Quantum disordered insulating phase in the frustrated cubic-lattice Hubbard model

Abstract

In the quest for quantum spin liquids in three spatial dimensions (3D), we study the half-filled Hubbard model on the simple cubic lattice with hopping processes up to third neighbors. Employing the variational cluster approach (VCA), we determine the zero-temperature phase diagram: In addition to a paramagnetic metal at small interaction strength $U$ and various antiferromagnetic insulators at large $U$, we find an intermediate-$U$ antiferromagnetic metal. Most interestingly, we also identify a non-magnetic insulating region, extending from intermediate to strong $U$. Using VCA results in the large-$U$ limit, we establish the phase diagram of the corresponding $J_1$-$J_2$-$J_3$ Heisenberg model. This is qualitatively confirmed - including the non-magnetic region - using spin-wave theory. Further analysis reveals a striking similarity to the behavior of the $J_1$-$J_2$ square-lattice Heisenberg model, suggesting that the non-magnetic region hosts a 3D spin-liquid phase.

5 pages, 4 figures; final version incl. discussion about materials

References in corpus (37)

• Spin Ice State in Frustrated Magnetic Pyrochlore Materials
• Quantum Cluster Theories
• Mott physics and band topology in materials with strong spin-orbit interaction
• Pyrochlore Photons: The U(1) Spin Liquid in a S=1/2 Three-Dimensional Frustrated Magnet
• Spin-Liquid State in the S = 1/2 Hyperkagome Antiferromagnet Na4Ir3O8
• Fractionalized Fermi liquids
• Spin Liquid Ground State of the Spin-1/2 Square $J_1$-$J_2$ Heisenberg Model
• Self-energy-functional approach to systems of correlated electrons
• Variational cluster approach to correlated electron systems in low dimensions
• Coulombic Quantum Liquids in Spin-1/2 Pyrochlores
• Plaquette Ordered Phase and Quantum Phase Diagram in the Spin-1/2 J1-J2 Square Heisenberg Model
• Li${}_2$VO(Si,Ge)O${}_4$, a prototype of a two-dimensional frustrated quantum Heisenberg antiferromagnet
• Direct evidence for a gapless $Z_2$ spin liquid by frustrating Néel antiferromagnetism
• Self-energy-functional approach: Analytical results and the Mott-Hubbard transition
• Three dimensional resonating valence bond liquids and their excitations
• Topological order in a 3D toric code at finite temperature
• Magnetic properties of BaCdVO(PO_4)_2: a strongly frustrated spin-1/2 square lattice close to the quantum critical regime
• Correlation effects on 3D topological phases: from bulk to boundary
• Is the Yb2Ti2O7 pyrochlore a quantum spin ice?
• Thermodynamics of the 3D Hubbard model on approach to the Neel transition
• Weyl spin liquids
• Hierarchical mean-field approach to the $J_1$-$J_2$ Heisenberg model on a square lattice
• Realization of a large J_2 quasi-2D spin-half Heisenberg system: Li2VOSiO4
• Rashba spin orbit coupling in the Kane-Mele-Hubbard model
• Low-energy singlet and triplet excitations in the spin-liquid phase of the two-dimensional J1-J2 model
• Spin-1/2 J1-J2 Heisenberg antiferromagnet on a square lattice: a plaquette renormalized tensor network study
• Frustrated spin-1/2 square lattice in the layered perovskite PbVO(3)
• Interacting Weyl semimetals: characterization via the topological Hamiltonian and its breakdown
• SU(2)-invariant spin-1/2 Hamiltonians with RVB and other valence bond phases
• Spectral properties of the three-dimensional Hubbard model
• Second-order quantum corrections for the frustrated, spatially anisotropic, spin-1/2 Heisenberg antiferromagnet on a square lattice
• Spontaneous dimer order, excitation spectrum, and quantum phase transitions in the J1-J2 Heisenberg model
• Hubbard Model on the Pyrochlore Lattice: a 3D Quantum Spin Liquid
• Zero temperature phases of the frustrated J1-J2 antiferromagnetic spin-1/2 Heisenberg model on a simple cubic lattice
• Quantum paramagnet in a $\pi$ flux triangular lattice Hubbard model
• Non-linear bond-operator theory and 1/d expansion for coupled-dimer magnets II: Antiferromagnetic phase and quantum phase transition
• Thermodynamics of the frustrated $J_1$-$J_2$ Heisenberg ferromagnet on the body-centered cubic lattice with arbitrary spin

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• Degenerate manifolds, helimagnets, and multi-$\mathbf{Q}$ chiral phases in the classical Heisenberg antiferromagnet on the face-centered-cubic lattice
• Correlation-driven charge order in a frustrated two-dimensional atom lattice
• Three-band Hubbard model for Na${}_2$IrO${}_3$: Topological insulator, zigzag antiferromagnet, and Kitaev-Heisenberg material
• Projective symmetry group classifications of quantum spin liquids on the simple cubic, body centered cubic, and face centered cubic lattices
• Variational cluster approach to superconductivity and magnetism in the Kondo lattice model
• Brillouin-zone integration scheme for many-body density of states: Tetrahedron method combined with cluster perturbation theory
• Temperature flow in pseudo-Majorana functional renormalization for quantum spins
• Spin liquid versus long range magnetic order in the frustrated body-centered tetragonal lattice
• Spin liquid versus long range magnetic order in the frustrated body-centered tetragonal lattice
• Spin-$1$ $J_1-J_2-J_3$ ferromagnetic Heisenberg model with an easy-plane crystal field on the cubic lattice: A bosonic approach