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/9909435 · Physical review. B, Condensed matter

Spin picture of the one-dimensional Hubbard model: Two-fluid structure and phase dynamics

Arianna Montorsi, Vittorio Penna

Published Nov 1, 1999• 2 citations
arXivHTMLPDF

Abstract

We propose a scheme for investigating the quantum dynamics of interacting electron models by means of a time-dependent variational principle and spin coherent states of space lattice operators. We apply such a scheme to the one-dimensional Hubbard model, and solve the resulting equations in different regimes. In particular, we find that at low densities the dynamics is mapped into two coupled nonlinear Schr\"odinger equations, whereas near half-filling the model is described by two coupled Josephson-junction arrays. Focusing then to the case in which only the phases of the spin variables are dynamically active, we examine a number of different solutions corresponding to the excitations of few macroscopic modes. Based on fixed-point equations of the simpler among them, we show that the standard one-band ground-state phase space is found.

DOI
10.1103/physrevb.60.12069

Related papers

Dynamics of the Hubbard model: A general approach by the time-dependent variational principle

Arianna Montorsi, Vittorio Penna

We describe the quantum dynamics of the Hubbard model at the semiclassical level, by implementing the time-dependent variational principle (TDVP) procedure on appropriate macroscopic wave functions constructed in terms of SU(2)-coherent states. Within the TDVP procedure, such states turn out to include a time-dependent quantum phase, part of which can be recognized as Berry's phase. We derive two semiclassical model Hamiltonians for describing the dynamics in the paramagnetic, superconducting, antiferromagnetic and charge-density wave phases and solve the corresponding canonical equations of motion in various cases. Noticeably, a vortexlike ground-state phase dynamics is found to take place for U>0 away from half filling. Moreover, it appears that an oscillatorylike ground-state dynamics survives at the Fermi surface at half filling for any U. The low-energy dynamics is also exactly solved by separating fast and slow variables. The role of the time-dependent phase is shown to be particularly interesting in the ordered phases.

arXiv:cond-mat/9611231•Physical review. B, Condensed matter•Apr 1, 1997•15 citations

One-flipped-spin sector of the Hubbard model: A search for non-Fermi-liquid behavior

David M. Frenkel

One flipped spin in the spin-polarized sector of the Hubbard model away from half-filling is considered. Aspects other than stability of the Nagaoka solution or viability of the Gutzwiller approximation (considered previously by other authors) are focused on. It is argued that understanding the phase-coherence properties of the flipped spin may be a good starting point in an attempt to prove or disprove the violation of the Fermi-liquid-like behavior in the two-dimensional (2D) Hubbard model, an outcome that has been strongly advocated by P. W. Anderson. The system is analyzed in the weak-coupling limit via a variational wave function in 1D and 2D. The variational problem is reduced to solving a nonlinear Schr\"odinger equation in both of these dimensionalities. It is found that a solitonic type of solution emerges in weak coupling in 1D, but not in 2D. This implies a conventional Fermi-liquid-like behavior in our system in 2D in the weak-coupling limit. A discussion of possible loopholes in our approach is presented, and the remaining possibility of non-Fermi-liquid-like behavior in the strong-coupling limit at finite densities in 2D is noted. An interesting connection with the existing work on heavy mobile impurities in metals and in $^{3}\mathrm{He}$ is pointed out.

Physical review. B, Condensed matter•Dec 15, 1992•11 citations

Phase Diagram of the Two-Dimensional Anderson-Hubbard Model

Jaichul Yi Lizeng Zhang, Geoffrey Canright

We study the ground state of the two-dimensional Anderson-Hubbard model using a quantum real space renormalization group method. We obtain the phase diagram near half filling. The system is always insulating with disorder. At half filling, the system undergoes a transition from a gapless (Anderson) insulator to an incompressible (Mott-Hubbard) insulator as the interaction $U$ reaches a critical value $U_c$. Away from half filling, the insulating phase is always gapless and is found to be controlled by the Anderson fixed point at half filling. This result is similar to that obtained in the corresponding one dimensional system and suggests strongly the importance of the electron-electron correlation in this gapless insulating phase.

arXiv:cond-mat/9403002•Mar 1, 1994•0 citations

Dynamics of the Hubbard model: weakly excited pairing states

Arianna Montorsi, Vittorio Penna

According to a recent proposal, we describe the quantum dynamics of the Hubbard model at the semiclassical level by implementing the Time-Dependent Variational Principle (TDVP) approach on appropriate macroscopic wave-functions constructed in terms of su(2)-coherent states. Within the TDVP procedure, such states turn out to include a time-dependent quantum phase, part of which can be recognized as Berry's phase. In particular, here we investigate the dynamics of the weakly excited states with non-vanishing pairing, away from half-filling and for repulsive Coulomb interaction.

•Jan 1, 1996•0 citations

Phase diagram of the two-dimensional Anderson-Hubbard model

Jaichul Yi, Lizeng Zhang, Geoffrey Canright

We study the ground state of the two-dimensional Anderson-Hubbard model using a quantum real space renormalization group method. We obtain the phase diagram near half filling. The system is always insulating with disorder. At half filling, the system undergoes a transition from a gapless (Anderson) insulator to an incompressible (Mott-Hubbard) insulator as the interaction U reaches a critical value ${\mathit{U}}_{\mathit{c}}$. Away from half filling, the insulating phase is always gapless and is found to be controlled by the Anderson fixed point at half filling. This result is similar to that obtained in the corresponding one-dimensional system and suggests strongly the importance of the electron-electron correlation in this gapless insulating phase.

