  (2021-07-20T18:44:06Z)
• $\mathbb{Z}_N$ lattice gauge theory in a ladder geometry [0.0]
  Hamiltonian lattice gauge theories defined in two-leg ladders. We consider a model that includes both gauge boson and Higgs matter degrees of freedom with local $mathbbZ_N$ gauge symmetries.
  arXiv  Detail & Related papers  (2020-11-12T17:48:25Z)
• Entanglement and Complexity of Purification in (1+1)-dimensional free Conformal Field Theories [55.53519491066413]
  We find pure states in an enlarged Hilbert space that encode the mixed state of a quantum field theory as a partial trace. We analyze these quantities for two intervals in the vacuum of free bosonic and Ising conformal field theories.
  arXiv  Detail & Related papers  (2020-09-24T18:00:13Z)

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.