We study the effects of an artificial gauge field on the ground-state phases of the Bose-Hubbard model on a checkerboard superlattice in two dimensions, including the superfluid phase and the Mott and alternating Mott insulators. First, we discuss the single-particle Hofstadter problem, and show that the presence of a checkerboard superlattice gives rise to a magnetic flux-independent energy gap in the excitation spectrum. Then, we consider the many-particle problem, and derive an analytical mean-field expression for the superfluid-Mott and superfluid--alternating-Mott insulator phase transition boundaries. Finally, since the phase diagram of the Bose-Hubbard model on a checkerboard superlattice is in many ways similar to that of the extended Bose-Hubbard model, we comment on the effects of magnetic field on the latter model, and derive an analytical mean-field expression for the superfluid-insulator phase transition boundaries as well.We study the effects of an artificial gauge field on the ground-state phases of the Bose-Hubbard model on a checkerboard superlattice in two dimensions, including the superfluid phase and the Mott and alternating Mott insulators. First, we discuss the single-particle Hofstadter problem, and show that the presence of a checkerboard superlattice gives rise to a magnetic flux-independent energy gap in the excitation spectrum. Then, we consider the many-particle problem, and derive an analytical mean-field expression for the superfluid-Mott and superfluid--alternating-Mott insulator phase transition boundaries. Finally, since the phase diagram of the Bose-Hubbard model on a checkerboard superlattice is in many ways similar to that of the extended Bose-Hubbard model, we comment on the effects of magnetic field on the latter model, and derive an analytical mean-field expression for the superfluid-insulator phase transition boundaries as well.

Jan 3, 20110 citations

THE PHASE DIAGRAM OF THE HUBBARD MODEL

M W Long

Series on advances in statistical mechanicsJul 1, 19910 citations

Superconductivity in inhomogeneous Hubbard models

Wei-Feng Tsai, Steven Allan Kivelson

We present a controlled perturbative approach to the low-temperature phase diagram of highly inhomogeneous Hubbard models in the limit of small coupling, ${t}^{\ensuremath{'}}$, between clusters. We apply this to the dimerized and checkerboard models. The dimerized model is found to behave like a doped semiconductor, with a Fermi-liquid groundstate with parameters (e.g., the effective mass) which are smooth functions of the Hubbard interaction, $U$ . By contrast, the checkerboard model has a Fermi liquid phase at large $U>{U}_{c}=4.58$ , a $d$ -wave superconducting state with a full gap for ${U}_{c}>U>0$ , and a narrow strip of an intermediate $d$ -wave superconducting phase with gapless ``nodal'' quasiparticles for $\ensuremath{\mid}U\ensuremath{-}{U}_{c}\ensuremath{\mid}<\mathcal{O}({t}^{\ensuremath{'}})$.We present a controlled perturbative approach to the low-temperature phase diagram of highly inhomogeneous Hubbard models in the limit of small coupling, ${t}^{\ensuremath{'}}$, between clusters. We apply this to the dimerized and checkerboard models. The dimerized model is found to behave like a doped semiconductor, with a Fermi-liquid groundstate with parameters (e.g., the effective mass) which are smooth functions of the Hubbard interaction, $U$. By contrast, the checkerboard model has a Fermi liquid phase at large $U>{U}_{c}=4.58$, a $d$-wave superconducting state with a full gap for ${U}_{c}>U>0$, and a narrow strip of an intermediate $d$-wave superconducting phase with gapless ``nodal'' quasiparticles for $\ensuremath{\mid}U\ensuremath{-}{U}_{c}\ensuremath{\mid}<\mathcal{O}({t}^{\ensuremath{'}})$.

arXiv:cond-mat/0601113Physical Review BJun 9, 200662 citations

Systematic analysis of the Hubbard model on the checkerboard lattice

昌久古賀, Akihisa Koga

Jan 1, 20070 citations

On the Phase Diagram of the Hubbard Model

J. Monecke

physica status solidi (b)Mar 1, 19767 citations

Frustration effects in an anisotropic checkerboard lattice Hubbard model

Takuya Yoshioka, Akihisa Koga, Norio Kawakami

We study the ground-state properties of the geometrically frustrated Hubbard model on the anisotropic checkerboard lattice with nearest-neighbor hopping $t$ and next-nearest-neighbor hopping ${t}^{\ensuremath{'}}$. By using the path-integral renormalization-group method, we study the phase diagram in the parameter space of the Hubbard interaction $U$ and the frustration-control parameter ${t}^{\ensuremath{'}}/t$. Close examinations of the effective hopping, the double occupancy, the momentum distribution, and the spin- and charge-correlation functions allow us to determine the phase diagram at zero temperature, at which the plaquette-singlet insulator emerges besides the antiferromagnetic insulator and the paramagnetic metal. Spin-liquid insulating states without any kind of symmetry breaking cannot be found in our frustrated model.We study the ground-state properties of the geometrically frustrated Hubbard model on the anisotropic checkerboard lattice with nearest-neighbor hopping $t$ and next-nearest-neighbor hopping ${t}^{\ensuremath{'}}$. By using the path-integral renormalization-group method, we study the phase diagram in the parameter space of the Hubbard interaction $U$ and the frustration-control parameter ${t}^{\ensuremath{'}}/t$. Close examinations of the effective hopping, the double occupancy, the momentum distribution, and the spin- and charge-correlation functions allow us to determine the phase diagram at zero temperature, at which the plaquette-singlet insulator emerges besides the antiferromagnetic insulator and the paramagnetic metal. Spin-liquid insulating states without any kind of symmetry breaking cannot be found in our frustrated model.

arXiv:0808.1573Physical Review BOct 14, 200815 citations

U

. By contrast, the checkerboard model has a Fermi liquid phase at large

U>{U}_{c}=4.58

, a

d

-wave superconducting state with a full gap for

{U}_{c}>U>0

, and a narrow strip of an intermediate

d

-wave superconducting phase with gapless ``nodal'' quasiparticles for $\ensuremath{\mid}U\ensuremath{-}{U}_{c}\ensuremath{\mid}<\mathcal{O}({t}^{\ensuremath{'}})$.

We study the ground-state properties of the geometrically frustrated Hubbard model on the anisotropic checkerboard lattice with nearest-neighbor hopping

t

and next-nearest-neighbor hopping ${t}^{\ensuremath{'}}$. By using the path-integral renormalization-group method, we study the phase diagram in the parameter space of the Hubbard interaction

U

and the frustration-control parameter ${t}^{\ensuremath{'}}/t$. Close examinations of the effective hopping, the double occupancy, the momentum distribution, and the spin- and charge-correlation functions allow us to determine the phase diagram at zero temperature, at which the plaquette-singlet insulator emerges besides the antiferromagnetic insulator and the paramagnetic metal. Spin-liquid insulating states without any kind of symmetry breaking cannot be found in our frustrated model.