Mott physics in the half-filled Hubbard model on a family of vortex-full square lattices

Abstract

We study the half-filled Hubbard model on a one-parameter family of vortex-full square lattices ranging from the isotropic case to weakly coupled Hubbard dimers. The ground-state phase diagram consists of four phases: A semi-metal and a band insulator which are connected to the weak-coupling limit, and a magnetically ordered Néel phase and a valence bond crystal (VBC) which are linked to the strong-coupling Mott limit. The phase diagram is obained by quantum Monte Carlo (QMC) and continuous unitary transformations (CUTs). The CUT is performed in a two-step process: Non-perturbative graph-based CUTs are used in the Mott insulating phase to integrate out charge fluctuations. The resulting effective spin model is tackled by perturbative CUTs about the isolated dimer limit yielding the breakdown of the VBC by triplon condensation. We find three scenarios when varying the interaction for a fixed anisotropy of hopping amplitudes: i) one direct phase transition from Néel to semi-metal, ii) two phase transitions VBC to Néel and Néel to semi-metal, or iii) a smooth crossover from VBC to the band insultor. Our results are consistent with the absence of spin-liquid phases in the whole phase diagram.

References in corpus (13)

• Quantum spin-liquid emerging in two-dimensional correlated Dirac fermions
• Absence of a Spin Liquid Phase in the Hubbard Model on the Honeycomb Lattice
• Theory of interacting electrons on the honeycomb lattice
• Mott Transition, Antiferromagnetism, and d-wave Superconductivity in Two-Dimensional Organic Conductors
• Effective spin model for the spin-liquid phase of the Hubbard model on the triangular lattice
• The Hubbard model on the triangular lattice: Spiral order and spin liquid
• Role of backflow correlations for the non-magnetic phase of the t-t' Hubbard model
• Evidence of Unconventional Universality Class in a Two-Dimensional Dimerized Quantum Heisenberg Model
• Calculating the energy spectra of magnetic molecules: application of real- and spin-space symmetries
• Systematic Mapping of the Hubbard Model to the Generalized t-J Model
• Effective models for gapped phases of strongly correlated quantum lattice models
• Effective Spin Couplings in the Mott Insulator of the Honeycomb Lattice Hubbard Model
• Derivation of the t-J model for finite doping

Cited by in corpus (11)

• Fermionic quantum criticality in honeycomb and $\pi$-flux Hubbard models: Finite-size scaling of renormalization-group-invariant observables from quantum Monte Carlo
• Dirac electrons in the square lattice Hubbard model with a $d$-wave pairing field: chiral Heisenberg universality class revisited
• Quantum paramagnet in a $\pi$ flux triangular lattice Hubbard model
• Phase diagram of the square lattice Hubbard model with Rashba-type antisymmetric spin-orbit coupling
• A generalized perspective on non-perturbative linked cluster expansions
• Linked Cluster Expansions via Hypergraph Decompositions
• Metal-Insulator Transition of Dirac Fermions: Variational Cluster Study
• The ALF (Algorithms for Lattice Fermions) project release 2.4. Documentation for the auxiliary-field quantum Monte Carlo code
• Kekulé valence bond order in the Hubbard model on the honeycomb lattice with possible lattice distortions for graphene
• QMC study of the chiral Heisenberg Gross-Neveu universality class
• Emergence of topological defects and spin liquid in a two-orbital spin-fermion model on the honeycomb lattice