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

arXiv:cond-mat/9810301 · Physical Review Letters

Charge Fluctuations Close to Phase Separation in the Two-Dimensional t−J Model

Matteo Calandra, Federico Becca, Sandro Sorella

Published Dec 7, 1998• 58 citations
arXivHTMLPDF

Abstract

We have studied the $t\ensuremath{-}J$ model using the Green function Monte Carlo technique. We have obtained accurate energies well converged in the thermodynamic limit by performing simulations for up to $242$ lattice sites. By studying the energy as a function of hole doping we conclude that there is no phase separation in the physical region relevant for high- ${T}_{c}$ superconductors. This finding is further supported by the hole-hole correlation function calculation. Remarkably, near the phase separation instability, for ${J}_{c}/t\ensuremath{\sim}0.5$ this function displays enhanced fluctuations at incommensurate wave vectors that scale linearly with the doping, in agreement with experimental findings.

DOI
10.1103/physrevlett.81.5185

Related papers

Phase Separation at all Interaction Strengths in thet-JModel

C. Stephen Hellberg, Efstratios Manousakis

We investigate the phase diagram of the two-dimensional t-J model using a recently developed Green's function Monte Carlo method for lattice fermions. We use the technique to calculate exact ground-state energies of the model on large lattices. In contrast to many previous studies, we find the model phase separates for all values of $J/t$. In particular, it is unstable at the hole dopings and interaction strengths at which the model was thought to describe the cuprate superconductors.

arXiv:cond-mat/9611195•Physical Review Letters•Jun 16, 1997•137 citations

Finite compressibility in the low-doping region of the two-dimensional t−J model

Massimo Lugas, Leonardo Spanu, Federico Becca +1 more

We reexamine the important issue of charge fluctuations in the two-dimensional $t\text{\ensuremath{-}}J$ model by using an improved variational method based on a wave function that contains both antiferromagnetic and $d$-wave superconducting order parameters. In particular, we generalize the wave function introduced some time ago by Bouchaud, Georges, and Lhuillier [J. Phys. (Paris) 49, 553 (1988)] by considering also a long-range spin-spin Jastrow factor, in order to correctly reproduce the small-$q$ behavior of the spin fluctuations. We mainly focus our attention on the physically relevant region $J∕t\ensuremath{\sim}0.4$ and find that, contrary to a previous variational ansatz, this state is stable against phase separation for small hole doping. Moreover, by performing projection Monte Carlo methods based on the so-called fixed-node approach, we obtain clear evidence that the $t\text{\ensuremath{-}}J$ model does not phase separate for $J∕t\ensuremath{\lesssim}0.7$ and that the compressibility remains finite close to the antiferromagnetic insulating state.

arXiv:cond-mat/0606659•Physical Review B•Oct 31, 2006•37 citations

Spatially homogeneous ground state of the two-dimensional Hubbard model

Federico Becca, Massimo Capone, Sandro Sorella

We investigate the stability with respect to phase separation or charge-density-wave formation of the two-dimensional Hubbard model for various values of the local Coulomb repulsion and electron densities using Green-function Monte Carlo techniques. The well known sign problem is particularly serious in the relevant region of small hole doping. We show that the difference in accuracy for different doping makes it very difficult to probe the phase separation instability using only energy calculations, even in the weak-coupling limit $(U=4t)$ where reliable results are available. By contrast, the knowledge of the charge correlation functions allows us to provide clear evidence of a spatially homogeneous ground state up to $U=10t.$

arXiv:cond-mat/0010165•Physical review. B, Condensed matter•Nov 15, 2000•56 citations

Phase separation and stripes in a boson version of a doped quantum antiferromagnet

Massimo Boninsegni

A theoretical investigation of boson versions of the $t\ensuremath{-}J$ and $t\ensuremath{-}{J}_{z}$ models on the square lattice is carried out, by means of Green's function Monte Carlo simulations. Accurate ground-state energy estimates as a function of hole doping are obtained, allowing one to investigate the stability of the uniform phase against separation of the system into hole-rich and hole-free phases. In the boson $t\ensuremath{-}{J}_{z}$ model, such a separation is found to occur for arbitrarily small values of ${J}_{z},$ at sufficiently low hole doping. Phase separation is suppressed in the boson $t\ensuremath{-}J$ model, which features a uniform ground state at any doping, for $J/t\ensuremath{\lesssim}1.5.$ Relevance of this study to the corresponding fermion models is discussed. Fermi statistics enhances the tendency toward phase separation; in particular, phase separation at low doping is predicted in the fermion $t\ensuremath{-}{J}_{z}$ model at any ${J}_{z}>0.$ The possible formation of stripes of holes is investigated for systems featuring both periodic and cylindrical boundary conditions. No evidence of a striped ground state is found in either the $t\ensuremath{-}J$ or $t\ensuremath{-}{J}_{z}$ boson models.

