Single- and many-electron calculations and related dynamics are presented for a dimer and small Hubbard clusters. The Floquet-Bloch picture for a periodic dimer is discussed with regard to the time dependence of the Peierls gap and the expectation of the current operator. In driven Fermi-Hubbard clusters, the time dependence of charge gaps and phase separation along with charge pairing at various cluster sizes indicate the presence and absence of paired electron states. We examine the effect of electromagnetic time-dependent external perturbations on Hubbard many-electron systems in our search of for precursors to superconducting states and time crystals. Two principally different kinds of electromagnetic excitations are analyzed: 1) the recently demonstrated dynamic modulation of Hubbard parameters due to excitation of certain phonon modes within the far-infrared domain, and 2) the Hubbard Hamiltonian, with fixed parameters in an electromagnetic field, resonant with transitions between the ground state and high-energy excited states as possible precursors to superconductivity, within visible–near-infrared domains.Single- and many-electron calculations and related dynamics are presented for a dimer and small Hubbard clusters. The Floquet-Bloch picture for a periodic dimer is discussed with regard to the time dependence of the Peierls gap and the expectation of the current operator. In driven Fermi-Hubbard clusters, the time dependence of charge gaps and phase separation along with charge pairing at various cluster sizes indicate the presence and absence of paired electron states. We examine the effect of electromagnetic time-dependent external perturbations on Hubbard many-electron systems in our search of for precursors to superconducting states and time crystals. Two principally different kinds of electromagnetic excitations are analyzed: 1) the recently demonstrated dynamic modulation of Hubbard parameters due to excitation of certain phonon modes within the far-infrared domain, and 2) the Hubbard Hamiltonian, with fixed parameters in an electromagnetic field, resonant with transitions between the ground state and high-energy excited states as possible precursors to superconductivity, within visible–near-infrared domains.

Europhysics Letters (EPL)May 1, 20210 citations

Electron Correlation in the Small Hubbard Model

Arisato Kawabata

Springer series in solid-state sciencesJan 1, 19810 citations

Phase separation and electron pairing in repulsive Hubbard clusters

Gayanath Fernando, ARMEN N. KOCHARIAN, Kalum Palandage +2 more

Exact thermal studies of small (4-site and 8-site) Hubbard clusters with local electron repulsion yield intriguing insight into phase separation, charge-spin separation, pseudogaps, condensation, and, in particular, pairing fluctuations away from half-filling. These exact calculations, carried out in canonical and grand canonical ensembles, monitoring variations in temperature $T$ and magnetic field $h$ , show rich phase diagrams in a $T\ensuremath{-}\ensuremath{\mu}$ space consisting of pairing fluctuations and signatures of condensation. Corresponding electron pairing instabilities are seen when the on-site Coulomb interaction $U$ is smaller than a critical value ${U}_{c}(T)$ and they point to a possible electron pairing mechanism. The specific heat, magnetization, charge pairing, and spin pairing provide strong support for the existence of competing (paired and unpaired) phases near optimal doping in these clusters, and numerous similarities with experiments on high ${T}_{c}$ superconductors are pointed out. In addition, these ideas may be linked to superconducting carbon nanotubes where a purely electronic mechanism could be responsible for superconductivity.Exact thermal studies of small (4-site and 8-site) Hubbard clusters with local electron repulsion yield intriguing insight into phase separation, charge-spin separation, pseudogaps, condensation, and, in particular, pairing fluctuations away from half-filling. These exact calculations, carried out in canonical and grand canonical ensembles, monitoring variations in temperature $T$ and magnetic field $h$, show rich phase diagrams in a $T\ensuremath{-}\ensuremath{\mu}$ space consisting of pairing fluctuations and signatures of condensation. Corresponding electron pairing instabilities are seen when the on-site Coulomb interaction $U$ is smaller than a critical value ${U}_{c}(T)$ and they point to a possible electron pairing mechanism. The specific heat, magnetization, charge pairing, and spin pairing provide strong support for the existence of competing (paired and unpaired) phases near optimal doping in these clusters, and numerous similarities with experiments on high ${T}_{c}$ superconductors are pointed out. In addition, these ideas may be linked to superconducting carbon nanotubes where a purely electronic mechanism could be responsible for superconductivity.

arXiv:cond-mat/0608579Physical Review BFeb 28, 200717 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

T

and magnetic field

h

, show rich phase diagrams in a $T\ensuremath{-}\ensuremath{\mu}$ space consisting of pairing fluctuations and signatures of condensation. Corresponding electron pairing instabilities are seen when the on-site Coulomb interaction

U

is smaller than a critical value

{U}_{c}(T)

and they point to a possible electron pairing mechanism. The specific heat, magnetization, charge pairing, and spin pairing provide strong support for the existence of competing (paired and unpaired) phases near optimal doping in these clusters, and numerous similarities with experiments on high

{T}_{c}

superconductors are pointed out. In addition, these ideas may be linked to superconducting carbon nanotubes where a purely electronic mechanism could be responsible for superconductivity.

(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.