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Bulletin of the American Physical Society

Entanglement properties of the antiferromagnetic-singlet transition in the two dimensional Hubbard model

Richard T. Scalettar, Chia‐Chen Chang, Rajiv R. P. Singh

Published Mar 5, 2014• 0 citations
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We calculate the bipartite R\'enyi entanglement entropy of an $L\ifmmode\times\else\texttimes\fi{}L\ifmmode\times\else\texttimes\fi{}2$ bilayer Hubbard model using a determinantal quantum Monte Carlo method recently proposed by Grover [Phys. Rev. Lett. 111, 130402 (2013)]. Two types of bipartition are studied: (i) one that divides the lattice into two $L\ifmmode\times\else\texttimes\fi{}L$ planes and (ii) one that divides the lattice into two equal-size ($L\ifmmode\times\else\texttimes\fi{}L/2\ifmmode\times\else\texttimes\fi{}2$) bilayers. We compare our calculations with those for the tight-binding model studied by the correlation matrix method. As expected, the entropy for bipartition (i) scales as ${L}^{2}$, while the latter scales with $L$ with possible logarithmic corrections. The onset of the antiferromagnet to singlet transition shows up by a saturation of the former to a maximal value and the latter to a small value in the singlet phase. We comment on the large uncertainties in the numerical results with increasing $U$, which would have to be overcome before the critical behavior and logarithmic corrections could be quantified.

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Using grand canonical quantum Monte Carlo (QMC) simulations combined with maximum entropy analytic continuation, as well as analytical methods, we examine the one- and two-particle dynamical properties of the Hubbard model on two coupled chains at half-filling. The one-particle spectral weight function, A(k,\ensuremath{\omega}), undergoes a qualitative change with interchain hopping ${\mathit{t}}_{\mathrm{\ensuremath{\perp}}}$ associated with a transition from a four-band insulator to a two-band insulator. A simple analytical model based on the propagation of exact rung singlet states gives a good description of the features at large ${\mathit{t}}_{\mathrm{\ensuremath{\perp}}}$. For smaller ${\mathit{t}}_{\mathrm{\ensuremath{\perp}}}$, A(k,\ensuremath{\omega}) is similar to that of the one-dimensional model, with a coherent band of width the effective antiferromagnetic exchange J which is reasonably well described by renormalized spin-wave theory. The coherent band rides on a broad background of width several times the parallel hopping integral t, an incoherent structure similar to that found in calculations on both the one- and two-dimensional models. We also present QMC results for the two-particle spin and charge excitation spectra, and relate their behavior to the rung singlet picture for large ${\mathit{t}}_{\mathrm{\ensuremath{\perp}}}$ and to the results of spin-wave theory for small ${\mathit{t}}_{\mathrm{\ensuremath{\perp}}}$. \textcopyright{} 1996 The American Physical Society.