Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical review. B, Condensed matter

Phase diagram of a generalizedt-Jmodel: Renormalization-group approach

Sergio Alejandro Cannas, Constantino Tsallis

Published Sep 1, 1992• 2 citations
Publisher

Abstract

A generalized t-J Hamiltonian is analyzed within the framework of a quantum real-space renormalization group. Besides the usual hopping (t), exchange (J), and chemical-potential (\ensuremath{\mu}) terms, the Hamiltonian contains a nearest-neighbor charge interaction term and is invariant under the renormalization. The finite-temperature phase diagram of the d=2 and d=3 model is calculated in the full range of the parameters. Our results show that many of the critical properties of the La- and Y-based high-${\mathit{T}}_{\mathit{c}}$ superconductors can be explained by the present model.

DOI
10.1103/physrevb.46.6261

Related papers

Finite-temperature phase diagram of thet-Jmodel: Renormalization-group theory

Alexis Falicov, A. Nihat Berker

The finite-temperature phase diagram of the t-J model of electronic conduction is calculated in d dimensions, using the Migdal-Kadanoff renormalization-group procedure. No finite-temperature phase transition in d=1 and a finite-temperature first-order boundary ending at a critical point in d=2 are found. In d=3, a remarkably complex multicritical phase diagram is found, with a new phase, between hole dopings of 0.3 and 0.4 and temperatures 1/J below 0.4, in which the hopping strength t renormalizes to infinity under rescaling. Our results are confirmed by comparison of calculated electron densities, kinetic energies, and nearest-neighbor density-density and spin-spin correlation functions with exact finite-cluster results.

Physical review. B, Condensed matter•May 1, 1995•16 citations

A renormalization-group study of the t-J model

E. V. L. de Mello

The t-J model has been proposed to describe the physics of copper oxide planes in high-temperature superconductors. A real-space quantum renormalization-group method is developed in order to study the t-J Hamiltonian in a square lattice. The zero-temperature phase diagram is analysed for electron concentrations near the half-filled band and ratio J/t. A critical line is found that separates two distinct regions: one of a gas of holes in an antiferromagnetic background, and the other consisting of a phase in which holes segregate into a hole-rich and a pure antiferromagnetic region, as demonstrated by chemical-potential eigenvalue calculations near the phase attractor. The results are close to the experimental observations.

Journal of Physics Condensed Matter•Jan 3, 1994•2 citations

Global phase diagram of D-wave superconductivity in the square-lattice t-J model

Feng Chen, F. D. M. Haldane, D. N. Sheng

The Hubbard and closely related t-J models are exciting platforms for unconventional superconductivity (SC). Through state-of-the-art density matrix renormalization group calculations using the grand canonical ensemble, we address open issues regarding the ground-state phase diagram of the extended t-J model on a square lattice in the parameter regime relevant to cuprate superconductors. On large 8-leg cylinders, we demonstrate that the pure t-J model with only nearest-neighbor hoppings and superexchange interactions, for a wide range of doping ( δ = 0.1 to 0.2 ), hosts robust d-wave superconductivity possibly coexisting with weak unidirectional pair density wave. Furthermore, a small next nearest neighbor hopping t 2 suppresses pair and charge density waves, resulting in a uniform d-wave SC phase in both electron- and hole-doped cuprate model systems. Our work validates the t-J model as a proper minimum model for the emergence of superconductivity in cuprate superconductors.

arXiv:2311.15092•Proceedings of the National Academy of Sciences•Mar 21, 2025•27 citations

Field-free quantum-spin-1/2 XXZ model in three-dimensions:phases, phase transitions, and phase diagrams by renormalization group theory

Ozan S. Sarıyer

The field-free quantum-spin-1/2 XXZ model is studied in three-dimensions using renormalization group theory. We obtain global phase diagrams and critical properties. We identify zero-temperature quantum phase transitions at isotropic points, as well as long-range order below critical temperatures at all anisotropies. We show that the excitation spectrum is gapless in XY-like, and gapped in Ising-like anisotropy regimes. Besides, internal energy density, specific heat, nearest-neighbor entanglement measures and spin-spin correlations are obtained globally at all temperatures. Our numerical results cover the global range of anisotropy parameter, for both ferromagnetic and antiferromagnetic cases.

TURKISH JOURNAL OF PHYSICS•Apr 14, 2020•2 citations

The generalized Hubbard model in one dimension: a renormalization group study

B Bhattacharyya, Sanchita Sil

We have modified an existing real space renormalization group scheme to remove some physically inconsistent features and used the rectified method to study the ground state of the one-dimensional Hubbard model with nearest-neighbour repulsion and the bond-charge interaction for half filling. For the nearest-neighbour interaction we find a phase diagram which agrees nicely with the Monte Carlo results. For the case of bond-charge interaction we have reproduced some available exact results and found some interesting information in the parameter regime where no exact solution is available.

Journal of Physics Condensed Matter•Aug 14, 1995•5 citations

Blume-Emery-Griffiths-Potts model in two dimensions: Phase diagram and critical properties from a position-space renormalization group

A. Nihat Berker, Michael Wortis

The spin-1 Ising model on the square lattice with nearest-neighbor ferromagnetic exchange interactions [both bilinear ($J$) and biquadratic ($K$) and crystal-field interaction ($\ensuremath{\Delta}$) is studied via a renormalization-group transformation in position space. The phase diagram in $J$, $K$, $\ensuremath{\Delta}$ space is found to have one surface of critical phase transitions and two surfaces of first-order phase transitions. These surfaces are variously bounded by an ordinary tricritical line, an isolated critical line, and a line of critical end points. These three lines joint at a special tricritical point corresponding to the transition of the three-state Potts model. The over-all phase diagram is qualitatively similar to that obtained with the mean-field approximation, except in the vicinity of the Potts transition where a four-phase coexistence line in mean-field theory shrinks into a special tricritical point in renormalization-group theory. Symmetry considerations guide the construction of our truncated renormalization-group transformation. The global connectivity and local exponents of the thirteen separate fixed points underlying this quite complicated structure are determined. Local analysis with respect to magnetic field ($H$) and another odd interaction ($L$) is performed. A one-adjusted-parameter version of our transformation yields remarkably quantitative results, predicting the Potts transition temperature, for example, within 0.3% of the exact value.