Physical review. B, Condensed matter•Mar 12, 2002•14 citations

Antiferromagnetic to superconducting phase transition in the hole- and electron-doped Hubbard model at zero temperature

Markus Aichhorn, Enrico Arrigoni, Michael Potthoff +1 more

The competition between $d$-wave superconductivity (SC) and antiferromagnetism (AF) in the high-${T}_{c}$ cuprates is investigated by studying the hole- and electron-doped two-dimensional Hubbard model with a recently proposed variational quantum-cluster theory. The approach is shown to provide a thermodynamically consistent determination of the particle number, provided that an overall shift of the on-site energies is treated as a variational parameter. The consequences for the single-particle excitation spectra and for the phase diagram are explored. By comparing the single-particle spectra with quantum Monte Carlo and experimental data, we verify that the low-energy excitations in a strongly correlated electronic system are described appropriately. The cluster calculations also reproduce the overall ground-state phase diagram of the high-temperature superconductors. In particular, they include salient features such as the enhanced robustness of the antiferromagnetic state as a function of electron doping and the tendency towards phase separation into a mixed antiferromagnetic-superconducting phase at low doping and a pure superconducting phase at high (both hole and electron) doping.

arXiv:cond-mat/0511460•Physical Review B•Jul 13, 2006•154 citations

Green’s-function Monte Carlo for lattice fermions: Application to the t−J model

C. Stephen Hellberg, Efstratios Manousakis

We develop a general numerical method to study the zero-temperature properties of strongly correlated electron models on large lattices. The technique, which resembles Green's-function Monte Carlo, projects the ground-state component from a trial wave function with no approximations. We use this method to determine the phase diagram of the two-dimensional $t\ensuremath{-}J$ model, using the Maxwell construction to investigate electronic phase separation. The shell effects of fermions on finite-sized periodic lattices are minimized by keeping the number of electrons fixed at a closed-shell configuration and varying the size of the lattice. Results obtained for various electron numbers corresponding to different closed shells indicate that the finite-size effects in our calculation are small. For any value of interaction strength, we find that there is always a value of the electron density above which the system can lower its energy by forming a two-component phase separated state. Our results are compared with other calculations on the $t\ensuremath{-}J$ model. We find that the most accurate results are consistent with phase separation at all interaction strengths.

