Correlation length of the 1D Hubbard Model at half-filling : equal-time one-particle Green's function

A useful concept for finding numerically the dominant correlations of a given ground state in an interacting quantum lattice system in an unbiased way is the correlation density matrix. For two disjoint, separated clusters, it is defined to be the density matrix of their union minus the direct product of their individual density matrices and contains all correlations between the two clusters. We show how to extract from the correlation density matrix a general overview of the...

We present a numerical study of noise correlations, i.e., density-density correlations in momentum space, in the extended fermionic Hubbard model in one dimension. In experiments with ultracold atoms, these noise correlations can be extracted from time-of-flight images of the expanding cloud. Using the density-matrix renormalization group method to investigate the Hubbard model at various fillings and interactions, we confirm that the shot noise contains full information on t...

The Hubbard model represents the fundamental model for interacting quantum systems and electronic correlations. Using the two-dimensional half-filled Hubbard model at weak coupling as a testing ground, we perform a comparative study of a comprehensive set of state of the art quantum many-body methods. Upon cooling into its insulating antiferromagnetic ground-state, the model hosts a rich sequence of distinct physical regimes with crossovers between a high-temperature incohere...

We report on a non-perturbative approach to the 1D and 2D Hubbard models that is capable of recovering both strong and weak-coupling limits. We first show that even when the on-site Coulomb repulsion, U, is much smaller than the bandwith, the Mott-Hubbard gap never closes at half-filling in both 1D and 2D. Consequently, the Hubbard model at half-filling is always in the strong-coupling non-perturbative regime. For both large and small U, we find that the population of nearest...

We study quantum entanglement in one-dimensional correlated fermionic system. Our results show, for the first time, that entanglement can be used to identify quantum phase transitions in fermionic systems.

We explore the non-equilibrium dynamics of a one-dimensional Fermi-Hubbard system as a sensitive testbed for the capabilities of the time-dependent two-particle reduced density matrix (TD2RDM) theory to accurately describe time-dependent correlated systems. We follow the time evolution of the out-of-equilibrium finite-size Fermi-Hubbard model initialized by a quench over extended periods of time. By comparison with exact calculations for small systems and with matrix product ...

Optical lattice experiments with ultracold fermion atoms and quantum gas microscopy have recently realized direct measurements of magnetic correlations at the site-resolved level. We calculate the short-range spin correlation functions in the ground state of the two-dimensional repulsive Hubbard model with the auxiliary-field Quantum Monte Carlo (AFQMC) method. The results are numerically exact at half filling where the fermion sign problem is absent. Away from half-filling, ...

We examine the density-density correlation function in the Tomonaga-Luttinger liquid state for the one-dimensional extended Hubbard model with the on-site Coulomb repulsion $U$ and the intersite repulsion $V$ at quarter filling. By taking into account the effect of the marginally irrelevant umklapp scattering operator by utilizing the renormalization-group technique based on the bosonization method, we obtain the generalized analytical form of the correlation function. We sho...

We study a non-Hermitian generalization of strongly correlated quantum systems in which the transfer energy of electrons is asymmetric. It is known that a non-Hermitian critical point is equal to the inverse localization length of a Hermitian non-interacting random electron system. We here conjecture that we can obtain in the same way the correlation length of a Hermitian interacting non-random system. We confirm the conjecture using exact solutions and numerical finite-size ...

The one-dimensional Hubbard model at half-filling is studied in the framework of the Composite Operator Method using a static approximation. A solution characterized by strong antiferromagnetic correlations and a gap for any nonzero on-site interaction U is found. The corresponding ground-state energy, double occupancy and specific heat are in excellent agreement with those obtained within the Bethe Ansatz. These results show that the Composite Operator Method is an appropria...