Two-dimensional Hubbard Model Research Articles

Antiferromagnetic pseudogap in the two-dimensional Hubbard model deep in the renormalized classical regime

Antiferromagnetic pseudogap in the two-dimensional Hubbard model deep in the renormalized classical regime

Origin and fate of the pseudogap in the doped Hubbard model

The relationship between the pseudogap and underlying ground-state phases has not yet been rigorously established. We investigated the doped two-dimensional Hubbard model at finite temperature using controlled diagrammatic Monte Carlo calculations, allowing for the computation of spectral properties in the infinite-size limit and with arbitrary momentum resolution. We found three distinct regimes as a function of doping and interaction strength: a weakly correlated metal, a correlated metal with strong interaction effects, and a pseudogap regime at low doping. We show that the pseudogap forms both at weak coupling, when the magnetic correlation length is large, and at strong coupling, when it is shorter. As the temperature goes to zero, the pseudogap regime extrapolates precisely to the ordered stripe phase found by ground-state methods.

Systematic large flavor fTWA approach to interaction quenches in the Hubbard model

Abstract We study the nonequilibrium dynamics after an interaction quench in the two-dimensional Hubbard model using the recently introduced fermionic truncated Wigner approximation (fTWA). To assess the range of validity of the method in a systematic way, we consider the SU(N) Hubbard model with the fermion degeneracy N as a natural semiclassical expansion parameter. Using both a numerical and a perturbative analytical approach we show that fTWA is exact at least up to and including the prethermalization dynamics. We discuss the limitations of the method beyond this regime.

Antiferromagnetic and spin spiral correlations in the doped two-dimensional Hubbard model: Gauge symmetry, Ward identities, and dynamical mean-field theory analysis

Antiferromagnetic and spin spiral correlations in the doped two-dimensional Hubbard model: Gauge symmetry, Ward identities, and dynamical mean-field theory analysis

Spiral to stripe transition in the two-dimensional Hubbard model

We obtain an almost complete understanding of the mean-field phase diagram of the two-dimensional Hubbard model on a square lattice with a sizable next-nearest-neighbor hopping and a moderate interaction strength. In particular, we clarify the nature of the transition region between the spiral and the stripe phase. Complementing previous [] real-space Hartree-Fock calculations on large finite lattices, we solve the mean-field equations for coplanar unidirectional magnetic order directly in the thermodynamic limit, and we determine the nature of the magnetic states right below the mean-field critical temperature T* by a Landau free-energy analysis. While the magnetic order for filling factors n≥1 is always of Néel type, for n≤1 the following sequence of magnetic states is found as a function of increasing hole-doping: Néel, planar circular spiral, multispiral, and collinear spin-charge stripe states. Multispiral states are superpositions of several spirals with distinct wave vectors, and lead to concomitant charge order. We finally point out that nematic and charge orders inherited from the magnetic order can survive even in the presence of fluctuations, and we present a corresponding qualitative phase diagram. Published by the American Physical Society 2024

Auxiliary field Quantum Monte Carlo for dilute neutrons on the lattice.

We employ constrained path Auxiliary Field Quantum Monte Carlo (AFQMC) in the pursuit of studying physical nuclear systems using a lattice formalism. Since AFQMC has been widely used in the study of condensed-matter systems such as the Hubbard model, we benchmark our method against published results for both one- and two-dimensional Hubbard model calculations. We then turn our attention to cold atomic and nuclear systems. We use an onsite contact interaction that can be tuned in order to reproduce the known scattering length and effective range of a given interaction. Developing this machinery allows us to extend our calculations to study nuclear systems within a lattice formalism. We perform initial calculations for a range of nuclear systems from two- to few-body neutron systems. This article is part of the theme issue 'The liminal position of Nuclear Physics: from hadrons to neutron stars'.

The interplay between a pseudogap and superconductivity in a two-dimensional Hubbard model

Strongly correlated electrons systems may exhibit a variety of interesting phenomena, for instance, superconductivity and pseudogap, as is the case of cuprates and pnictides. In strongly correlated electron systems, it is considered essential to understand, not only the nature of the pseudogap, but also the relationship between superconductivity and the pseudogap. In order to address this question, in the present work, we investigated a one-band Hubbard model treated by the Green's function method within an n-pole approximation. In the strongly correlated regime, antiferromagnetic correlations give rise to nearly flat band regions in the nodal points of the quasiparticle bands. As a consequence, a pseudogap emerges at the antinodal points of the Fermi surface. The obtained results indicate that the same antiferromagnetic correlations responsible for a pseudogap, can also favor superconductivity, providing an increase in the superconducting critical temperature Tc.

