The charge spin-separation, pseudogap formation and phase diagrams are studied in two and four site Hubbard clusters using analytical diagonalization and grand canonical ensemble method in a multidimensional parameter space of temperature, magnetic field, on-site Coulomb interaction ( $U\ge 0$ ), and chemical potential. The numerically evaluated, exact expressions for charge and spin susceptibilities provide clear evidence for the existence of true gaps in the ground state and pseudogaps in a limited range of temperature. In particular, Mott-Hubbard type charge crossover, spin pseudogap and magnetic correlations with antiferromagnetic (spin) pseudogap structure for two and four site clusters closely resemble the pseudogap phenomena and the normal-state phase diagram in high T $_c$ superconductors. ~ ~The charge spin-separation, pseudogap formation and phase diagrams are studied in two and four site Hubbard clusters using analytical diagonalization and grand canonical ensemble method in a multidimensional parameter space of temperature, magnetic field, on-site Coulomb interaction ($U\ge 0$), and chemical potential. The numerically evaluated, exact expressions for charge and spin susceptibilities provide clear evidence for the existence of true gaps in the ground state and pseudogaps in a limited range of temperature. In particular, Mott-Hubbard type charge crossover, spin pseudogap and magnetic correlations with antiferromagnetic (spin) pseudogap structure for two and four site clusters closely resemble the pseudogap phenomena and the normal-state phase diagram in high T$_c$ superconductors. ~ ~

arXiv:cond-mat/0510609Oct 23, 20051 citation

Phase diagram and dynamics simulations of two-dimensional spin clusters

Philippe Depondt, Franz, Mertens, G.

Jan 1, 20090 citations

Charge and spin separation in one-dimensional systems

C. A. Balseiro, E. A. Jagla, K. Hallberg

Sep 1, 19950 citations

Exact study of charge-spin separation, pairing fluctuations, and pseudogaps in four-site Hubbard clusters

ARMEN N. KOCHARIAN, Gayanath Fernando, Kalum Palandage +1 more

An exact study of charge-spin separation, pairing fluctuations, and pseudogaps is carried out by combining the analytical eigenvalues of the four-site Hubbard clusters with the grand canonical and canonical ensemble approaches in a multidimensional parameter space of temperature $(T)$ , magnetic field $(h)$ , on-site interaction $(U)$ , and chemical potential $(\ensuremath{\mu})$. Our results, near the average number of electrons $⟨N⟩\ensuremath{\approx}3$, strongly suggest the existence of a critical parameter ${U}_{c}(T)$ for the localization of electrons and a particle-hole binding (positive) gap ${\ensuremath{\Delta}}^{e\text{\ensuremath{-}}h}(T)>0$ at $U>{U}_{c}(T)$ , with a zero temperature critical value, ${U}_{c}(0)=4.584$ . For $U<{U}_{c}(T)$ , the particle-particle pair binding is found with a (positive) pairing gap ${\ensuremath{\Delta}}^{P}(T)>0$. The ground state degeneracy is lifted at $U>{U}_{c}(T)$ and the cluster becomes a Mott-Hubbard like insulator due to the presence of energy gaps at all (allowed) integer numbers $(1\ensuremath{\le}N\ensuremath{\le}8)$ of electrons. In contrast, for $U\ensuremath{\le}{U}_{c}(T)$, we find an electron pair binding instability at finite temperature near $⟨N⟩\ensuremath{\approx}3$, which manifests a possible pairing mechanism, a precursor to superconductivity in small clusters. Rigorous criteria for the existence of many-body Mott-Hubbard like particle-hole and particle-particle pairings, spin pairing, (spin) pseudogap, and (spin) antiferromagnetic critical crossover temperatures, at which the corresponding pseudogaps disappear, are also formulated. In particular, the resulting phase diagram consisting of charge and spin pseudogaps, antiferromagnetic correlations, hole pairing with competing hole-rich $(⟨N⟩=2)$ , hole-poor $(⟨N⟩=4)$ , and magnetic $(⟨N⟩=3)$ regions in the ensemble of clusters near 1/8 filling closely resembles the phase diagrams and inhomogeneous phase separation recently found in the family of doped high- ${\mathrm{T}}_{\mathrm{c}}$ cuprates.An exact study of charge-spin separation, pairing fluctuations, and pseudogaps is carried out by combining the analytical eigenvalues of the four-site Hubbard clusters with the grand canonical and canonical ensemble approaches in a multidimensional parameter space of temperature $(T)$, magnetic field $(h)$, on-site interaction $(U)$, and chemical potential $(\ensuremath{\mu})$. Our results, near the average number of electrons $⟨N⟩\ensuremath{\approx}3$, strongly suggest the existence of a critical parameter ${U}_{c}(T)$ for the localization of electrons and a particle-hole binding (positive) gap ${\ensuremath{\Delta}}^{e\text{\ensuremath{-}}h}(T)>0$ at $U>{U}_{c}(T)$, with a zero temperature critical value, ${U}_{c}(0)=4.584$. For $U<{U}_{c}(T)$, the particle-particle pair binding is found with a (positive) pairing gap ${\ensuremath{\Delta}}^{P}(T)>0$. The ground state degeneracy is lifted at $U>{U}_{c}(T)$ and the cluster becomes a Mott-Hubbard like insulator due to the presence of energy gaps at all (allowed) integer numbers $(1\ensuremath{\le}N\ensuremath{\le}8)$ of electrons. In contrast, for $U\ensuremath{\le}{U}_{c}(T)$, we find an electron pair binding instability at finite temperature near $⟨N⟩\ensuremath{\approx}3$, which manifests a possible pairing mechanism, a precursor to superconductivity in small clusters. Rigorous criteria for the existence of many-body Mott-Hubbard like particle-hole and particle-particle pairings, spin pairing, (spin) pseudogap, and (spin) antiferromagnetic critical crossover temperatures, at which the corresponding pseudogaps disappear, are also formulated. In particular, the resulting phase diagram consisting of charge and spin pseudogaps, antiferromagnetic correlations, hole pairing with competing hole-rich $(⟨N⟩=2)$, hole-poor $(⟨N⟩=4)$, and magnetic $(⟨N⟩=3)$ regions in the ensemble of clusters near 1/8 filling closely resembles the phase diagrams and inhomogeneous phase separation recently found in the family of doped high-${\mathrm{T}}_{\mathrm{c}}$ cuprates.

