The thermodynamic and correlation functions for one- and three- dimensional systems described by the half-filled band Hubbard Hamiltonians are evaluated in the pair-approximation of cluster variation method. The energy, specific heat, magnetization, susceptibility and various equilibrium correlation functions are computed as functions of temperature as well as the external magnetic field for different values of coulomb energies. Our solutions correspond to Bethe approximation in which the relevant pair-correlation functions are included in our formulation. It is observed that the chemical potential for the half-filled band is exactly half of the coulomb energy at all temperatures, irrespective of the value of the applied magnetic field.The thermodynamic and correlation functions for one- and three- dimensional systems described by the half-filled band Hubbard Hamiltonians are evaluated in the pair-approximation of cluster variation method. The energy, specific heat, magnetization, susceptibility and various equilibrium correlation functions are computed as functions of temperature as well as the external magnetic field for different values of coulomb energies. Our solutions correspond to Bethe approximation in which the relevant pair-correlation functions are included in our formulation. It is observed that the chemical potential for the half-filled band is exactly half of the coulomb energy at all temperatures, irrespective of the value of the applied magnetic field.

Journal of Applied PhysicsMar 1, 19795 citations

Local-chemical-potential approach to small-cluster many-body systems

Amitesh Maiti, L. M. Falicov

Thermodynamic local-occupation averages and local-number-occupation fluctuations are studied in small-cluster many-body systems by introducing a single-site chemical potential at a particular site. This procedure allows the study of differential properties of thermodynamic functions by providing continuous variation of local occupations. The method, which starts from the quantum-mechanical grand canonical ensemble, gives a criterion to distinguish particular features of the small cluster that are likely to survive in the thermodynamic limit from those discontinuities that are characteristic of the finiteness of the cluster and the resulting discreteness of the energy spectrum. In particular the Mott-insulating state (a discontinuity in the chemical potential at a particular occupation) can be clearly tested this way. Similar indications are obtained for spin-polarized states and for particle-pairing conditions. Two four-site Hubbard-model clusters--a ring and a tetrahedron--are used as examples.Thermodynamic local-occupation averages and local-number-occupation fluctuations are studied in small-cluster many-body systems by introducing a single-site chemical potential at a particular site. This procedure allows the study of differential properties of thermodynamic functions by providing continuous variation of local occupations. The method, which starts from the quantum-mechanical grand canonical ensemble, gives a criterion to distinguish particular features of the small cluster that are likely to survive in the thermodynamic limit from those discontinuities that are characteristic of the finiteness of the cluster and the resulting discreteness of the energy spectrum. In particular the Mott-insulating state (a discontinuity in the chemical potential at a particular occupation) can be clearly tested this way. Similar indications are obtained for spin-polarized states and for particle-pairing conditions. Two four-site Hubbard-model clusters--a ring and a tetrahedron--are used as examples.

Physical review. B, Condensed matterJan 1, 19913 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

On the Chemical Potential of the Hubbard Model

J. Monecke

De Gruyter eBooksDec 31, 19740 citations

(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.