Ground-state phase diagram of a half-filled one-dimensional extended hubbard model

Doping dependence of the phase diagram in one-dimensional extended Hubbard model: a functional renormalization group study

Using functional renormalization group method, we studied the phase diagram of the one-dimensional extended Hubbard model at different dopings. At half filling, variety of states strongly compete with each other. These states include spin-density wave, charge-density wave, s-wave and p -wave superconductivity, phase separation, and an exotic bond-order wave. By doping, system favours superconductivity more than density waves. At 1/8 doping, a new area of extended s-wave superconductivity emerges between charge density wave and bond-order wave regions. If the system is doped to 1/4-doping, a new area of p -wave superconductivity emerges between charge-density wave and spin-density wave regions.

Interplay of Site and Bond Electron-Phonon Coupling in One Dimension

The interplay of bond and charge correlations is studied in a one-dimensional model with both Holstein and Su-Schrieffer-Heeger (SSH) couplings to quantum phonons. The problem is solved exactly by quantum Monte Carlo simulations. If one of the couplings dominates, the ground state is a Peierls insulator with long-range bond or charge order. At weak coupling, the results suggest a spin-gapped and repulsive metallic phase arising from the competing order parameters and lattice fluctuations. Such a phase is absent from the pure SSH model even for quantum phonons. At strong coupling, evidence for a continuous transition between the two Peierls states is presented.

Thermal Conductivity of the One-Dimensional Fermi-Hubbard Model

We study the thermal conductivity of the one-dimensional Fermi-Hubbard model at a finite temperature using a density matrix renormalization group approach. The integrability of this model gives rise to ballistic thermal transport. We calculate the temperature dependence of the thermal Drude weight at half filling for various interaction strengths. The finite-frequency contributions originating from the fact that the energy current is not a conserved quantity are investigated as well. We report evidence that breaking the integrability through a nearest-neighbor interaction leads to vanishing Drude weights and diffusive energy transport. Moreover, we demonstrate that energy spreads ballistically in local quenches with initially inhomogeneous energy density profiles in the integrable case. We discuss the relevance of our results for thermalization in ultracold quantum-gas experiments and for transport measurements with quasi-one-dimensional materials.

Quantum coherence and quantum phase transitions

We study the connections between local quantum coherence (LQC) based on Wigner-Yanase skew information and quantum phase transitions (QPTs). When applied on the one-dimensional Hubbard, XY spin chain with three-spin interaction, and Su-Schrieffer-Heeger models, the LQC and its derivatives are used successfully to detect different types of QPTs in these spin and fermionic systems. Furthermore, the LQC is effective as the quantum discord (QD) in detecting QPTs at finite temperatures, where the entanglement has lost its effectiveness. We also demonstrate that the LQC can exhibit different behaviors in many forms compared with the QD.

Scaling phenomena driven by inhomogeneous conditions at first-order quantum transitions

We investigate the effects of smooth inhomogeneities at first-order quantum transitions (FOQTs), such as those arising in the presence of a space-dependent external field, which smooths out the discontinuities of the low-energy properties at the transition. We argue that a universal scaling behavior emerges in the space transition region close to the point in which the external field takes the value for which the homogeneous system undergoes the FOQT. We verify the general theory in two model systems. We consider the quantum Ising chain in the ferromagnetic phase and the q-state Potts chain for q=10, investigating the scaling behavior which arises in the presence of an additional inhomogeneous parallel and transverse magnetic field, respectively. Numerical results are in full agreement with the general theory.

Wigner crystal versus fermionization for one-dimensional Hubbard models with and without long-range interactions

The ground state properties of the Hubbard model with or without long-range interactions in the regime with strongly repulsive on-site interactions are investigated by means of the exact diagonalization method. We show that the appearance of N-crests in the density profile of a trapped N-fermion system is a natural result of 'fermionization' between antiparallel-spin fermions in the strongly repulsive limit and cannot be taken as the only signature of the Wigner crystal phase, as the static structure factor does not show any signature of crystallization. In contrast, both the density distribution and the static structure factor of the Hubbard model with strong long-range interactions display clear signatures of the Wigner crystal phase. Our results indicate the important role of long-range interaction in the formation of the Wigner crystal phase.

