Comparison of variational approaches for the exactly solvable 1/r-Hubbard chain

Gebhard, Florian; Girndt, A.

doi:10.1007/bf01314250

Cited by 13 publications

(12 citation statements)

References 22 publications

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“…Appendix C: Properties of the weak-coupling ground state of the 1/r Hubbard chain For the 1/r Hubbard chain the kinetic energy per lattice site ǫ kin (U ) can be obtained from the fact that the ground-state energy is given by the variational Gutzwiller energy up to O(U 2 ), 58 which yields (W : bandwidth, L = number of lattice sites)…”

Section: Discussionmentioning

confidence: 99%

Generalized Gibbs ensemble prediction of prethermalization plateaus and their relation to nonthermal steady states in integrable systems

2011

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A quantum many-body system which is prepared in the ground state of an integrable Hamiltonian does not directly thermalize after a sudden small parameter quench away from integrability. Rather, it will be trapped in a prethermalized state and can thermalize only at a later stage. We discuss several examples for which this prethermalized state shares some properties with the nonthermal steady state that emerges in the corresponding integrable system. These examples support the notion that nonthermal steady states in integrable systems may be viewed as prethermalized states that never decay further. Furthermore we show that prethermalization plateaus are under certain conditions correctly predicted by generalized Gibbs ensembles, which are the appropriate extension of standard statistical mechanics in the presence of many constants of motion. This establishes that the relaxation behaviors of integrable and nearly integrable systems are continuously connected and described by the same statistical theory.

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Section: Discussionmentioning

confidence: 99%

Generalized Gibbs ensemble prediction of prethermalization plateaus and their relation to nonthermal steady states in integrable systems

2011

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“…At half-filling a Mott-Hubbard metal-insulator transition occurs at interaction strength U c = W , with the Mott gap given by ∆ = U − U c for U ≥ U c [22]. This metal-insulator transition is also captured by correlated variational wave functions [34,35].…”

Section: /R Hubbard Chainmentioning

confidence: 99%

“…where ∆ = 2π/L, K F = (2n − 1)π, and the prime indicates that only every other bosonic pseudomomentum K ∈ (−π, π) appears. The Hamiltonian (4) only acts separately on each space spanned by the bracketed configurations [↑ ↓] ≡ 1 0 and [• •] ≡ 0 1 for neighboring pseudomomenta, K and K + ∆ [22,34],…”

Section: Bosonic Representationmentioning

confidence: 99%

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Relaxation of a one-dimensional Mott insulator after an interaction quench

2008

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We obtain the exact time evolution for the one-dimensional integrable fermionic 1/r Hubbard model after a sudden change of its interaction parameter, starting from either a metallic or a Mottinsulating eigenstate. In all cases the system relaxes to a new steady state, showing that the presence of the Mott gap does not inhibit relaxation. The properties of the final state are described by a generalized Gibbs ensemble. We discuss under which conditions such ensembles provide the correct statistical description of isolated integrable systems in general. We find that generalized Gibbs ensembles do predict the properties of the steady state correctly, provided that the observables or initial states are sufficiently uncorrelated in terms of the constants of motion.

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“…where we used the abbreviationn b,σ = 1 −n b,σ . Due to the constraints (36), (37), and (38), we can cast P + GPG d into a form where local Hartree bubbles are absent,…”

Section: Discussionmentioning

confidence: 99%

Gutzwiller variational approach to the two-impurity Anderson model for a metallic host at particle-hole symmetry

Linneweber

Bünemann

Mahmoud

et al. 2017

J. Phys.: Condens. Matter

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We study Gutzwiller-correlated wave functions as variational ground states for the two-impurity Anderson model (TIAM) at particle-hole symmetry as a function of the impurity separation [Formula: see text]. Our variational state is obtained by applying the Gutzwiller many-particle correlator to a single-particle product state. We determine the optimal single-particle product state fully variationally from an effective non-interacting TIAM that contains a direct electron transfer between the impurities as variational degree of freedom. For a large Hubbard interaction U between the electrons on the impurities, the impurity spins experience a Heisenberg coupling proportional to [Formula: see text] where V parameterizes the strength of the on-site hybridization. For small Hubbard interactions we observe weakly coupled impurities. In general, for a three-dimensional simple cubic lattice we find discontinuous quantum phase transitions that separate weakly interacting impurities for small interactions from singlet pairs for large interactions.

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Comparison of variational approaches for the exactly solvable 1/r-Hubbard chain

Cited by 13 publications

References 22 publications

Generalized Gibbs ensemble prediction of prethermalization plateaus and their relation to nonthermal steady states in integrable systems

Generalized Gibbs ensemble prediction of prethermalization plateaus and their relation to nonthermal steady states in integrable systems

Relaxation of a one-dimensional Mott insulator after an interaction quench

Gutzwiller variational approach to the two-impurity Anderson model for a metallic host at particle-hole symmetry

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