Universality Class of the Antiferromagnetic Transition in the Two Dimensional Hubbard Model (original) (raw)
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The dynamics of a single hole (or electron) in the two dimensional Hubbard model is investigated. The antiferromagnetic background is described by a Nèel state, and the hopping of the carrier is analyzed within a configuration interaction approach. Results are in agreement with other methods and with experimental data when available. All data are compatible with the opening of a mean field gap in a Fermi liquid of spin polarons, the so called Slater type of transition. In particular, this hypothesis explains the unusual dispersion relation of the quasiparticle bands near the transition. Recent photoemission data for Ca2CuO2Cl2 are analyzed within this context.
Europhysics Letters (EPL), 2000
The Mott-Hubbard transition is studied in the context of the two-dimensional Hubbard model. Analytical calculations show the existence of a critical value Uc of the potential strength which separates a paramagnetic metallic phase from a paramagnetic insulating phase. Calculations of the density of states and double occupancy show that the ground state in the insulating phase contains always a small fraction of empty and doubly occupied sites. The structure of the ground state is studied by considering the probability amplitude of intersite hopping. The results indicate that the ground state of the Mott insulator is characterized by a local antiferromagnetic order; the electrons keep some mobility, but this mobility must be compatible with the local ordering. The vanishing of some intersite probability amplitudes at U = Uc puts a constrain on the electron mobility. It is suggested that such quantities might be taken as the quantities which control the order in the insulating phase.
First-Order Pairing Transition and SingleParticle Spectral Function in the Attractive Hubbard Model
Physical Review Letters, 2002
A Dynamical Mean Field Theory analysis of the attractive Hubbard model in the normal phase is carried out upon restricting to solutions where superconducting order is not allowed. A clear first-order pairing transition as a function of the coupling takes place at all the electron densities out of half-filling between a Fermi liquid, stable for U < Uc, and an insulating bound pairs phase for U > Uc, and it is accompanied by phase separation. The spectral function in the metallic phase is constituted by a low energy structure around the Fermi level, which disappears discontinuously at U = Uc, and two high energy features (Hubbard bands), which persist in the insulating phase. 71.10.Fd, The experimental finding that the (zero-temperature) coherence length of cuprate superconductors is much smaller than for conventional superconductors has suggested that these compounds lie in an intermediate coupling regime, between the weak-coupling and the strongcoupling limits . Moreover, the recent finding from angular resolved photoemission of the existence of a (pseudo) gap in the single-particle spectrum well above the superconducting critical temperature, i.e., in the normal phase, has been usually interpreted in terms of preformed Cooper pairs with no phase coherence. This gave emphasis to the relevant theoretical issues related to the description of the superconducting phase in the crossover regime between the standard BCS and the Bose-Einstein (BE) condensation together with the description of the normal state, where preformed pairs or dynamical superconducting fluctuations give rise to the pseudogap phenomenology. Regarding the pseudogap regime, various perturbative schemes have been adopted, without a firm unambiguous understanding of the electron pairing in the normal state .
Electronic phase transitions in the half-filled ionic Hubbard model
Physical Review B, 2008
A detailed study of electronic phase transitions in the ionic Hubbard model at half filling is presented. Within the dynamical mean field approximation a series of transitions from the band insulator via a metallic state to a Mott-Hubbard insulating phase is found at intermediate values of the one-body potential ∆ with increasing the Coulomb interaction U . We obtain a critical region in which the metallic phase disappears and a novel coexistence phase between the band and the Mott insulating state sets in. Our results are consistent with those obtained at low dimensions, thus they provide a concrete description for the charge degrees of freedom of the ionic Hubbard model.
Observation of antiferromagnetic correlations in the Hubbard model with ultracold atoms
Nature, 2015
Ultracold atoms in optical lattices are a versatile platform for creating quantum many-body states of matter. These systems may be able to address some of the most important issues in many-body physics, such as high-temperature (high-Tc) superconductivity. Almost thirty years ago, Anderson suggested that the Hubbard model, a simplified representation of fermions moving on a periodic lattice, may contain the essence of cuprate superconductivity . The Hubbard model describes many of the features shared by the cuprates, including an interaction-driven Mott insulating state and antiferromagnetism (AFM). Optical lattices filled with a two-spin-component Fermi gas of ultracold atoms can faithfully realize the Hubbard model with readily tunable parameters, and thus provide a platform for its systematic exploration . Realization of strongly correlated phases in optical lattices, however, has been hindered by the need to cool the atoms to temperatures as low as the magnetic exchange energy, and also by the lack of reliable thermometry . Here we demonstrate spin-sensitive Bragg scattering of light, in analogy to neutron scattering in condensed matter, and use it to measure the spin correlations at temperatures down to 1.4 times that of the AFM phase transition. We achieve these low temperatures using a novel compensated lattice to flatten the confining potential, tune the density, and mitigate heating in the lattice . We deduce the temperature of the atoms in the lattice by comparing the light scattering to determinantal quantum Monte Carlo (DQMC) and numerical linked-cluster expansion (NLCE) calculations, using the local density approximation (LDA) to account for the inhomogeneity of the density. Further refinement of the compensated lattice may produce even lower temperatures which, along with light scattering thermometry, has important implications for achieving other novel quantum states and addressing the role of the Hubbard model in cuprate superconductivity.
Antiferromagnetism in the two-dimensional Hubbard model
Physical review letters, 1989
Magnetic properties of the two-dimensional Hubbard-model are inferred from results of Monte Carlo simulations. Lattice sizes up to 8x8 and temperatures down to T=t/20 (t =hopping) were studied. The half-filled system is found to exhibit antiferromagnetic long-range order for all values of the Coulomb repulsion U. The low-temperature magnetic properties are found to be well described by spinwave theory with renormalized local moment and spin-wave velocity. Numerical evidence presented suggests that when doped the system loses the long-range order immediately away from half filling.
Physical Review B, 2006
The competition between d-wave superconductivity (SC) and antiferromagnetism (AF) in the high-Tc cuprates is investigated by studying the hole-and electron-doped two-dimensional Hubbard model with a recently proposed variational quantum-cluster theory. The approach is shown to provide a thermodynamically consistent determination of the particle number, provided that an overall shift of the on-site energies is treated as a variational parameter. The consequences for the single-particle excitation spectra and for the phase diagram are explored. By comparing the single-particle spectra with quantum Monte-Carlo (QMC) and experimental data, we verify that the low-energy excitations in a strongly-correlated electronic system are described appropriately. The cluster calculations also reproduce the overall ground-state phase diagram of the high-temperature superconductors. In particular, they include salient features such as the enhanced robustness of the antiferromagnetic state as a function of electron doping and the tendency towards phase separation into a mixed antiferromagnetic-superconducting phase at low-doping and a pure superconducting phase at high (both hole and electron) doping.
O ct 2 00 2 Antiferromagnetism in the 2 D Hubbard Model – Phase Transition and Local Quantities
2002
We present a first study of the antiferromagnetic state in the 2D U–t–t′ model at finite temperatures by the composite operator method, providing simultaneously a fully self–consistent treatment of the paramagnetic and the AF phase. Near half filling the critical value of the Coulomb repulsion as a function of t′ and the temperature dependence of the magnetization and internal energy have been studied.