Exact spectrum for n electrons in the single band Hubbard model

Caspers, W.J.; Iske, P.L.

doi:10.1016/0378-4371(89)90079-4

Cited by 41 publications

(45 citation statements)

References 3 publications

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“…However, any finite value of J will lift this degeneracy and give the spin excitations a finite bandwidth. Notice that in finite systems, the spin degree of freedom affects the charge through an effective magnetic flux, which in the examples shown here is always identically zero [13][14][15] . Let us assume that we antiferromagnetically couple our chain to a bath of spins.…”

Section: Introductionmentioning

confidence: 89%

Class of variational Ansätze for the spin-incoherent ground state of a Luttinger liquid coupled to a spin bath

Soltanieh-ha

Feiguin

2012

Phys. Rev. B

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Interacting one-dimensional electron systems are generally referred to as "Luttinger liquids", after the effective low-energy theory in which spin and charge behave as separate degrees of freedom with independent energy scales. The "spin-incoherent Luttinger liquid" describes a finite-temperature regime that is realized when the temperature is very small relative to the Fermi energy, but larger than the characteristic spin energy scale. Similar physics can take place in the ground-state, when a Luttinger Liquid is coupled to a spin bath, which effectively introduces a "spin temperature" through its entanglement with the spin degree of freedom. We show that the spin-incoherent state can be exactly written as a factorized wave-function, with a spin wave-function that can be described within a valence bond formalism. This enables us to calculate exact expressions for the momentum distribution function and the entanglement entropy. This picture holds not only for two antiferromagnetically coupled t − J chains, but also for the t − J-Kondo chain with strongly interacting conduction electrons. We argue that this theory is quite universal and may describe a family of problems that could be dubbed "spin-incoherent".

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Section: Introductionmentioning

confidence: 89%

Class of variational Ansätze for the spin-incoherent ground state of a Luttinger liquid coupled to a spin bath

Soltanieh-ha

Feiguin

2012

Phys. Rev. B

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“…In this strongly interacting regime, it is convenient to work in the real-space basis of the ABR. In this limit, the 1D Hubbard model is exactly solvable [33][34][35][36]. We discuss the energy spectrum and wave functions of the hole in a half-filled ABR dressed by the spin excitations of the remaining electrons.…”

Section: Electronic Structure Of Charged Artificial Benzene Ringmentioning

confidence: 99%

“…Single [1,2], double [3][4][5], triple [6][7][8][9][10][11][12], and quadruple lateral gated quantum dot molecules in GaAlAs/GaAs heterojunctions or with dangling bonds on silicon surface have been demonstrated experimentally [13][14][15] and extensively studied theoretically [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31]. The capability to localize electrons in artificial lateral quantum dot molecules opens up the possibility of exploring the properties of the 1D Hubbard model, a model of strongly correlated electrons [32][33][34][35][36][37][38]. The 1D Hubbard model of benzene rings is of recent interest in the context of charge separation in mesoscopic rings [39][40][41][42], optical properties of strongly correlated oxides [38], quantum tunneling in vertically coupled rings [30], inelastic co-tunnelling in double, triple, and benzenelike quantum dot molecules …”

Section: Introductionmentioning

confidence: 99%

“…In the strongly interacting case, U ≫ t and V = 0, the 1D Hubbard model is exactly solvable [33][34][35][36]. The spectrum of the hole in a halffilled ABR dressed by the spin excitations of the remaining electrons can be interpreted in terms of the appearance of a topological phase associated with an effective gauge field piercing through the ring [16,19,29,33,41,42]. We classify the hole spectrum by the total electron spin and we show that the maximally spin-polarized (S = 5/2) and maximally spindepolarized (S = 1/2) states are the lowest energy, orbitally nondegenerate states.…”

Section: Introductionmentioning

confidence: 99%

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Electron-electron interactions, topological phase, and optical properties of a charged artificial benzene ring