Physical review. B, Condensed matter•Jun 1, 1994•9 citations

Numerical study of the two-dimensional Hubbard model

Steven R. White, Douglas J. Scalapino, Robert L. Sugar +3 more

We report on a numerical study of the two-dimensional Hubbard model and describe two new algorithms for the simulation of many-electron systems. These algorithms allow one to carry out simulations within the grand canonical ensemble at significantly lower temperatures than had previously been obtained and to calculate ground-state properties with fixed numbers of electrons. We present results for the two-dimensional Hubbard model with half- and quarter-filled bands. Our results support the existence of long-range antiferromagnetic order in the ground state at half-filling and its absence at quarter-filling. Results for the magnetic susceptibility and the momentum occupation along with an upper bound to the spin-wave spectrum are given. We find evidence for an attractive effective d-wave pairing interaction near half-filling but have not found evidence for a phase transition to a superconducting state.

Physical review. B, Condensed matter•Jul 1, 1989•947 citations
We propose a scheme for investigating the quantum dynamics of interacting electron models by means of a time-dependent variational principle and spin coherent states of space lattice operators. We apply such a scheme to the one-dimensional Hubbard model, and solve the resulting equations in different regimes. In particular, we find that at low densities the dynamics is mapped into two coupled nonlinear Schr"odinger equations, whereas near half-filling the model is described by two coupled Josephson-junction arrays. Focusing then to the case in which only the phases of the spin variables are dynamically active, we examine a number of different solutions corresponding to the excitations of few macroscopic modes. Based on fixed-point equations of the simpler among them, we show that the standard one-band ground-state phase space is found.
We describe the quantum dynamics of the Hubbard model at the semiclassical level, by implementing the time-dependent variational principle (TDVP) procedure on appropriate macroscopic wave functions constructed in terms of SU(2)-coherent states. Within the TDVP procedure, such states turn out to include a time-dependent quantum phase, part of which can be recognized as Berry's phase. We derive two semiclassical model Hamiltonians for describing the dynamics in the paramagnetic, superconducting, antiferromagnetic and charge-density wave phases and solve the corresponding canonical equations of motion in various cases. Noticeably, a vortexlike ground-state phase dynamics is found to take place for U>0 away from half filling. Moreover, it appears that an oscillatorylike ground-state dynamics survives at the Fermi surface at half filling for any U. The low-energy dynamics is also exactly solved by separating fast and slow variables. The role of the time-dependent phase is shown to be particularly interesting in the ordered phases.
One flipped spin in the spin-polarized sector of the Hubbard model away from half-filling is considered. Aspects other than stability of the Nagaoka solution or viability of the Gutzwiller approximation (considered previously by other authors) are focused on. It is argued that understanding the phase-coherence properties of the flipped spin may be a good starting point in an attempt to prove or disprove the violation of the Fermi-liquid-like behavior in the two-dimensional (2D) Hubbard model, an outcome that has been strongly advocated by P. W. Anderson. The system is analyzed in the weak-coupling limit via a variational wave function in 1D and 2D. The variational problem is reduced to solving a nonlinear Schr\"odinger equation in both of these dimensionalities. It is found that a solitonic type of solution emerges in weak coupling in 1D, but not in 2D. This implies a conventional Fermi-liquid-like behavior in our system in 2D in the weak-coupling limit. A discussion of possible loopholes in our approach is presented, and the remaining possibility of non-Fermi-liquid-like behavior in the strong-coupling limit at finite densities in 2D is noted. An interesting connection with the existing work on heavy mobile impurities in metals and in 3He^{3}\mathrm{He}3He is pointed out.
We study the ground state of the two-dimensional Anderson-Hubbard model using a quantum real space renormalization group method. We obtain the phase diagram near half filling. The system is always insulating with disorder. At half filling, the system undergoes a transition from a gapless (Anderson) insulator to an incompressible (Mott-Hubbard) insulator as the interaction UUU reaches a critical value UcU_cUc​. Away from half filling, the insulating phase is always gapless and is found to be controlled by the Anderson fixed point at half filling. This result is similar to that obtained in the corresponding one dimensional system and suggests strongly the importance of the electron-electron correlation in this gapless insulating phase.
According to a recent proposal, we describe the quantum dynamics of the Hubbard model at the semiclassical level by implementing the Time-Dependent Variational Principle (TDVP) approach on appropriate macroscopic wave-functions constructed in terms of su(2)-coherent states. Within the TDVP procedure, such states turn out to include a time-dependent quantum phase, part of which can be recognized as Berry's phase. In particular, here we investigate the dynamics of the weakly excited states with non-vanishing pairing, away from half-filling and for repulsive Coulomb interaction.
We study the ground state of the two-dimensional Anderson-Hubbard model using a quantum real space renormalization group method. We obtain the phase diagram near half filling. The system is always insulating with disorder. At half filling, the system undergoes a transition from a gapless (Anderson) insulator to an incompressible (Mott-Hubbard) insulator as the interaction U reaches a critical value Uc{\mathit{U}}_{\mathit{c}}Uc​. Away from half filling, the insulating phase is always gapless and is found to be controlled by the Anderson fixed point at half filling. This result is similar to that obtained in the corresponding one-dimensional system and suggests strongly the importance of the electron-electron correlation in this gapless insulating phase.
We report on a numerical study of the two-dimensional Hubbard model and describe two new algorithms for the simulation of many-electron systems. These algorithms allow one to carry out simulations within the grand canonical ensemble at significantly lower temperatures than had previously been obtained and to calculate ground-state properties with fixed numbers of electrons. We present results for the two-dimensional Hubbard model with half- and quarter-filled bands. Our results support the existence of long-range antiferromagnetic order in the ground state at half-filling and its absence at quarter-filling. Results for the magnetic susceptibility and the momentum occupation along with an upper bound to the spin-wave spectrum are given. We find evidence for an attractive effective d-wave pairing interaction near half-filling but have not found evidence for a phase transition to a superconducting state.