We perform a systematic determinant quantum Monte Carlo (DQMC) study of the dominating pairing symmetry in a doped honeycomb lattice. The Hubbard model is simulated over a full range of filling levels for both weak and strong interactions. For weak couplings, the d-wave state dominates. The effective susceptibility as a function of filling shows a peak, and its position moves toward half filling as the temperature is increased, from which the optimal filling of the superconducting ground state is estimated. Although the sign problem becomes severe for strong couplings, the simulations access the lowest temperature at which the DQMC method generates reliable results. As the coupling is strengthened, the d-wave state is enhanced in the high-filling region. Our systematic DQMC results provide new insights into the superconducting pairing symmetry in the doped honeycomb lattice.
Spinless fermions on the honeycomb lattice with repulsive nearest-neighbor interactions are known to harbour a quantum critical point at half-filling, with critical behavior in the Gross-Neveu (chiral Ising) universality class. The critical interaction strength separates a weak-coupling semimetallic regime from a commensurate charge-density-wave phase. The phase diagram of this basic model of correlated fermions on the honeycomb lattice beyond half-filling is, however, less well established. Here, we perform an analysis of its many-body instabilities using the functional renormalization group method with a basic Fermi surface patching scheme, which allows us to treat instabilities in competing channels on equal footing also away from half-filling. Between half-filling and the Van Hove filling, the free Fermi surface is holelike and we again find a charge-density wave instability to be dominant at large interactions. Moreover, its characteristics are those of the half-filled case. Directly at the Van Hove filling, the nesting property of the free Fermi surface stabilizes a dimerized bond-order phase. At lower filling, the free Fermi surface becomes electronlike and a superconducting instability with
f-wave symmetry is found to emerge from the interplay of intra-unit-cell repulsion and collective fluctuations in the proximity to the charge-density wave instability. We estimate the extent of the various phases and extract the corresponding order parameters from the effective low-energy Hamiltonians.
The search for superconductivity with unconventional pairing symmetry has been a central focus in the study of strongly correlated electron systems. In this work, we report a numerically exact study of the spin-triplet pairing in a two-dimensional Hubbard model with repulsive interactions, employing the determinant quantum Monte Carlo method. The model includes next-nearest-neighbor and third-nearest-neighbor hopping terms and maintains spin balance. By tuning the fermion filling close to a type-II Van Hove singularity (VHS) in the model, we numerically investigate the ordering tendencies of several possible pairing channels with different symmetries. Our numerical results provide clear evidence of the spin-triplet
p-wave pairing instability approaching low temperatures, as revealed by the vertex contribution to the pairing susceptibility. This signature becomes increasingly pronounced as the interaction strength increases in the weak to intermediate regime. We further find that, near the type-II VHS, the dominant spin-spin correlations in the system are ferromagnetic, suggesting its close relation to the spin-triplet pairing instability. Our findings offer a reliable approach to realize spin-triplet
p-wave superfluidity in the repulsive Hubbard model from an unbiased numerical perspective.
We study the attractive fermionic Hubbard model on a honeycomb lattice using determinantal quantum Monte Carlo simulations. By increasing the interaction strength
U (relative to the hopping parameter
t) at half filling and zero temperature, the system undergoes a quantum phase transition at
5.0<Uc/t<5.1 from a semimetal to a phase displaying simultaneously superfluid behavior and density order. Doping away from half filling, and increasing the interaction strength at finite but low temperature
T, the system always appears to be a superfluid exhibiting a crossover between a BCS and a molecular regime. These different regimes are analyzed by studying the spectral function. The formation of pairs and the emergence of phase coherence throughout the sample are studied as
U is increased and
T is lowered.
Using finite-temperature determinantal quantum Monte Carlo calculations, we find that the dominant pairing symmetries in the standard Hubbard model on the honeycomb lattice depend on the electron filling. When the electron density $\ensuremath{\rho}$ is larger than around 0.25, the dominant pairing symmetry is the
d+id-wave; when the electron density is low enough ($\ensuremath{\rho}\ensuremath{\lesssim}0.25$), the dominant pairing symmetry is the
p+ip wave. For two electron densities $\ensuremath{\rho}=0.1$ and $\ensuremath{\rho}=0.4$, where the dominant pairing symmetries are
p+ip wave and
d+id wave separately, we study the effect of two types of hopping inhomogeneities (the plaquette and the quasi-
1D hopping inhomogeneities) on the pairing symmetries. For $\ensuremath{\rho}=0.1$, the plaquette hopping inhomogeneity drives the dominant
p+ip-wave pairing symmetry into the
d+id-wave; while the quasi-
1D hopping inhomogeneity almost does not affect the
p+ip wave, and arises the
f wave, causing the coexistence of
p+ip-wave and
f-wave pairing. For $\ensuremath{\rho}=0.4$, both the plaquette and the quasi-
1D hopping inhomogeneities destroy the
d+id-wave pairing symmetry, without causing other pairing symmetry. Our results suggest that the effect of hopping inhomogeneity on the pairing symmetries is robust and depends on the electron filling. This finding may be useful for the design of artificial graphene superconductors with different kinds of pairing, especially for the realization of the
d+id-wave,
p+ip-wave, or
f-wave superconductors at low filling.
In view of quite recent experimental activities on magnetic and superconducting properties of honeycomb and hexagonal lattice based materials, in this thesis we have used field-theoretic and many-body methods to investigate magnetic and superconducting properties of the large-U Hubbard model on the honeycomb lattice at half-filling and in the hole-doped regime. Within the framework of a functional-integral approach, we obtain the Lagrangian density associated with the charge (Grassmann fields) and spin [SU(2) gauge fields] degrees of freedom. The Hamiltonian related to the charge degrees of freedom is exactly diagonalized. In the strong-coupling regime, we derive a perturbative low-energy theory suitable to describe the (quantum) magnetic and superconducting phases at half-filling and in the hole-doped regime. At half-filling, we deal with the underlying spin degrees of freedom of the quantum antiferromagnetic (AF) Heisenberg model by employing a second-order spin-wave analysis, in which case we have calculated the ground-state energy and the staggered magnetization; the results are in very good agreement with previous studies. Further, in the continuum, we derive a nonlinear σ-model with a topological Hopf term that describes the AF-VBS (valence bond solid) competition. In the challenging hole-doped regime, our approach allows the derivation of a t-J Hamiltonian, and the analysis of the role played by charge and spin quantum fluctuations on the ground-state energy and, particularly, on the breakdown of the AF order at a critical hole doping; the results are benchmarked against recent Grassmann tensor product state simulations. In addition, we have performed an extensive study of the electronic structure of the doped system for each competing phase: AF, ferromagnetic (FM), and (spin-singlet pairing) s-, dx₂₋ʏ₂ – and idxʏ -wave superconducting (SC) state induced by purely electronic effects. In this context, an energetic analysis of the ground state of these phases reveal that the AF order prevails for low hole doping, while a dominantly chiral dx₂₋ʏ₂ + idxʏ superconducting state was found in the vicinity of the Van Hove singularity (high hole doping). We also stress that a thermodynamic analysis of the superconducting phase shows that the critical temperature is directly related to the exchange constant J = 4t²/U, in which t denotes the hopping amplitude and U the on-site Coulomb repulsion of the Hubbard model (purely electronic origin). Remarkably, the competition between the AF and dx₂₋ʏ₂ + idxʏ SC phases takes place by the occurrence of a first-order transition accompanied by a spatial phase separation of the referred phases.