et al. 2015

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/npsi/ctrl?action=rtdoc&an=21277409&lang=en http://nparc.cisti-icist.nrc-cnrc.gc.ca/npsi/ctrl?action=rtdoc&an=21277409&lang=fr READ THESE TERMS AND CONDITIONS CAREFULLY BEFORE USING THIS WEBSITE.http://nparc.cisti-icist.nrc-cnrc.gc.ca/npsi/jsp/nparc_cp.jsp?lang=en Vous avez des questions? Nous pouvons vous aider. Pour communiquer directement avec un auteur, consultez la première page de la revue dans laquelle son article a été publié afin de trouver ses coordonnées. Si vous n'arrivez pas à les repérer, communiquez avec nous à PublicationsArchive-ArchivesPublications@nrc-cnrc.gc.ca. Questions?Contact the NRC Publications Archive team at PublicationsArchive-ArchivesPublications@nrc-cnrc.gc.ca. If you wish to email the authors directly, please see the first page of the publication for their contact information. NRC Publications Archive Archives des publications du CNRCThis publication could be one of several versions: author's original, accepted manuscript or the publisher's version. / La version de cette publication peut être l'une des suivantes : la version prépublication de l'auteur, la version acceptée du manuscrit ou la version de l'éditeur. For the publisher's version, please access the DOI link below./ Pour consulter la version de l'éditeur, utilisez le lien DOI ci-dessous.http://doi.org/10.1103/PhysRevB.92.245304Physical Review B -Condensed Matter and Materials Physics, 92, 24, 2015-12-08 PHYSICAL REVIEW B 92, 245304 (2015) Electron-electron interactions, topological phase, and optical properties of a charged artificial benzene ring We present a theory of the electronic and optical properties of a charged artificial benzene ring (ABR). The ABR is described by the extended Hubbard model solved using exact diagonalization methods in both real and Fourier space as a function of the tunneling matrix element t, Hubbard on-site repulsion U , and interdot interaction V . In the strongly interacting case, we discuss exact analytical results for the spectrum of the hole in a half-filled ABR dressed by the spin excitations of the remaining electrons. The spectrum is interpreted in terms of the appearance of a topological phase associated with an effective gauge field piercing through the ring. We show that the maximally spin-polarized (S = 5/2) and maximally spin-depolarized (S = 1/2) states are the lowest energy, orbitally nondegenerate, states. We discuss the evolution of the phase diagram and level crossings as interactions are switched off and the ground state becomes spin nondegenerate but orbitally degenerate S = 1/2. We present a theory of optical absorption spectra and show that the evolution of the ground and excited states, level crossings, and presence of artificial gauge can be detected optically.

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“…For J = 0 each element of C N commutes with H ring . In each subspace of states whose spin wave function is characterized by the quantum number k s , the problem may be mapped to that of a non-interacting, spinless system with effective flux [19] …”

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confidence: 99%

Spin-Charge Separation in Aharonov-Bohm Rings of Interacting Electrons

et al. 2004

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We investigate the properties of strongly correlated electronic models on a flux-threaded ring connected to semi-infinite free-electron leads. The interference pattern of such an Aharonov-Bohm ring shows sharp dips at certain flux values, determined by the filling, which are a consequence of spin-charge separation in a nanoscopic system. PACS numbers: 75.40. Gb, 75.10.Jm, 76.60.Es In interacting electron systems in reduced spatial dimensions, correlation effects are strongly enhanced and the conventional quasiparticle description of Fermi liquids may become inapplicable. In particular, for onedimensional (1d) systems the low-energy excitations are entirely collective in nature and the Luttinger-liquid (LL) concept provides the appropriate framework to characterize the electronic properties. A hallmark of the LL is the fractionalization of the electronic excitations into separate collective spin and charge modes, a phenomenon known as spin-charge separation (SCS) [1,2].With the advent of new materials and artificial structures of quasi-1d electronic character in the last decade, a variety of experiments has been reported which seek evidence of SCS. Prominent examples of candidate materials include the organic Bechgaard and Fabre salts [3], molybdenum bronzes and chalcogenides [4], cuprate chain and ladder compounds [5], and also carbon nanotube systems [6]. The non-Fermi-liquid normal-state properties of high temperature superconductors have also led to attempts to trace their origin to the possible realization of SCS in strongly correlated electron systems in 2d [7]. Different approaches for the identification of SCS have included the analysis of non-universal power-law I-V characteristics [4], the search for characteristic dispersive features by angle-resolved photoemission spectroscopy (ARPES) [8], establishing a violation of the Wiedemann-Franz law [9], and analyzing spin and charge conductivities [8,10]. While the interpretation of experimental results has been considered ambiguous in some cases, a verification of SCS has been reported from ARPES data on SrCuO 2 [11].Theoretical methods for detecting and visualizing SCS were proposed and demonstrated many years ago. Direct calculations of the real-time evolution of electronic wave packets in Hubbard rings revealed that the spin and charge densities dispersed with different velocities as an immediate consequence of SCS [12]. Equally striking was the analysis of transmission through AharonovBohm (AB) rings [13]. The motion of the electrons in the ring was described by a LL propagator, where different charge and spin velocities, respectively v c and v s , are included explicitly. With this assumption the fluxdependence of the transmission is no longer periodic only in multiples of a flux quantum Φ 0 = hc/e, but instead new structures appear at fractional flux values which are determined by the ratio v s /v c . In essence, these structures arise because transmission requires the separated spin and charge degrees of freedom of an injected electron to recombine...

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Exact spectrum for n electrons in the single band Hubbard model

Cited by 41 publications

References 3 publications

Class of variational Ansätze for the spin-incoherent ground state of a Luttinger liquid coupled to a spin bath

Class of variational Ansätze for the spin-incoherent ground state of a Luttinger liquid coupled to a spin bath

Electron-electron interactions, topological phase, and optical properties of a charged artificial benzene ring

Spin-Charge Separation in Aharonov-Bohm Rings of Interacting Electrons

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