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arXiv:cond-mat/0701134 · Physical Review B

SU(2) gauge theory of the Hubbard model and application to the honeycomb lattice

Michael Hermele

Published Jul 31, 2007• 85 citations
arXivHTMLPDF

Abstract

Motivated by recent experiments on the triangular lattice Mott-Hubbard system $\ensuremath{\kappa}\text{\ensuremath{-}}{(\mathrm{BEDT}\text{\ensuremath{-}}\mathrm{TTF})}_{2}{\mathrm{Cu}}_{2}{(\mathrm{C}\mathrm{N})}_{3}$, we develop a general formalism to investigate quantum spin liquid insulators adjacent to the Mott transition in Hubbard models. This formalism, dubbed the SU(2) slave-rotor formulation, is an extension of the SU(2) gauge theory of the Heisenberg model to the case of the Hubbard model. Furthermore, we propose the honeycomb lattice Hubbard model (at half filling) as a candidate for a spin liquid ground state near the Mott transition; this is an appealing possibility, as this model can be studied via quantum Monte Carlo simulation without a sign problem. The pseudospin symmetry of Hubbard models on bipartite lattices turns out to play a crucial role in our analysis, and we develop our formalism primarily for the case of a bipartite lattice. We also sketch its development for a general Hubbard model. We develop a mean-field theory to describe spin liquids and some competing states, and apply it to the honeycomb lattice. On the insulating side of the Mott transition, we find an SU(2) algebraic spin liquid (ASL), described by gapless $S=1∕2$ Dirac fermions (spinons) coupled to a fluctuating SU(2) gauge field. This result contrasts with that obtained via a U(1) slave-rotor approach, which instead found a U(1) ASL. That formulation does not respect the pseudospin symmetry, and is therefore not correct on the honeycomb lattice. We construct a low-energy effective theory describing the ASL phase, the conducting semimetal phase and the Mott transition between them. This physics can be detected in numerical simulations via the simultaneous presence of substantial antiferromagnetic and valence-bond solid correlations. In the SU(2) ASL, these observables have slowly decaying fluctuations in space and time, described by power laws with the same critical exponent. We recover the results of the U(1) slave-rotor formulation in the presence of a strong breaking of pseudospin symmetry. Our analysis suggests that both a third-neighbor electron hopping, and/or pseudospin-breaking terms such as a nearest-neighbor density interaction, may help to stabilize a spin liquid phase.

DOI
10.1103/physrevb.76.035125

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We study how to incorporate Mott physics in the BCS-type superconductor, motivated by the fact that high Tc{T}_{c}Tc​ superconductivity results from a Mott insulator via hole doping. The U(1) slave-rotor representation was proposed to take local-density fluctuations into account nonperturbatively, describing the Mott-Hubbard transition at half filling. Since this decomposition cannot control local pairing fluctuations, the U(1) slave-rotor representation does not give a satisfactory treatment for charge fluctuations. Extending the U(1) slave-rotor representation, we introduce an SU(2) slave-rotor representation to allow not only local-density fluctuations but also local pairing excitations. We find an SU(2) slave-rotor gauge theory of the Hubbard model in terms of two kinds of collective boson excitations associated with density and pairing fluctuations that interact with gapless fermion excitations via SU(2) gauge fluctuations. An interesting observation in this effective description is that phase fluctuations of fermion pairs arise as SU(2) gauge fluctuations. Thus, fermion-pairing excitations can be controlled by the dynamics of collective bosons in the SU(2) slave-rotor gauge theory. Performing the standard saddle-point analysis based on the SU(2) slave-rotor action, we find an interesting phase described by partial freezing of charge fluctuations near the Mott-Hubbard critical point, where local-density-fluctuation modes are condensed but local pair-excitation modes are gapped. Partial freezing of charge fluctuations causes fermion pairing to be incoherent as a result of reconciliation of superconductivity and Mott physics. The nature of this nonsuperconducting phase is identified with an anomalous metal due to the presence of incoherent pairing.
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Theory of Dirac Spin-Orbital Liquids: monopoles, anomalies, and applications to SU(4)SU(4)SU(4) honeycomb models
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