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Bulletin of the American Physical Society

Block-block entanglement and quantum phase transition in the one-dimensional extended Hubbard model at 1/2-filling

Shusa Deng, Shi-Jian Gu, Hai‐Qing Lin

Published Mar 21, 2005• 0 citations
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Block-block entanglement and quantum phase transitions in the one-dimensional extended Hubbard model

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In this paper, we study block-block entanglement in the ground state of a one-dimensional extended Hubbard model. Our results show that the phase diagram derived from the block-block entanglement manifests a richer structure than that of the local (single-site) entanglement because it comprises nonlocal correlation. Besides phases characterized by the charge-density wave, the spin-density wave, and phase separation, which can be sketched out by the local entanglement, singlet superconductivity phase could be identified on the contour map of the block-block entanglement if the block size is larger than 1. Scaling analysis shows that ${\mathrm{log}}_{2}(l)$ behavior of the block-block entanglement may exist in both the noncritical and critical regions, while some local extremum are induced by the finite-size effect. We also study the block-block entanglement defined in the momentum space and discuss its relation to the phase transition from singlet superconducting state to the charge-density-wave state.

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Existence of Bond-Order-Wave Phase in One-Dimensional Extended Hubbard Model

Guanghua Liu, Chun‐Hai Wang

By using the density matrix renormalization group technique, the phase diagram of the half-filling extended Hubbard model is investigated. The conventional order parameter, the two-site entanglement entropy, and the block-block entanglement entropy are analyzed in detail. According to the numerical results, in the weak coupling region, an intermediate bond-order-wave (BOW) phase is shown to exist indeed between the charge-density-wave (CDW) and the spin-density-wave (SDW) phases. The critical phase transition points are determined by the singularity of the first order derivative of two-site entanglement entropy. In strong coupling region, a direct phase transition occurs from SDW phase to CDW phase, and shows discontinuous (first order) character accompanied with energy level crossing. The numerical results support the phase diagram proposed previously by some authors Sengupta et al., (2002); Sandvik et al., (2004); Zhang, (2004). Therefore, the quantum entanglement is a sensitive tool to describe quantum phase transitions in strongly correlated electron systems.

Communications in Theoretical Physics•Apr 1, 2011•5 citations
In this paper, we study block-block entanglement in the ground state of a one-dimensional extended Hubbard model. Our results show that the phase diagram derived from the block-block entanglement manifests a richer structure than that of the local (single-site) entanglement because it comprises nonlocal correlation. Besides phases characterized by the charge-density wave, the spin-density wave, and phase separation, which can be sketched out by the local entanglement, singlet superconductivity phase could be identified on the contour map of the block-block entanglement if the block size is larger than 1. Scaling analysis shows that log2(l){\mathrm{log}}_{2}(l)log2​(l) behavior of the block-block entanglement may exist in both the noncritical and critical regions, while some local extremum are induced by the finite-size effect. We also study the block-block entanglement defined in the momentum space and discuss its relation to the phase transition from singlet superconducting state to the charge-density-wave state.
By using the density matrix renormalization group technique, the phase diagram of the half-filling extended Hubbard model is investigated. The conventional order parameter, the two-site entanglement entropy, and the block-block entanglement entropy are analyzed in detail. According to the numerical results, in the weak coupling region, an intermediate bond-order-wave (BOW) phase is shown to exist indeed between the charge-density-wave (CDW) and the spin-density-wave (SDW) phases. The critical phase transition points are determined by the singularity of the first order derivative of two-site entanglement entropy. In strong coupling region, a direct phase transition occurs from SDW phase to CDW phase, and shows discontinuous (first order) character accompanied with energy level crossing. The numerical results support the phase diagram proposed previously by some authors Sengupta et al., (2002); Sandvik et al., (2004); Zhang, (2004). Therefore, the quantum entanglement is a sensitive tool to describe quantum phase transitions in strongly correlated electron systems.