Local and Nonlocal Electronic Correlations at the Metal-Insulator Transition in the Two-Dimensional Hubbard Model.

Elucidating the physics of the single-orbital Hubbard model in its intermediate-coupling regime is a key missing ingredient to our understanding of metal-insulator transitions in real materials. Using recent nonperturbative many-body techniques that are able to interpolate between the spin-fluctuation-dominated Slater regime at weak coupling and the Mott insulator at strong coupling, we obtain the momentum-resolved spectral function in the intermediate regime and disentangle the effects of antiferromagnetic fluctuations and local electronic correlations in the formation of an insulating state. This allows us to identify the Slater and Heisenberg regimes in the phase diagram, which are separated by a crossover region of competing spatial and local electronic correlations. We identify the crossover regime by investigating the behavior of the local magnetic moment, shedding light on the formation of the insulating state at intermediate couplings.

Selected Nonorthogonal Configuration Interaction with Compressed Single and Double Excitations.

Addressing both dynamic and static correlations accurately is a primary goal in electronic structure theory. Nonorthogonal configuration interaction (NOCI) is a versatile tool for treating static correlation, offering chemical insights by combining diverse reference states. Nevertheless, achieving quantitative accuracy requires the inclusion of the missing dynamic correlation. This work introduces a framework for compressing orthogonal single and double excitations into a NOCI of a much smaller dimension. This compression is repeated with each Slater determinant in a reference NOCI, resulting in another NOCI that includes all of its single and double excitations (NOCISD), effectively recovering the missing dynamic correlations from the reference. This compressed NOCISD is further refined through a selection process using metric and energy tests (SNOCISD). We validate the effectiveness of SNOCISD through its application to the dissociation of the nitrogen molecule and the hole-doped two-dimensional Hubbard model at various interaction strengths.

Coexistence of superconductivity with partially filled stripes in the Hubbard model

The Hubbard model is an iconic model in quantum many-body physics and has been intensely studied, especially since the discovery of high-temperature cuprate superconductors. Combining the complementary capabilities of two computational methods, we found superconductivity in both the electron- and hole-doped regimes of the two-dimensional Hubbard model with next-nearest-neighbor hopping. In the electron-doped regime, superconductivity was weaker and was accompanied by antiferromagnetic Néel correlations at low doping. The strong superconductivity on the hole-doped side coexisted with stripe order, which persisted into the overdoped region with weaker hole-density modulation. These stripe orders varied in fillings between 0.6 and 0.8. Our results suggest the applicability of the Hubbard model with next-nearest hopping for describing cuprate high–transition temperature ( T c ) superconductivity.

Excitonic enhancement of cavity-mediated interactions in a two-band Hubbard model

We study cavity-mediated interactions that are generated in a two-dimensional two-band Hubbard model coupled to an optical cavity, when it is driven in-gap by a strong laser. Starting from a Floquet description of the driven system, we derive effective low-energy Hamiltonians by projecting out the high-energy degrees of freedom and treating intrinsic interactions on a mean-field level. We then investigate how the emergence of high-energy Frenkel excitons from the electronic interband coupling, which form near the upper electronic band, affects the interactions as well as the laser-induced Floquet renormalization of the electronic band structure. Cavity-mediated interactions are enhanced strongly when the light couples to an excitonic transition. Additionally, the interaction as well as the Floquet renormalization are strongly broadened in reciprocal space, which could further boost the impact of cavity-mediated interactions on the driven-dissipative steady state. Published by the American Physical Society 2024

Automatic order detection and restoration through systematically improvable variational wave functions

Variational wave function are an invaluable tool to study the properties of strongly correlated systems. We propose such a wave function, based on the theory of auxiliary fields and combining aspects of auxiliary-field quantum Monte Carlo and modern variational optimization techniques including automatic differentiation. The resulting , consisting of several slices of optimized projectors, is highly expressive and systematically improvable. We benchmark this form on the two-dimensional Hubbard model, using both cylindrical and large, fully periodic supercells. The computed ground-state energies are competitive with the best variational results. Moreover, the optimized wave functions predict the correct ground-state order with near full symmetry restoration (i.e., translation invariance) despite initial states with incorrect orders. The can become a tool for local order prediction, leading to a new paradigm for variational studies of bulk systems. It can also be viewed as an approach to produce accurate and systematically improvable wave functions in a convenient form of nonorthogonal Slater determinants (e.g., for quantum chemistry) at polynomial computational cost. Published by the American Physical Society 2024

Dc conductivity of two-dimensional ionic Hubbard model extracted by analytic continuation

The ionic Hubbard model in a two-dimensional square lattice is revisited using determinant quantum Monte Carlo (DQMC) and numerical analytic continuation. From the dc conductivity extracted by stochastic maximum entropy of the DQMC data, we find that the band insulator induced by a staggered potential [Formula: see text] goes through a metallic phase before entering a Mott insulator as the on-site Hubbard interaction U is increased. Moreover, we map out the phase diagram in the [Formula: see text] plane, and reveal a smaller metallic region than that found in the previous studies. Our results provide a more exact location of the phase boundaries, and are an important complement to those obtained by an approximate approach.