Physical review. B, Solid state•Dec 1, 1976•371 citations
A generalized t-J Hamiltonian is analyzed within the framework of a quantum real-space renormalization group. Besides the usual hopping (t), exchange (J), and chemical-potential (\ensuremath{\mu}) terms, the Hamiltonian contains a nearest-neighbor charge interaction term and is invariant under the renormalization. The finite-temperature phase diagram of the d=2 and d=3 model is calculated in the full range of the parameters. Our results show that many of the critical properties of the La- and Y-based high-Tc{\mathit{T}}_{\mathit{c}}Tc​ superconductors can be explained by the present model.
The finite-temperature phase diagram of the t-J model of electronic conduction is calculated in d dimensions, using the Migdal-Kadanoff renormalization-group procedure. No finite-temperature phase transition in d=1 and a finite-temperature first-order boundary ending at a critical point in d=2 are found. In d=3, a remarkably complex multicritical phase diagram is found, with a new phase, between hole dopings of 0.3 and 0.4 and temperatures 1/J below 0.4, in which the hopping strength t renormalizes to infinity under rescaling. Our results are confirmed by comparison of calculated electron densities, kinetic energies, and nearest-neighbor density-density and spin-spin correlation functions with exact finite-cluster results.
The t-J model has been proposed to describe the physics of copper oxide planes in high-temperature superconductors. A real-space quantum renormalization-group method is developed in order to study the t-J Hamiltonian in a square lattice. The zero-temperature phase diagram is analysed for electron concentrations near the half-filled band and ratio J/t. A critical line is found that separates two distinct regions: one of a gas of holes in an antiferromagnetic background, and the other consisting of a phase in which holes segregate into a hole-rich and a pure antiferromagnetic region, as demonstrated by chemical-potential eigenvalue calculations near the phase attractor. The results are close to the experimental observations.
The Hubbard and closely related t-J models are exciting platforms for unconventional superconductivity (SC). Through state-of-the-art density matrix renormalization group calculations using the grand canonical ensemble, we address open issues regarding the ground-state phase diagram of the extended t-J model on a square lattice in the parameter regime relevant to cuprate superconductors. On large 8-leg cylinders, we demonstrate that the pure t-J model with only nearest-neighbor hoppings and superexchange interactions, for a wide range of doping ( δ = 0.1 to 0.2 ), hosts robust d-wave superconductivity possibly coexisting with weak unidirectional pair density wave. Furthermore, a small next nearest neighbor hopping t 2 suppresses pair and charge density waves, resulting in a uniform d-wave SC phase in both electron- and hole-doped cuprate model systems. Our work validates the t-J model as a proper minimum model for the emergence of superconductivity in cuprate superconductors.
The field-free quantum-spin-1/2 XXZ model is studied in three-dimensions using renormalization group theory. We obtain global phase diagrams and critical properties. We identify zero-temperature quantum phase transitions at isotropic points, as well as long-range order below critical temperatures at all anisotropies. We show that the excitation spectrum is gapless in XY-like, and gapped in Ising-like anisotropy regimes. Besides, internal energy density, specific heat, nearest-neighbor entanglement measures and spin-spin correlations are obtained globally at all temperatures. Our numerical results cover the global range of anisotropy parameter, for both ferromagnetic and antiferromagnetic cases.
We have modified an existing real space renormalization group scheme to remove some physically inconsistent features and used the rectified method to study the ground state of the one-dimensional Hubbard model with nearest-neighbour repulsion and the bond-charge interaction for half filling. For the nearest-neighbour interaction we find a phase diagram which agrees nicely with the Monte Carlo results. For the case of bond-charge interaction we have reproduced some available exact results and found some interesting information in the parameter regime where no exact solution is available.
The spin-1 Ising model on the square lattice with nearest-neighbor ferromagnetic exchange interactions [both bilinear (JJJ) and biquadratic (KKK) and crystal-field interaction ($\ensuremath{\Delta}$) is studied via a renormalization-group transformation in position space. The phase diagram in JJJ, KKK, $\ensuremath{\Delta}$ space is found to have one surface of critical phase transitions and two surfaces of first-order phase transitions. These surfaces are variously bounded by an ordinary tricritical line, an isolated critical line, and a line of critical end points. These three lines joint at a special tricritical point corresponding to the transition of the three-state Potts model. The over-all phase diagram is qualitatively similar to that obtained with the mean-field approximation, except in the vicinity of the Potts transition where a four-phase coexistence line in mean-field theory shrinks into a special tricritical point in renormalization-group theory. Symmetry considerations guide the construction of our truncated renormalization-group transformation. The global connectivity and local exponents of the thirteen separate fixed points underlying this quite complicated structure are determined. Local analysis with respect to magnetic field (HHH) and another odd interaction (LLL) is performed. A one-adjusted-parameter version of our transformation yields remarkably quantitative results, predicting the Potts transition temperature, for example, within 0.3% of the exact value.