Current in Hubbard rings manipulated via magnetic flux

We study currents in a quantum ring threaded by a magnetic flux which is varied in an arbitrary way from an initial constant value φ(1) at time t(1) to a final constant value φ(2) at time t(2). We analyze how the induced currents for t > t(2) can be controlled by the rate of flux variation [Formula: see text]. The dynamics of electrons in the ring is described using the Hubbard and the extended Hubbard models. In the Hubbard model with infinite on-site repulsion the current for t > t(2) is shown to be independent of the flux variation before t(2) and is fully determined by a solution of the initial equilibrium problem and by the value φ(2) of the flux. For intermediate values of the interaction strength the current displays regular or irregular time oscillations and the amplitude of oscillations is sensitive to the rate of the flux changing [Formula: see text]: slow changes of the flux result in small amplitudes of the current oscillations and vice versa. We demonstrate that the time dependence of the induced current bears information on electronic correlations. Our results have important implications for not only mesoscopic rings but also the designing of quantum motors built out of ring-shaped optical lattices.

The metal-insulator transition in the half-filled extended Hubbard model on a triangular lattice

In this paper, we have investigated the metal-insulator transition (MIT) in a two-dimensional half-filled extended Hubbard model on an isotropic triangular lattice with a real space block renormalization group technique. It has been found that the MIT can be driven nontrivially by either the on-site interaction U or the nearest-neighbor one V, but with different critical exponents. Depending upon the values of V, the system could have one, two or three MIT critical points. Moreover, for the metallic regime, we have also studied the competition effect from the spin density wave and charge density wave phases by using a mean-field theory based upon Hartree-Fock approximations. Finally, the single-site entanglement is also calculated and its first derivative with respect to U shows a jump along the critical line of the MIT.

Understanding the electronic structure and magnetism of correlated nanosystems

In this paper we review recent developments towards a realistic description of the electronic structure and magnetism of correlated nanosystems. A new class of so-called continuous-time solvers for the quantum impurity problem is discussed, which provides a numerically exact solution without systematic errors due to imaginary time discretization. These solvers are able to handle general interactions, like the full Coulomb vertex. We further show how four-point or higher-order correlation functions of the impurity problem can be computed. This allows the calculation of dynamical susceptibilities which provide information about spin excitations. Moreover, we discuss a principally new many-body scheme recently proposed for the description of non-local correlations in strongly correlated systems. This approach provides a basis for a many-body description of extended correlated nanostructures on a substrate.

Persistent currents in one dimension: the counterpart of Leggett's theorem

We discuss the sign of the persistent current of N electrons in one dimensional rings. Using a topology argument, we establish lower bounds for the free energy in the presence of arbitrary electron-electron interactions and external potentials. Those bounds are the counterparts of upper bounds derived by Leggett. Rings with odd (even) numbers of polarized electrons are always diamagnetic (paramagnetic). We show that unpolarized electrons with N being a multiple of four exhibit either paramagnetic behavior or a superconductorlike current-phase relation.