Quasi-particle functional renormalisation group calculations in the two-dimensional t-t'-Hubbard model

We extend and apply a recently introduced quasi-particle functional renormalisation group scheme to the two-dimensional Hubbard model with next-nearest-neighbour hopping and away from half filling. We confirm the generation of superconducting correlations in some regions of the phase diagram, but also find that the inclusion of self-energy feedback by means of a decreasing quasi-particle weight can suppress superconducting tendencies more than anti-ferromagnetic correlations by which they are generated. As a supplement, we provide sample results for the self-energy in second-order perturbation theory and address some conceptual matters.

Two-dimensional extended Hubbard model: doping, next-nearest neighbor hopping and phase diagrams

Using the strong coupling diagram technique, we investigate the extended Hubbard model on a two-dimensional square lattice. This approach allows for charge and spin fluctuations and a short-range antiferromagnetic order at nonzero temperatures. The model features the first-order phase transition to states with alternating site occupations (SAO) at the intersite repulsion v = v c . In this work, we show that doping decreases v c . For a nonzero next-nearest neighbor hopping , less mobile carriers produce a stronger fall in v c . For half-filling and , we consider phase diagrams for a fixed temperature T, on-site U, and intersite repulsions. The diagrams contain regions of SAO, Mott insulator, and several metallic states distinguished by their densities of states. Two of them are characterized by a dip and a peak at the Fermi level. The dip originates from the Slater mechanism for itinerant electrons, while the peak to bound states of electrons with localized magnetic moments. The existence of these two metallic regions in the phase diagram is a manifestation of the Pomeranchuk effect. The boundary between these regions reveals itself as a kink in the curve v c (T) and as a maximum in the T dependence of the double occupancy D. Our calculated D for different values of v, U, and T are in semiquantitative agreement with Monte Carlo results.

Thermoelectric effect on diffusion in the two-dimensional Hubbard model

Thermoelectric effect on diffusion in the two-dimensional Hubbard model

Slow semiclassical dynamics of a two-dimensional Hubbard model in disorder-free potentials

Slow semiclassical dynamics of a two-dimensional Hubbard model in disorder-free potentials

Gaussian variational method to Fermi-Hubbard model in one and two dimensions

The study of ground-state properties of the Fermi-Hubbard model is a long-lasting task in the research of strongly correlated systems, and is crucial for the understanding of notable quantum phenomena including superconductivity and magnetism. Owing to the exponentially growing complexity of the system, a quantitative analysis usually demands high computational cost and is restricted to small samples, especially in two or higher dimensions. Here, we introduce a variational method in the frame of fermionic Gaussian states, and obtain the ground states of one- and two-dimensional attractive Hubbard models via imaginary-time evolution. We calculate the total energy and benchmark the results in a wide range of interaction strength and filling factor with those obtained via exact two-body results, the density matrix renormalization group based on matrix product states (MPS), and projector Quantum Monte Carlo (QMC) method. For both 1D and 2D cases, the Gaussian variational method presents accurate results for total energy with a maximum systematic error in the intermediate interaction region. The accuracy of these results has negligible dependence on the system size. We further calculate the double occupancy and find excellent agreement with MPS and QMC, as well as the experimental results of cold quantum gases in optical lattices. The results suggest that the Gaussian pairing state is a good approximation to the ground states of attractive Hubbard model, in particular in the strong and weak coupling limits. Moreover, we generalize the method to the attractive Hubbard model with a finite spin-polarization, which can be mapped to the repulsive interaction case via particle-hole transformation, and obtain accurate results of ground state energy and double occupancy. Our work demonstrates the ability of the Gaussian variational method to extract ground state properties of strongly correlated many-body systems with negligible computational cost, especially of large size and in higher dimensions.

Superconductivity in the two-dimensional Hubbard model with cellular dynamical mean-field theory: A quantum impurity model analysis

Superconductivity in the two-dimensional Hubbard model with cellular dynamical mean-field theory: A quantum impurity model analysis

Comprehensive mean-field analysis of magnetic and charge orders in the two-dimensional Hubbard model

Comprehensive mean-field analysis of magnetic and charge orders in the two-dimensional Hubbard model