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arXiv:1402.5622 · Physical Review B

Intermediate and spin-liquid phase of the half-filled honeycomb Hubbard model

Qiaoni Chen, George H. Booth, Sandeep Sharma, Gerald Knizia, Garnet Kin‐Lic Chan

Published Apr 28, 2014• 63 citations
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Abstract

We obtain the phase diagram of the half-filled honeycomb Hubbard model with density matrix embedding theory, to address recent controversy at intermediate couplings. We use clusters from 2--12 sites and lattices at the thermodynamic limit. We identify a paramagnetic insulating state, with possible hexagonal cluster order, competitive with the antiferromagnetic phase at intermediate coupling. However, its stability is strongly cluster and lattice size dependent, explaining controversies in earlier work. Our results support the paramagnetic insulator as being a metastable, rather than a true, intermediate phase, in the thermodynamic limit.

DOI
10.1103/physrevb.89.165134

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Motivated by the recent discovery of a spin-liquid phase for the Hubbard model on the honeycomb lattice at half-filling (Meng et al 2010 Nature 88 487), we apply both perturbative and non-perturbative techniques to derive effective spin Hamiltonians describing the low-energy physics of the Mott-insulating phase of the system. Exact diagonalizations of the so-derived models on small clusters are performed, in order to assess the quality of the effective low-energy theory in the spin-liquid regime. We show that six-spin interactions on the elementary loop of the honeycomb lattice are the dominant sub-leading effective couplings. A minimal spin model is shown to reproduce most of the energetic properties of the Hubbard model on the honeycomb lattice in its spin-liquid phase. Surprisingly, a more elaborate effective low-energy spin model obtained by a systematic graph expansion rather disagrees beyond a certain point with the numerical results for the Hubbard model at intermediate couplings.
Abstract. Motivated by the recent discovery of a spin liquid phase for the Hubbard model on the honeycomb lattice at half-filling [11], we apply both perturbative and non-perturbative techniques to derive effective spin Hamiltonians describing the low-energy physics of the Mott-insulating phase of the system. Exact diagonalizations of the so-derived models on small clusters are performed, in order to assess the quality of the effective low-energy theory in the spin-liquid regime. We show that six-spin interactions on the elementary loop of the honeycomb lattice are the dominant sub-leading effective couplings. A minimal spin model is shown to reproduce most of the energetic properties of the Hubbard model on the honeycomb lattice in its spin-liquid phase. Surprisingly, a more elaborate effective low-energy spin model obtained by a systematic graph expansion rather disagrees beyond a certain point with the numerical results for the Hubbard model at intermediate couplings.
We report the cluster dynamical mean field theory calculations performed for the ground state of the half filled Hubbard model on a honeycomb lattice with exact diagonalization on the cluster-impurity solver. Through using elaborate numerical analytic continuation, we identify the existence of a ``spin liquid'' from the on-site interaction U=0U=0U=0 to Uc{U}_{c}Uc​ (between 4.6t4.6t4.6t and 4.85t4.85t4.85t) with a smooth crossover correspondingly from the charge fluctuation dominating phase into the charge correlation dominating phase. The semimetallic state exits only at U=0U=0U=0. We further find that the magnetic phase transition at Uc{U}_{c}Uc​ from the spin liquid to the N\'eel antiferromagnetic Mott insulating phase is a first-order quantum phase transition. We also show that the charge fluctuation plays a substantial role on keeping the spin liquid phase against the emergence of a magnetic order.
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 Hubbard model encapsulates the physics of strongly correlated quantum systems in its most basic form. It has been studied intensively in the context of the high-temperature superconductivity. A number of novel phases were recently proposed for Hubbard-like models on the honeycomb lattice, the structure of graphene. We analyzed the Hubbard model of spin- 12\frac{1}{2}21​ fermions on the honeycomb lattice at half-filling using large-scale quantum Monte Carlo simulations. We find that the weak coupling semimetal and the antiferromagnetic Mott insulator at strong interaction are separated by an extended gapped phase in an intermediate coupling regime. Exploring excitation gaps, various correlation functions as well as probing for flux quantization, we conclude that a quantum spin liquid, lacking any conventional order, emerges with local charge and spin correlations, best described by a resonating valence bonds state.
We investigate the quantum phase transitions in the half-filled Hubbard model on the triangular lattice by means of the path-integral renormalization group method with a new iteration and truncation scheme proposed recently. It is found for a cluster of 36 sites that as the Hubbard interaction U increases, the paramagnetic metallic state undergoes a first-order phase transition to a nonmagnetic insulating (NMI) state at Uc1 approximately 7.4t, which is followed by another first-order transition to a 120 degrees Néel ordered state at Uc2 approximately 9.2t, where t is the transfer integral. The size dependence of the results is also addressed. Our results suggest the existence of the intermediate NMI phase and resolve some controversial arguments on the nature of the previously proposed quantum phase transitions.