Ground-state properties of the one-dimensional extended Hubbard model at half filling

Nishimoto, Sei‐ichi

doi:10.1016/j.jpcs.2008.06.122

Cited by 3 publications

(5 citation statements)

References 22 publications

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“…Using standard notations, the Hubbard model reads [35] H t c c U n n h.c. . includes an additional nearest-neighbor Coulomb interaction of strength V. DMRG has been previously employed to study its ground-state phase diagram [36,37]. One-particle spectral properties [38][39][40] as well as dynamical spin-and charge-correlation functions [41,42] have been computed using the dynamical DMRG method [36] and time-dependent DMRG [15].…”

Section: Model and Methodsmentioning

confidence: 99%

“…DMRG has been previously employed to study its ground-state phase diagram. 36,37 One-particle spectral properties [38][39][40] as well as dynamical spin-and charge-correlation functions 41,42 have been computed using the dynamical DMRG method 36 and time-dependent DMRG. 15 Our goal is to compute the local two-particle spectral function…”

Section: Model and Methodsmentioning

confidence: 99%

“…Let us first discuss the numerical results. Equation (37) can be used to approximate the two-hole spectrum with a calculation for a system with open boundaries. In this case, the k-summation of A k , 2 hole w ( ) -(equation (38)) yields the local spectrum, but averaged over all sites, rather than the local spectral function at the central site i, as defined in equation (5).…”

Section: Infinite Doublon Lifetime For K P =mentioning

confidence: 99%

“…for k p = , the transition operator in the Lehmann representation of the k-resolved two-hole spectral function, equation (37), is just proportional to η. For the case of half-filling this implies…”

Section: Infinite Doublon Lifetime For K P =mentioning

confidence: 99%

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Multiplons in the two-hole excitation spectra of the one-dimensional Hubbard model

Rausch

Potthoff

2016

New J. Phys.

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Using the density-matrix renormalization group in combination with the Chebyshev polynomial expansion technique, we study the two-hole excitation spectrum of the one-dimensional Hubbard model in the entire filling range from the completely occupied band (n = 2) down to half-filling (n = 1). For strong interactions, the spectra reveal multiplon physics, i.e., relevant final states are characterized by two (doublon), three (triplon), four (quadruplon) and more holes, potentially forming stable compound objects or resonances with finite lifetime. These give rise to several satellites in the spectra with largely different spectral weights as well as to different two-hole, doublon-hole, two-doublon etc continua. The complex multiplon phenomenology is analyzed by interpreting not only local and k-resolved two-hole spectra but also three-and four-hole spectra for the Hubbard model and by referring to effective low-energy models. In addition, a filter-operator technique is presented and applied which allows to extract specific information on the final states at a given excitation energy. While multiplons composed of an odd number of holes do neither form stable compounds nor well-defined resonances unless a nearest-neighbor density interaction V is added to the Hamiltonian, the doublon and the quadruplon are well-defined resonances. The k-resolved fourhole spectrum at n=2 represents an interesting special case where a completely stable quadruplon turns into a resonance by merging with the doublon-doublon continuum at a critical wave vector. For all fillings with n 1 > , the doublon lifetime is strongly k-dependent and is even infinite at the Brillouin zone edges as demonstrated by k-resolved two-hole spectra. This can be traced back to the 'hidden' charge-SU(2) symmetry of the model which is explicitly broken off half-filling and gives rise to a massive collective excitation, even for arbitrary higher-dimensional but bipartite lattices. available for a dissociation into two particles moving independently through the lattice [8]. The latter situation is described by states which belong to a scattering continuum at energies within twice the bandwidth W 2 . If there is, on the other hand, a finite concentration of bosons or fermions [9] in the conduction band, the doublon may decay by transferring its energy Ũ in a high-order scattering process to several low-lying excitations of the continuum. This implies a finite lifetime of the doublon and poses an intricate many-body problem. The lifetime has been measured [10] for a well-controlled Fermi gas trapped in an optical lattice and was estimated theoretically for Fermi [10,11] and for Bose systems [12]. Studies of the real-time dynamics of an initially doubly occupied state t c t c t 0, where 0ñ | is the vacuum state or the few-particle ground state, have been done with exact-diagonalization methods [13,14]. For 0ñ | being the ground state of the extended Hubbard model at half-filling, time-dependent density-matrix renormalization group (DMRG) [15,16] has been used to stud...

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Section: Model and Methodsmentioning

confidence: 99%

Section: Model and Methodsmentioning

confidence: 99%

Section: Infinite Doublon Lifetime For K P =mentioning

confidence: 99%

Section: Infinite Doublon Lifetime For K P =mentioning

confidence: 99%

See 2 more Smart Citations

Multiplons in the two-hole excitation spectra of the one-dimensional Hubbard model

Rausch

Potthoff

2016

New J. Phys.

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“…state with gapped excitations and alternating bonds between neighboring sites and is separated from a Spin Density Wave (SDW) region by a Berezinskii-Kosterlitz-Thouless (BKT) transition and from a Charge Density Wave (CDW) region by a second-order transition curve that changes at a tricritical point into a 1 st -order transition before terminating at a multicritical point [2,[24][25][26][27][28][29][30][31][32]. In this study, we restrict ourselves to U = 4 in an effort to identify the second-order critical point, herein referred to as V Gauss , and the BKT-critical point, V BKT (denoted by star symbols in figure 1).…”

Section: Introductionmentioning

confidence: 99%

Critical entanglement for the half-filled extended Hubbard model

2019

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We study the ground state of the one-dimensional extended Hubbard model at half-filling using the entanglement entropy calculated by Density Matrix Renormalization Group (DMRG) techniques. We apply a novel curve fitting and scaling method to accurately identify a 2 nd order critical point as well as a Berezinskii-Kosterlitz-Thouless (BKT) critical point. Using open boundary conditions and medium-sized lattices with very small truncation errors, we are able to achieve similar accuracy to previous authors. We also report observations of finite-size and boundary effects that can be remedied with careful pinning. *

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Quantum phases of a one-dimensional dipolar Fermi gas

Mosadeq¹,

Asgari

2015

Phys. Rev. B

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We quantitatively obtain the quantum ground-state phases of a Fermi system with on-site and dipole-dipole interactions in one-dimensional lattice chains within the density matrix renormalization group. We show, at a given spin polarization, the existence of six phases in the phase diagram and find that the phases are highly dependent on the spin degree of freedom. These phases can be constructed using available experimental techniques.Comment: 10 pages, 8 figure

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Ground-state properties of the one-dimensional extended Hubbard model at half filling

Cited by 3 publications

References 22 publications

Multiplons in the two-hole excitation spectra of the one-dimensional Hubbard model

Multiplons in the two-hole excitation spectra of the one-dimensional Hubbard model

Critical entanglement for the half-filled extended Hubbard model

Quantum phases of a one-dimensional dipolar Fermi gas

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