arXiv:cond-mat/9911071•Physical review. B, Condensed matter•May 1, 2000•46 citations
We have studied the t\ensuremath−Jt\ensuremath{-}Jt\ensuremath−J model using the Green function Monte Carlo technique. We have obtained accurate energies well converged in the thermodynamic limit by performing simulations for up to 242242242 lattice sites. By studying the energy as a function of hole doping we conclude that there is no phase separation in the physical region relevant for high- Tc{T}_{c}Tc​ superconductors. This finding is further supported by the hole-hole correlation function calculation. Remarkably, near the phase separation instability, for Jc/t\ensuremath∼0.5{J}_{c}/t\ensuremath{\sim}0.5Jc​/t\ensuremath∼0.5 this function displays enhanced fluctuations at incommensurate wave vectors that scale linearly with the doping, in agreement with experimental findings.
We investigate the phase diagram of the two-dimensional t-J model using a recently developed Green's function Monte Carlo method for lattice fermions. We use the technique to calculate exact ground-state energies of the model on large lattices. In contrast to many previous studies, we find the model phase separates for all values of J/tJ/tJ/t. In particular, it is unstable at the hole dopings and interaction strengths at which the model was thought to describe the cuprate superconductors.
We reexamine the important issue of charge fluctuations in the two-dimensional $t\text{\ensuremath{-}}J$ model by using an improved variational method based on a wave function that contains both antiferromagnetic and ddd-wave superconducting order parameters. In particular, we generalize the wave function introduced some time ago by Bouchaud, Georges, and Lhuillier [J. Phys. (Paris) 49, 553 (1988)] by considering also a long-range spin-spin Jastrow factor, in order to correctly reproduce the small-qqq behavior of the spin fluctuations. We mainly focus our attention on the physically relevant region $J∕t\ensuremath{\sim}0.4$ and find that, contrary to a previous variational ansatz, this state is stable against phase separation for small hole doping. Moreover, by performing projection Monte Carlo methods based on the so-called fixed-node approach, we obtain clear evidence that the $t\text{\ensuremath{-}}J$ model does not phase separate for $J∕t\ensuremath{\lesssim}0.7$ and that the compressibility remains finite close to the antiferromagnetic insulating state.
We investigate the stability with respect to phase separation or charge-density-wave formation of the two-dimensional Hubbard model for various values of the local Coulomb repulsion and electron densities using Green-function Monte Carlo techniques. The well known sign problem is particularly serious in the relevant region of small hole doping. We show that the difference in accuracy for different doping makes it very difficult to probe the phase separation instability using only energy calculations, even in the weak-coupling limit (U=4t)(U=4t)(U=4t) where reliable results are available. By contrast, the knowledge of the charge correlation functions allows us to provide clear evidence of a spatially homogeneous ground state up to U=10t.U=10t.U=10t.
A theoretical investigation of boson versions of the $t\ensuremath{-}J$ and $t\ensuremath{-}{J}_{z}$ models on the square lattice is carried out, by means of Green's function Monte Carlo simulations. Accurate ground-state energy estimates as a function of hole doping are obtained, allowing one to investigate the stability of the uniform phase against separation of the system into hole-rich and hole-free phases. In the boson $t\ensuremath{-}{J}_{z}$ model, such a separation is found to occur for arbitrarily small values of Jz,{J}_{z},Jz​, at sufficiently low hole doping. Phase separation is suppressed in the boson $t\ensuremath{-}J$ model, which features a uniform ground state at any doping, for $J/t\ensuremath{\lesssim}1.5.$ Relevance of this study to the corresponding fermion models is discussed. Fermi statistics enhances the tendency toward phase separation; in particular, phase separation at low doping is predicted in the fermion $t\ensuremath{-}{J}_{z}$ model at any Jz>0.{J}_{z}>0.Jz​>0. The possible formation of stripes of holes is investigated for systems featuring both periodic and cylindrical boundary conditions. No evidence of a striped ground state is found in either the $t\ensuremath{-}J$ or $t\ensuremath{-}{J}_{z}$ boson models.
The competition between ddd-wave superconductivity (SC) and antiferromagnetism (AF) in the high-Tc{T}_{c}Tc​ cuprates is investigated by studying the hole- and electron-doped two-dimensional Hubbard model with a recently proposed variational quantum-cluster theory. The approach is shown to provide a thermodynamically consistent determination of the particle number, provided that an overall shift of the on-site energies is treated as a variational parameter. The consequences for the single-particle excitation spectra and for the phase diagram are explored. By comparing the single-particle spectra with quantum Monte Carlo and experimental data, we verify that the low-energy excitations in a strongly correlated electronic system are described appropriately. The cluster calculations also reproduce the overall ground-state phase diagram of the high-temperature superconductors. In particular, they include salient features such as the enhanced robustness of the antiferromagnetic state as a function of electron doping and the tendency towards phase separation into a mixed antiferromagnetic-superconducting phase at low doping and a pure superconducting phase at high (both hole and electron) doping.
We develop a general numerical method to study the zero-temperature properties of strongly correlated electron models on large lattices. The technique, which resembles Green's-function Monte Carlo, projects the ground-state component from a trial wave function with no approximations. We use this method to determine the phase diagram of the two-dimensional $t\ensuremath{-}J$ model, using the Maxwell construction to investigate electronic phase separation. The shell effects of fermions on finite-sized periodic lattices are minimized by keeping the number of electrons fixed at a closed-shell configuration and varying the size of the lattice. Results obtained for various electron numbers corresponding to different closed shells indicate that the finite-size effects in our calculation are small. For any value of interaction strength, we find that there is always a value of the electron density above which the system can lower its energy by forming a two-component phase separated state. Our results are compared with other calculations on the $t\ensuremath{-}J$ model. We find that the most accurate results are consistent with phase separation at all interaction strengths.