We study the crossover between the sudden quench limit and the adiabatic dynamics of superconducting states in the attractive Hubbard model. We focus on the dynamics induced by the change of the attractive interaction during a finite ramp time. The ramp time is varied in order to track the evolution of the dynamical phase diagram from the sudden quench to the equilibrium limit. Two different dynamical regimes are realized for quenches towards weak and strong coupling interactions. At weak coupling the dynamics depends only on the energy injected into the system, whereas a dynamics retaining memory of the initial state takes place at strong coupling. We show that this is related to a sharp transition between a weak and a strong coupling quench dynamical regime, which defines the boundaries beyond which a dynamics independent from the initial state is recovered. Comparing the dynamics in the superconducting and nonsuperconducting phases, we argue that this is due to the lack of an adiabatic connection to the equilibrium ground state for nonequilibrium superconducting states in the strong coupling quench regime.We study the crossover between the sudden quench limit and the adiabatic dynamics of superconducting states in the attractive Hubbard model. We focus on the dynamics induced by the change of the attractive interaction during a finite ramp time. The ramp time is varied in order to track the evolution of the dynamical phase diagram from the sudden quench to the equilibrium limit. Two different dynamical regimes are realized for quenches towards weak and strong coupling interactions. At weak coupling the dynamics depends only on the energy injected into the system, whereas a dynamics retaining memory of the initial state takes place at strong coupling. We show that this is related to a sharp transition between a weak and a strong coupling quench dynamical regime, which defines the boundaries beyond which a dynamics independent from the initial state is recovered. Comparing the dynamics in the superconducting and nonsuperconducting phases, we argue that this is due to the lack of an adiabatic connection to the equilibrium ground state for nonequilibrium superconducting states in the strong coupling quench regime.

arXiv:1708.01096Physical review. B./Physical review. BNov 7, 201724 citations

Correlated pairs in the attractive Hubbard model

Philip A. Pincus, Paul M. Chaikin, Cornelius F. Coll

Solid State CommunicationsJun 1, 197349 citations

Superconductivity in the extended two-dimensional Hubbard model: Strong-coupling regime and hybridization effects

E.S. Caixeiro, A. Troper

In this work we have considered a two-dimensional two-band Hubbard model (extended Hubbard model) to study the effect of the nonlocal hybridization ${V}_{\mathbf{k}}$ on the superconductivity. In the strong-coupling regime and for a $d$ -wave superconducting gap, we have obtained the superconducting critical temperature ${T}_{c}$ and the zero-temperature superconducting gap ${\ensuremath{\Delta}}_{0}$ for different hybridizations. We have adopted hopping parameters suitable to describe the high-temperature superconductor materials. The results show that for a fixed value of the hybridization and the intraband $d\text{\ensuremath{-}}d$ attractive potential $U$ , the gap increases for low temperatures and diminishes as the temperatures increase toward ${T}_{c}$ . As the hybridization increases both, ${\ensuremath{\Delta}}_{0}$ and ${T}_{c}$ , diminish. For each hybridization, the quantity $2{\ensuremath{\Delta}}_{0}/{k}_{B}{T}_{c}$ increases and saturates in a particular value as $U$ increases. The relation between applied pressure $P$ and hybridization in the strong-coupling regime is also discussed.In this work we have considered a two-dimensional two-band Hubbard model (extended Hubbard model) to study the effect of the nonlocal hybridization ${V}_{\mathbf{k}}$ on the superconductivity. In the strong-coupling regime and for a $d$-wave superconducting gap, we have obtained the superconducting critical temperature ${T}_{c}$ and the zero-temperature superconducting gap ${\ensuremath{\Delta}}_{0}$ for different hybridizations. We have adopted hopping parameters suitable to describe the high-temperature superconductor materials. The results show that for a fixed value of the hybridization and the intraband $d\text{\ensuremath{-}}d$ attractive potential $U$, the gap increases for low temperatures and diminishes as the temperatures increase toward ${T}_{c}$. As the hybridization increases both, ${\ensuremath{\Delta}}_{0}$ and ${T}_{c}$, diminish. For each hybridization, the quantity $2{\ensuremath{\Delta}}_{0}/{k}_{B}{T}_{c}$ increases and saturates in a particular value as $U$ increases. The relation between applied pressure $P$ and hybridization in the strong-coupling regime is also discussed.

Physical Review BJul 1, 20108 citations

In this work we have considered a two-dimensional two-band Hubbard model (extended Hubbard model) to study the effect of the nonlocal hybridization

{V}_{\mathbf{k}}

on the superconductivity. In the strong-coupling regime and for a

d

-wave superconducting gap, we have obtained the superconducting critical temperature

{T}_{c}

and the zero-temperature superconducting gap ${\ensuremath{\Delta}}_{0}$ for different hybridizations. We have adopted hopping parameters suitable to describe the high-temperature superconductor materials. The results show that for a fixed value of the hybridization and the intraband $d\text{\ensuremath{-}}d$ attractive potential

U

, the gap increases for low temperatures and diminishes as the temperatures increase toward

{T}_{c}

. As the hybridization increases both, ${\ensuremath{\Delta}}_{0}$ and

{T}_{c}

, diminish. For each hybridization, the quantity $2{\ensuremath{\Delta}}_{0}/{k}_{B}{T}_{c}$ increases and saturates in a particular value as

U

increases. The relation between applied pressure

P

and hybridization in the strong-coupling regime is also discussed.