Path‐integral renormalization group (PIRG) method has been developed for studying strongly correlated electron systems. In a wide range of systems including Hubbard‐type models, this method overcomes a number of difficulties known in the Monte‐Carlo‐type methods such as the negative sign problem. This method has been combined with a procedure of quantum number projection and grand canonical ensemble method as well, which contribute to a wider applicability. The quantum‐number projected PIRG enables calculations of excited spectra with a specified momentum or spin. We review recent numerical results on strongly correlated electron systems studied by this method. By using the methods, we determine the phase diagram of the two‐dimensional Hubbard model in the parameter space of the onsite interaction U, strength of the geometrical frustration effects defined by the ratio between next‐nearest to nearest neighbor transfer integrals, t′/t, and the chemical potential. It reveals severe competitions of various phases. The phase diagram contains a remarkable nonmagnetic Mott insulator phase with gapless and dispersionless spin excitations, sandwitched by the first‐order Mott transition and the antiferromagnetic transition. The first‐order character becomes more continuous one with increasing the frustration effect.Path‐integral renormalization group (PIRG) method has been developed for studying strongly correlated electron systems. In a wide range of systems including Hubbard‐type models, this method overcomes a number of difficulties known in the Monte‐Carlo‐type methods such as the negative sign problem. This method has been combined with a procedure of quantum number projection and grand canonical ensemble method as well, which contribute to a wider applicability. The quantum‐number projected PIRG enables calculations of excited spectra with a specified momentum or spin. We review recent numerical results on strongly correlated electron systems studied by this method. By using the methods, we determine the phase diagram of the two‐dimensional Hubbard model in the parameter space of the onsite interaction U, strength of the geometrical frustration effects defined by the ratio between next‐nearest to nearest neighbor transfer integrals, t′/t, and the chemical potential. It reveals severe competitions of various phases. The phase diagram contains a remarkable nonmagnetic Mott insulator phase with gapless and dispersionless spin excitations, sandwitched by the first‐order Mott transition and the antiferromagnetic transition. The first‐order character becomes more continuous one with increasing the frustration effect.

AIP conference proceedingsJan 1, 20031 citation

Quantum-number projection in the path-integral renormalization group method

T. Mizusaki, Masatoshi Imada

We present a quantum-number projection technique which enables us to exactly treat spin, momentum, and other symmetries embedded in the Hubbard model. By combining this projection technique, we extend the path-integral renormalization-group method to improve the efficiency of numerical computations. By taking numerical calculations for the standard Hubbard model and the Hubbard model with next-nearest-neighbor transfer, we show that the present extended method can extremely enhance numerical accuracy and that it can handle excited states, in addition to the ground state.We present a quantum-number projection technique which enables us to exactly treat spin, momentum, and other symmetries embedded in the Hubbard model. By combining this projection technique, we extend the path-integral renormalization-group method to improve the efficiency of numerical computations. By taking numerical calculations for the standard Hubbard model and the Hubbard model with next-nearest-neighbor transfer, we show that the present extended method can extremely enhance numerical accuracy and that it can handle excited states, in addition to the ground state.

arXiv:cond-mat/0311005Physical Review BMar 23, 200469 citations

Path-integral renormalization group method with quantum-number projection

T. Mizusaki, Masatoshi Imada

Computer Physics CommunicationsApr 14, 20050 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

Application of Path Integral Methods: The Renormalization Group Approach

Jaime Merino, A. Levy Yeyati

UNITEXT for physicsJan 1, 20240 citations

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.