Hubbard Model on the Pyrochlore Lattice: A 3D Quantum Spin Liquid

Abstract

We demonstrate that the insulating one-band Hubbard model on the pyrochlore lattice contains, for realistic parameters, an extended quantum spin-liquid phase. This is a three-dimensional spin liquid formed from a highly degenerate manifold of dimer-based states, which is a subset of the classical dimer coverings obeying the ice rules. It possesses spinon excitations, which are both massive and deconfined, and on doping it exhibits spin-charge separation. We discuss the realization of this state in effective S = 1/2 pyrochlore materials.PACS numbers: 75.10. Jm, 75.10.Kt, 75.40.Gb The quantum spin liquid [1] has become the focal point for our understanding of many of the most fundamental issues in strongly correlated systems. These include exotic quantum phases, quantum critical physics, the relevance of broken symmetries, topological order, entanglement, and the possibly fractional nature of elementary excitations in both gapped and gapless states [2]. The search for theoretical realizations of these ideas has led to numerous proposed models, which while highly informative have generally been too simple or abstract to apply to real materials [3]. The search for materials realizations is a very active field where much current attention is focused on kagome systems [4], triangular organics [5], and other frustrated S = 1/2 and S = 1 quantum magnets. However, materials complexities such as impurities, Dzyaloshinskii-Moriya interactions, spin-orbit coupling, and other anisotropies in real and spin space have to date caused strong departures from theoretical ideals.Frustrated quantum magnets offer one of the most promising routes to spin-liquid behavior [1,2]. Frustration presents a formidable barricade to theoretical understanding, because the ground manifold is quite generally a set of highly degenerate basis states, with little or no separation emerging in an exact treatment of the interactions [6]. Numerical calculations converge very slowly due to this proliferation of near-ground states [7]. Fluctuations in such a manifold may lead to a range of exotic phenomena [8][9][10], and the departures mentioned above are strong because any perturbation is strongly relevant in a highly degenerate system. Few exact results are available, although these afford essential insight [11][12][13][14].In this Letter, we discuss the one-band Hubbard model, showing that on a half-filled pyrochlore lattice it gives a highly frustrated intratetrahedral spin model with only weak perturbations. This model contains an exactly solvable Klein point, about which there is an extended region of parameter space where the ground state is a three-dimensional (3D) quantum spin liquid. This state hosts massive spinon excitations, which are deconfined and move in all three dimensions within the lattice. The parameter range for the spin-liquid phase lies exactly in the regime of many magnetic materials.The pyrochlore lattice, shown in Fig. 1, is a 3D array of corner-sharing tetrahedra, has cubic symmetry, and is a geometry widespread in transitio...

Mott-Hubbard transition and spin-liquid state on the pyrochlore lattice

“…The ground state for S = 1/2 is argued to be a quantum spin liquid [27][28][29] . This spin-singlet ground state has a finite energy gap for triplet excitations.…”

“…This model has an exactly solvable Klein point, about which the ground state is a three-dimensional quantum spin liquid over an extended parameter region. This spin-liquid state hosts massive spinon excitations, which are deconfined and move in all three dimensions within the lattice 29 . For the Hubbard model on the pyrochlore lattice, the only work on the Mott transition, that we know of, suggests a transition from a semimetal to a spin liquid Mott insulator 34 .…”

“…Also, easy axis anisotropy, long-rage dipolar interaction, etc., lead to multiple-q ordered phases 33 . It has been argued that beyond the Heisenberg limit the half-filled Hubbard model on the pyrochlore lattice can be expressed as a highly frustrated intratetrahedral spin model with weak intertetrahedral perturbations 29 . This model has an exactly solvable Klein point, about which the ground state is a three-dimensional quantum spin liquid over an extended parameter region.…”

Fermionic spinon and holon statistics in the pyrochlore quantum spin liquid

“…a) The destruction of one singlet creates a defect tetrahedron (DT) with no dimer. b) This process creates two individual spins in a net triplet state and comes at an energetic cost 6 , meaning that the spin excitations are massive. c) Once created, the two individual spins may propagate separately at no further energetic cost by the rearrangement of dimers; hence it is appropriate to regard these S = 1/2 objects as spinons, which further are deconfined, their quantum dynamics allowing free propagation at T = 0.…”

“…Theoretical interest is driven by the possibility of understanding unconventional gapped and gapless quantum ground states, including their entanglement, topological properties, and fractional elementary excitations 1 . Although many QSL properties have been studied by considering somewhat abstract quantum dimer models (QDMs) 2,3 , Kitaev models 4 , SU(N) 5 , and other models, only recently have they been proven exactly in a physically relevant Hamiltonian, the one-band Hubbard model on the pyrochlore lattice 6 . In common with more abstract QSLs, the pyrochlore QSL is based on a highly degenerate ground manifold (of nearest-neighbor dimer coverings), occurring at an exactly solvable Klein point in a frustrated spin model 7,8 .…”