Effective models for gapped phases of strongly correlated quantum lattice models

Abstract

We present a robust scheme to derive effective models non-perturbatively for quantum lattice models when at least one degree of freedom is gapped. A combination of graph theory and the method of continuous unitary transformations (gCUTs) is shown to efficiently capture all zero-temperature fluctuations in a controlled spatial range. The gCUT can be used either for effective quasi-particle descriptions or for effective low-energy descriptions in case of infinitely degenerate subspaces. We illustrate the method for 1d and 2d lattice models yielding convincing results in the thermodynamic limit. We find that the recently discovered spin liquid in the Hubbard model on the honeycomb lattice lies outside the perturbative strong-coupling regime. Various extensions and perspectives of the gCUT are discussed.

6 pages, 5 figures, extended discussion on J2/J1 for the honeycomb Hubbard model and on the properties of different generators for the continuous unitary transformation

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• Enhanced Perturbative Continuous Unitary Transformations
• Magnetic chern bands and triplon Hall effect in an extended Shastry-Sutherland model
• Quantum Phase Transitions around the Staggered Valence Bond Solid
• Unusual magnetic phases in the strong interaction limit of two-dimensional topological band insulators in transition metal oxides
• Ground state properties, excitation spectra and phase transitions in the $S=1/2$ and $S=3/2$ bilayer Heisenberg models on the honeycomb Lattice
• Valence-bond crystalline order in the $s=1/2$ $J_1$--$J_2$ model on the honeycomb lattice
• Ground-state phases of the frustrated spin-1/2 $J_1$--$J_2$--$J_3$ Heisenberg ferromagnet ($J_1<0$) on the honeycomb lattice with $J_3=J_2>0$
• Microscopic mechanism for the 1/8 magnetization plateau in SrCu_2(BO_3)_2
• Effective Spin Couplings in the Mott Insulator of the Honeycomb Lattice Hubbard Model
• Exact ground states of a spin-1/2 Ising-Heisenberg model on the Shastry-Sutherland lattice in a magnetic field
• Numerical linked cluster expansions for quantum quenches in one dimensional lattices
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• Non-perturbative linked-cluster expansions for the trimerized ground state of the spin-one Kagome Heisenberg model
• Anisotropic frustrated Heisenberg model on the honeycomb lattice
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• Hybrid quantum-classical algorithm for the transverse-field Ising model in the thermodynamic limit
• Non-perturbative linked-cluster expansions in long-range ordered quantum systems
• From Gapped Excitons to Gapless Triplons in One Dimension
• Linked Cluster Expansions via Hypergraph Decompositions
• Massive spinons in $S=1/2$ spin chains: spinon-pair operator representation
• Extracting critical exponents for sequences of numerical data via series extrapolation techniques
• Evaluation of High Order Terms for the Hubbard Model in the Strong-coupling Limit
• Effective One-Dimensional Models from Matrix Product States
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• Comparison of computer-algebra strong-coupling perturbation theory and dynamical mean-field theory for the Mott-Hubbard insulator in high dimensions
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