Projective symmetry group classification of chiral $\mathbb{Z}_2$ spin liquids on the pyrochlore lattice: application to the spin-$1/2$ XXZ Heisenberg model

• URL: http://arxiv.org/abs/2107.13574v3
• Date: Tue, 11 Jan 2022 15:21:32 GMT
• Title: Projective symmetry group classification of chiral $\mathbb{Z}_2$ spin liquids on the pyrochlore lattice: application to the spin-$1/2$ XXZ Heisenberg model
• Authors: Benedikt Schneider, Jad C. Halimeh, Matthias Punk
• Abstract summary: We give a complete classification of fully symmetric as well as chiral $mathbbZ$ quantum spin liquids on the pyrochlore lattice. We find 50 independent ans"atze, including the 12 fully symmetric nearest-neighbor $mathbbZulo$ spin liquids. For each class we specify the most general symmetry-allowed mean-field Hamiltonian.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We give a complete classification of fully symmetric as well as chiral $\mathbb{Z}_2$ quantum spin liquids on the pyrochlore lattice using a projective symmetry group analysis of Schwinger boson mean-field states. We find 50 independent ans\"atze, including the 12 fully symmetric nearest-neighbor $\mathbb{Z}_2$ spin liquids that have been classified by Liu et al. [https://journals.aps.org/prb/abstract/10.1103/PhysRevB.100.075125]. For each class we specify the most general symmetry-allowed mean-field Hamiltonian. Additionally, we test the properties of a subset of the spin liquid ans\"atze by solving the mean-field equations for the spin-$1/2$ XXZ model near the antiferromagnetic Heisenberg point. We find four chiral spin liquids that break the screw symmetry of the lattice modulo time reversal symmetry. These states have a different symmetry than the previously studied monopole flux state and their unique characteristic is a $\frac{\pi}{3}$ flux enclosed by every rhombus of the lattice.

Related papers

• Entanglement asymmetry in the critical XXZ spin chain [0.0]
  We study the explicit breaking of a $SU(2)$ symmetry to a $U(1)$ subgroup employing the entanglement asymmetry. We consider as specific model the critical XXZ spin chain, which breaks the $SU(2)$ symmetry of spin rotations except at the isotropic point.
  arXiv  Detail & Related papers  (2024-07-08T22:16:22Z)
• Non-equilibrium entanglement asymmetry for discrete groups: the example of the XY spin chain [0.0]
  The entanglement asymmetry is a novel quantity that, using entanglement methods, measures how much a symmetry is broken in a part of an extended quantum system. We consider the XY spin chain, in which the ground state spontaneously breaks the $mathbbZ$ spin parity symmetry in the ferromagnetic phase. We thoroughly investigate the non-equilibrium dynamics of this symmetry after a global quantum quench, generalising known results for the standard order parameter.
  arXiv  Detail & Related papers  (2023-07-13T17:01:38Z)
• Quantum Current and Holographic Categorical Symmetry [62.07387569558919]
  A quantum current is defined as symmetric operators that can transport symmetry charges over an arbitrary long distance. The condition for quantum currents to be superconducting is also specified, which corresponds to condensation of anyons in one higher dimension.
  arXiv  Detail & Related papers  (2023-05-22T11:00:25Z)
• Average pure-state entanglement entropy in spin systems with SU(2) symmetry [0.0]
  We study the effect that the SU(2) symmetry, and the rich Hilbert space structure that it generates in lattice spin systems, has on the average entanglement entropy of local Hamiltonians and of random pure states. We provide numerical evidence that $s_A$ is smaller in highly excited eigenstates of integrable interacting Hamiltonians. In the context of Hamiltonian eigenstates we consider spins $mathfrakj=frac12$ and $1$, while for our calculations based on random pure states we focus on the spin $mathfrakj=frac12$ case
  arXiv  Detail & Related papers  (2023-05-18T18:00:00Z)
• Emergence of non-Abelian SU(2) invariance in Abelian frustrated fermionic ladders [37.69303106863453]
  We consider a system of interacting spinless fermions on a two-leg triangular ladder with $pi/2$ magnetic flux per triangular plaquette. Microscopically, the system exhibits a U(1) symmetry corresponding to the conservation of total fermionic charge, and a discrete $mathbbZ$ symmetry. At the intersection of the three phases, the system features a critical point with an emergent SU(2) symmetry.
  arXiv  Detail & Related papers  (2023-05-11T15:57:27Z)
• Projective symmetry group classification of Abrikosov fermion mean-field ans\"atze on the square-octagon lattice [0.0]
  We perform a projective symmetry group (PSG) classification of symmetric quantum spin liquids with different gauge groups on the square-octagon lattice. We discuss their ground state properties and spinon dispersions within a self-consistent treatment of the Heisenberg Hamiltonian with frustrating couplings.
  arXiv  Detail & Related papers  (2022-12-19T15:45:45Z)
• Towards Antisymmetric Neural Ansatz Separation [48.80300074254758]
  We study separations between two fundamental models of antisymmetric functions, that is, functions $f$ of the form $f(x_sigma(1), ldots, x_sigma(N)) These arise in the context of quantum chemistry, and are the basic modeling tool for wavefunctions of Fermionic systems.
  arXiv  Detail & Related papers  (2022-08-05T16:35:24Z)
• Quantum Many-Body Scars in Spin-1 Kitaev Chains [1.340610646365466]
  We study the many-body scars in the spin-1 Kitaev chain where the so-called PXP Hamiltonian is exactly embedded in the spectra. We find that the scarred state is stable for perturbations which obey $vertmathbbZ_krangle$, while it becomes unstable against Heisenberg-type perturbations.
  arXiv  Detail & Related papers  (2022-01-23T10:11:32Z)
• Annihilating Entanglement Between Cones [77.34726150561087]
  We show that Lorentz cones are the only cones with a symmetric base for which a certain stronger version of the resilience property is satisfied. Our proof exploits the symmetries of the Lorentz cones and applies two constructions resembling protocols for entanglement distillation.
  arXiv  Detail & Related papers  (2021-10-22T15:02:39Z)
• Chiral Dirac-like fermion in spin-orbit-free antiferromagnetic semimetals [21.85167942898987]
  Dirac semimetal is a phase of matter, whose elementary excitation is described by the relativistic Dirac equation. Inspired by the flavor symmetry in particle physics, we propose a massless Dirac-like equation yet linking two Weyl fields with the identical chirality. Our work reveals a counterpart of the flavor symmetry in magnetic electronic systems, leading to further possibilities of emergent phenomena in quantum materials.
  arXiv  Detail & Related papers  (2021-07-21T09:56:14Z)
• Fermion and meson mass generation in non-Hermitian Nambu--Jona-Lasinio models [77.34726150561087]
  We investigate the effects of non-Hermiticity on interacting fermionic systems. We do this by including non-Hermitian bilinear terms into the 3+1 dimensional Nambu--Jona-Lasinio (NJL) model.
  arXiv  Detail & Related papers  (2021-02-02T13:56:11Z)

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.