arXiv:cond-mat/0606165Physical Review BJul 17, 200653 citations

Theoretical Study of Electron Correlations in Small Clusters

G. M. Pastor, R. Hirsch, Bernhard Mühlschlegel

Springer eBooksJan 1, 19941 citation

U\ge 0

), and chemical potential. The numerically evaluated, exact expressions for charge and spin susceptibilities provide clear evidence for the existence of true gaps in the ground state and pseudogaps in a limited range of temperature. In particular, Mott-Hubbard type charge crossover, spin pseudogap and magnetic correlations with antiferromagnetic (spin) pseudogap structure for two and four site clusters closely resemble the pseudogap phenomena and the normal-state phase diagram in high T

_c

superconductors. ~ ~

(T)

, magnetic field

(h)

, on-site interaction

(U)

, and chemical potential $(\ensuremath{\mu})$. Our results, near the average number of electrons $⟨N⟩\ensuremath{\approx}3$, strongly suggest the existence of a critical parameter

{U}_{c}(T)

for the localization of electrons and a particle-hole binding (positive) gap ${\ensuremath{\Delta}}^{e\text{\ensuremath{-}}h}(T)>0$ at

U>{U}_{c}(T)

, with a zero temperature critical value,

{U}_{c}(0)=4.584

. For

U<{U}_{c}(T)

, the particle-particle pair binding is found with a (positive) pairing gap ${\ensuremath{\Delta}}^{P}(T)>0$. The ground state degeneracy is lifted at

U>{U}_{c}(T)

and the cluster becomes a Mott-Hubbard like insulator due to the presence of energy gaps at all (allowed) integer numbers $(1\ensuremath{\le}N\ensuremath{\le}8)$ of electrons. In contrast, for $U\ensuremath{\le}{U}_{c}(T)$, we find an electron pair binding instability at finite temperature near $⟨N⟩\ensuremath{\approx}3$, which manifests a possible pairing mechanism, a precursor to superconductivity in small clusters. Rigorous criteria for the existence of many-body Mott-Hubbard like particle-hole and particle-particle pairings, spin pairing, (spin) pseudogap, and (spin) antiferromagnetic critical crossover temperatures, at which the corresponding pseudogaps disappear, are also formulated. In particular, the resulting phase diagram consisting of charge and spin pseudogaps, antiferromagnetic correlations, hole pairing with competing hole-rich

(⟨N⟩=2)

, hole-poor

(⟨N⟩=4)

, and magnetic

(⟨N⟩=3)

regions in the ensemble of clusters near 1/8 filling closely resembles the phase diagrams and inhomogeneous phase separation recently found in the family of doped high-

{\mathrm{T}}_{\mathrm{c}}

cuprates.