One-dimensional extended Hubbard model in the atomic limit

We present the exact solution of the one-dimensional extended Hubbard model in the atomic limit within the Green's function and equations of motion formalism. We provide a comprehensive and systematic analysis of the model by considering all the relevant response and correlation functions as well as thermodynamic quantities in the whole parameters space. At zero temperature we identify four phases in the plane (U,n) ( U is the on-site potential and n is the filling) and relative phase transitions as well as different types of charge ordering. These features are endorsed by investigating at T=0 the chemical potential and pertinent local correlators, the particle and double occupancy correlation functions, the entropy, and by studying the behavior in the limit T-->0 of the charge and spin susceptibilities. A detailed study of the thermodynamic quantities is also presented at finite temperature. This study evidences that a finite-range order persists for a wide range of the temperature, as shown by the behavior of the correlation functions and by the two-peak structure exhibited by the charge susceptibility and by the entropy. Moreover, the equations of motion formalism, together with the use of composite operators, allows us to exactly determine the set of elementary excitations. As a result, the density of states can be determined and a detailed analysis of the specific heat allows for identifying the excitations and for ascribing its two-peak structure to a redistribution of the charge density.

Excitons in the one-dimensional Hubbard model: a real-time study

We study the real-time dynamics of a hole and doubly occupied site pair, namely, a holon and a doublon, in a 1D Hubbard insulator with on-site and nearest-neighbor Coulomb repulsion. Our analysis shows that the pair is long-lived and the expected decay mechanism to underlying spin excitations is actually inefficient. For a nonzero intersite Coulomb repulsion, we observe that part of the wave function remains in a bound state. Our study also provides insight on the holon-doublon propagation in real space. Because of the one-dimensional nature of the problem, these particles move in opposite directions even in the absence of an applied electric field. The potential relevance of our results to solar cell applications is discussed.

Phase diagram of the one-dimensional half-filled extended Hubbard model

We determine the ground-state phase diagram of the one-dimensional half-filled Hubbard model with on-site (nearest-neighbor) repulsive interaction U (V) and nearest-neighbor hopping t using the density-matrix renormalization group technique. Based on the results of the excitation gaps, Luttinger-liquid exponents, and bond-order-wave (BOW) order parameter, we confirm that the BOW phase appears in a substantial region between the charge-density-wave (CDW) and spin-density-wave phases. Each phase boundary is determined by multiple means and it allows us to make a cross-check on the validity of our estimations. We also find that the BOW-CDW transition changes from continuous to first order at the tricritical point (U(t),V(t)) approximately (5.89 t,3.10 t) and the BOW phase shrinks to zero at the critical end point (U(c),V(c)) approximately (9.25 t,4.76 t).

Functional renormalization group analysis of the half-filled one-dimensional extended Hubbard model

We study the phase diagram of the half-filled one-dimensional extended Hubbard model at weak coupling using a novel functional renormalization group (FRG) approach. The FRG method includes in a systematic manner the effects of the scattering processes involving electrons away from the Fermi points. Our results confirm the existence of a finite region of bond charge density wave, also known as a "bond order wave" near U=2V and clarify why earlier g-ology calculations have not found this phase. We argue that this is an example in which formally irrelevant corrections change the topology of the phase diagram. Whenever marginal terms lead to an accidental symmetry, this generalized FRG method may be crucial to characterize the phase diagram accurately.

Dimerization in a half-filled one-dimensional extended hubbard model

We use a density-matrix renormalization group method to study quantitatively the phase diagram of a one-dimensional extended Hubbard model at half filling by investigating the correlation functions and structure factors. We confirmed the existence of a novel narrow region with long-range bond-order-wave order that was highly controversial recently between the charge-density-wave phase and Mott insulator phase. We determined accurately the position of the bicritical point U(b) approximately 7.2t, V(b) approximately 3.746t, which is quite different from previous studies.

Ground state phases of the half-filled one-dimensional extended hubbard model

Using quantum Monte Carlo simulations, results of a strong-coupling expansion, and Luttinger liquid theory, we determine quantitatively the ground state phase diagram of the one-dimensional extended Hubbard model with on-site and nearest-neighbor repulsions U and V. We show that spin frustration stabilizes a bond-ordered (dimerized) state for U approximately V/2 up to U/t approximately 9, where t is the nearest-neighbor hopping. The transition from the dimerized state to the staggered charge-density-wave state for large V/U is continuous for U < or approximately 5.5 and first order for higher U.