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arXiv:cond-mat/0406074 · Physical Review B

Phase diagram of the half-filled two-dimensional SU ( N ) Hubbard-Heisenberg model: A quantum Monte Carlo study

Fakher F. Assaad

Published Feb 4, 2005• 139 citations
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Abstract

We investigate the phase diagram of the half-filled $\mathrm{SU}(N)$ Hubbard-Heisenberg model with hopping $t$, exchange $J$, and Hubbard $U$, on a two-dimensional square lattice. In the large-$N$ limit, and as a function of decreasing values of $t∕J$, the model shows a transition from a $d$-density wave state to a spin dimerized insulator. A similar behavior is observed at $N=6$ whereas at $N=2$ a spin density wave insulating ground state is stabilized. The $N=4$ model, has a $d$-density wave ground state at large values of $t∕J$ which as a function of decreasing values of $t∕J$ becomes unstable to an insulating state with no apparent lattice and spin broken symmetries. In this state, the staggered spin-spin correlations decay as a power law, resulting in gapless spin excitations at $\stackrel{P\vec}{q}=(\ensuremath{\pi},\ensuremath{\pi})$. Furthermore, low lying spin modes with small spectral weight are apparent around the wave vectors $\stackrel{P\vec}{q}=(0,\ensuremath{\pi})$ and $\stackrel{P\vec}{q}=(\ensuremath{\pi},0)$. This gapless spin liquid state is equally found in the SU(4) Heisenberg $(U∕t\ensuremath{\rightarrow}\ensuremath{\infty})$ model in the self-adjoint antisymmetric representation. An interpretation of this state in terms of a $\ensuremath{\pi}$-flux phase is offered. Our results stem from projective $(T=0)$ quantum Monte Carlo simulations on lattice sizes ranging up to $24\ifmmode\times\else\texttimes\fi{}24$.

DOI
10.1103/physrevb.71.075103

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We investigate the phase diagram of the half-filled SU(N)\mathrm{SU}(N)SU(N) Hubbard-Heisenberg model with hopping ttt, exchange JJJ, and Hubbard UUU, on a two-dimensional square lattice. In the large-NNN limit, and as a function of decreasing values of t∕Jt∕Jt∕J, the model shows a transition from a ddd-density wave state to a spin dimerized insulator. A similar behavior is observed at N=6N=6N=6 whereas at N=2N=2N=2 a spin density wave insulating ground state is stabilized. The N=4N=4N=4 model, has a ddd-density wave ground state at large values of t∕Jt∕Jt∕J which as a function of decreasing values of t∕Jt∕Jt∕J becomes unstable to an insulating state with no apparent lattice and spin broken symmetries. In this state, the staggered spin-spin correlations decay as a power law, resulting in gapless spin excitations at \stackrel{P\vec}{q}=(\ensuremath{\pi},\ensuremath{\pi}). Furthermore, low lying spin modes with small spectral weight are apparent around the wave vectors \stackrel{P\vec}{q}=(0,\ensuremath{\pi}) and \stackrel{P\vec}{q}=(\ensuremath{\pi},0). This gapless spin liquid state is equally found in the SU(4) Heisenberg (U∕t\ensuremath→\ensuremath∞)(U∕t\ensuremath{\rightarrow}\ensuremath{\infty})(U∕t\ensuremath→\ensuremath∞) model in the self-adjoint antisymmetric representation. An interpretation of this state in terms of a \ensuremathπ\ensuremath{\pi}\ensuremathπ-flux phase is offered. Our results stem from projective (T=0)(T=0)(T=0) quantum Monte Carlo simulations on lattice sizes ranging up to 24\ifmmode×\else\texttimes\fi2424\ifmmode\times\else\texttimes\fi{}2424\ifmmode×\else\texttimes\fi24.
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