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Physical review. B, Condensed matter

Hubbard model on the infinite-dimensional diamond lattice

Giuseppe E. Santoro, Marco Airoldi, Sandro Sorella, Erio Tosatti

Published Jun 15, 1993• 17 citations
Publisher

Abstract

We present and study the infinite-dimensional limit of the Hubbard model on a class of non-nested bipartite lattices which generalize the two-dimensional honeycomb and three-dimensional diamond lattice, and are characterized by a semimetallic noninteracting density of states. The infinite-dimensional limit is studied by the well-known mapping onto a self-consistent one-impurity problem. This is solved using quantum Monte Carlo and second-order perturbation theory. The (U,T) phase diagram at half-filling shows a nonmagnetic semimetallic region and an antiferromagnetic insulating phase with a critical value of U for the transition at T=0 which is strictly positive, ${\mathit{U}}_{\mathit{c}}$/t\ensuremath{\approxeq}2.3, in contrast with the hypercubic lattice, where antiferromagnetic order sets in at ${\mathit{U}}_{\mathit{c}}$=0.

DOI
10.1103/physrevb.47.16216

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Europhysics Letters (EPL)•Nov 1, 1993•25 citations
We present and study the infinite-dimensional limit of the Hubbard model on a class of non-nested bipartite lattices which generalize the two-dimensional honeycomb and three-dimensional diamond lattice, and are characterized by a semimetallic noninteracting density of states. The infinite-dimensional limit is studied by the well-known mapping onto a self-consistent one-impurity problem. This is solved using quantum Monte Carlo and second-order perturbation theory. The (U,T) phase diagram at half-filling shows a nonmagnetic semimetallic region and an antiferromagnetic insulating phase with a critical value of U for the transition at T=0 which is strictly positive, Uc{\mathit{U}}_{\mathit{c}}Uc​/t\ensuremath{\approxeq}2.3, in contrast with the hypercubic lattice, where antiferromagnetic order sets in at Uc{\mathit{U}}_{\mathit{c}}Uc​=0.
We investigate the phase diagram of the extended Hubbard model on a half-filled honeycomb lattice through determinant quantum Monte Carlo simulations. At zero temperature, the repulsive Hubbard model undergoes a transition to an antiferromagnetic state only for sufficiently strong on-site coupling UUU. However, the inclusion of a repulsive extended interaction VVV between fermions in nearest-neighbor orbitals induces a charge-ordered phase. For attractive interactions, we also identify superconducting and phase-separated phases. We have determined a complete phase diagram with the aid of structure factors associated with various orderings, combined with measurements of double occupancy and the average sign of fermionic determinants. We have established that the semimetallic phase forms a zone from which ordered phases are excluded, preventing the stabilization of a superconducting phase with ddd-wave symmetry, i.e., only sss-wave pairing is allowed.
A detailed quantitative study of the physical properties of the infinite-dimensional Hubbard model at half filling is presented. The method makes use of an exact mapping onto a single-impurity model supplemented by a self-consistency condition. This coupled problem is solved numerically. Results for thermodynamic quantities (specific heat, entropy, . . .), one-particle spectral properties, and magnetic properties (response to a uniform magnetic field) are presented and discussed. The nature of the Mott-Hubbard metal-insulator transition found in this model is investigated. A numerical solution of the mean-field equations inside the antiferromagnetic phase is also reported.
We consider an efficient scheme to simulate fermionic Hubbard models with nonlocal density-density interactions in two dimensions, based on bond-centered auxiliary-field quantum Monte Carlo. The simulations are shown to be sign-problem-free within a finite, restricted parameter range. Using this approach, we first study the Hubbard model on the half-filled square lattice bilayer, including an interlayer repulsion term in addition to the local repulsion, and present the ground-state phase diagram within the accessible parameter region. Starting from the antiferromagnetically ordered state in the absence of interlayer repulsion, the interlayer interactions are found to destabilize the antiferromagnetic order, leading to a band insulator state. Moreover, for sufficiently strong interlayer tunneling, we also observe the emergence of a direct dimer product state of mixed D-Mott and S-Mott character along the equal coupling line. We discuss the stability range of this state within strong-coupling perturbation theory. Furthermore, we consider the Hubbard model on the honeycomb lattice with next-nearest-neighbor interactions. Such an interaction is found to enhance both charge density and spin-current correlations within the semimetallic region. However, inside the accessible parameter region, they do not stabilize long-ranged charge density wave order nor a quantum spin Hall state, and the only insulating state that we observe exhibits long-range antiferromagnetism.
Recent numerical work [Z. Y. Meng et al., Nature (London) 464, 847 (2010)] indicates the existence of a spin liquid (SL) phase that intervenes between the antiferromagnetic and semimetallic phases of the half filled Hubbard model on a honeycomb lattice. To better understand the nature of this exotic phase, we study the quantum J(1)-J(2) spin model on the honeycomb lattice, which provides an effective description of the Mott insulating region of the Hubbard model. Employing the variational Monte Carlo approach, we analyze the phase diagram of the model. We find three phases-antiferromagnetic, an unusual Z(2) SL state, and a dimerized state with spontaneously broken rotational symmetry. We identify the Z(2) SL state as the likely candidate for the SL phase of the Hubbard model.
The influence of local disorder on the thermodynamics of interacting electrons is studied within the infinite-dimensional disordered Hubbard model.Using a finite-temperature quantum Monte Carlo method, the averaged local moment and staggered susceptibility are calculated and the magnetic phase diagram at half-filling is constructed.From the averaged compressibility in the paramagnetic and antiferromagnetic phase we determine the metalinsulator transitions of the system.A rich transition scenario is revealed.Quite unexpectedly the disorder is found to stabilize the magnetic order in the strong-coupling limit.Randomness can significantly influence the low-temperature behaviour of interacting systems.In particular, it may lead to new phases which have no analogue in non-random systems [l].In the case of electrons, the simplest lattice model including both interactions and random potentials is the disordered Hubbard model.It is now known that even in the .mean-field.limit d + CQ [2,3] the Hubbard interaction remains dynamical [4] and leads to a highly non-trivial single-site problem with infinitely many coupled quantum degrees of freedom [5].This problem is, in fact, equivalent to an Anderson impurity model complemented by a self-consistency condition [6] and is thus amenable to numerical investigations [7] within a finite-temperature quantum Monte Carlo approach [81.In the absence of disorder this technique was already used by several groups to investigate the magnetic phase diagram [7,9], the Mott-Hubbard transition [lo, 1 1 1 and lately also superconductivity in a two-band version [12] of the Hubbard model in d = C Q ; thereby important new insight was gained.In this letter we wish to concentrate on the combined effect of disorder and interaction.We will study the effect of diagonal disorder on the low-temperature properties of the Hubbard model in d = CQ , in particular the competition between correlation-induced