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Physical Review B

Quantum coherence and decoherence of correlated electron states in the one-dimensional charge-density-wave–spin-density-wave phase transition

Norikazu Tomita

Published Mar 10, 2006• 3 citations
Publisher

Abstract

The charge-density-wave (CDW)--spin-density-wave (SDW) phase transition of the one-dimensional extended Hubbard model is investigated in the strong correlation regime, from the viewpoint of the quantum coherence or decoherence of the two correlated states. In the finite-size system, the CDW wave function, near the phase boundary, has the significant quantum fluctuations due to the SDW domains. The superposition of these SDW domains leads to the quantum coherence between the CDW and SDW wave functions. However, the scaling analysis shows that the density of the SDW fluctuations becomes asymptotically zero in the infinite-size limit, which indicates the decoherence of the two states in the bulk phase transition.

DOI
10.1103/physrevb.73.115105

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Journal of the Physical Society of Japan•Jan 15, 1996•22 citations
The charge-density-wave (CDW)--spin-density-wave (SDW) phase transition of the one-dimensional extended Hubbard model is investigated in the strong correlation regime, from the viewpoint of the quantum coherence or decoherence of the two correlated states. In the finite-size system, the CDW wave function, near the phase boundary, has the significant quantum fluctuations due to the SDW domains. The superposition of these SDW domains leads to the quantum coherence between the CDW and SDW wave functions. However, the scaling analysis shows that the density of the SDW fluctuations becomes asymptotically zero in the infinite-size limit, which indicates the decoherence of the two states in the bulk phase transition.
Quantum antiferromagnetic (AF) fluctuations that promote the charge-density-wave (CDW)-AF state phase transition in the one-dimensional (1D) extended Hubbard model are clarified for the strong correlation regime. It is clearly shown that the CDW wave function contains quantum fluctuations due to the AF domains near the phase boundary. Though the size of these AF domains stays finite, its density to the system size becomes asymptotically zero in the infinite-size limit. This indicates the quantum decoherence, or the first order phase transition between the CDW and AF state. On the other hand, the survived AF domains would naturally evolve into the quantum nucleation that triggers the CDW-AF state phase transition.
The phase transition between charge- and spin-density-wave (CDW, SDW) phases is studied in the one-dimensional extended Hubbard model at half-filling. We discuss whether the transition can be described by the Gaussian and the spin-gap transitions under charge-spin separation, or by a direct CDW-SDW transition. We determine these phase boundaries by level crossings of excitation spectra which are identified according to discrete symmetries of wave functions. We conclude that the Gaussian and the spin-gap transitions take place separately from weak- to intermediate-coupling region. This means that the third phase exists between the CDW and the SDW states. Our results are also consistent with those of the strong-coupling perturbative expansion and of the direct evaluation of order parameters.
It has been well established that in both the weak- and strong-coupling limits, the phase transition from a spin-density wave (SDW) to a charge-density wave (CDW) in the half-filled extended-Hubbard model occurs precisely at the ratio U/Vc=2,{U/V}_{c}=2,U/Vc​=2, where U and V are the on-site and intersite electron-electron interactions, respectively. However, a recent density-matrix renormalization group (DMRG) study and a previous Monte Carlo simulation jointly suggest a picture that challenges the well-established weak-coupling result. Here, a careful calculation shows such a picture is questionable. In particular, it clarifies the DMRG result, even with a moderate number of states kept in the density matrix, agrees with both the weak- and strong-coupling findings, and predicts a CDW/SDW phase boundary smoothly links those two coupling limits. Possible sources of these previous failures are discussed.
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.
We theoretically investigate how the photoexcited states change across the phase boundary between the charge density wave (CDW) and the spin density wave (SDW) states in the one-dimensional (1D) and the two-dimensional (2D) Pariser–Parr–Pople models in the strong interaction case. In the 1D case, the CDW (singlet spin pair) droplet states dominate light absorption spectrum in the SDW (CDW) ground state region near the phase boundary. These photoexcited states exhibit crossover behavior across the phase boundary, that is, the density of the CDW region gradually increases across the phase boundary from the SDW to the CDW ground state region. On the contrary, in the 2D case, the bound holon–doublon (singlet spin) pair state dominates the light absorption spectrum, and the quantum fluctuations of the CDW or the singlet spin pair domain are negligible in the dominant photoexcited state even near the phase boundary. As a result, the transition occurs in the dominant photoexcited state at the ground state phase boundary.
We study the SDW-CDW phase transition in the one dimensional extended Hubbard model at a half-filling. A scaling analysis using the resonating Hartree-Fock method with the numbers of electrons from 8 to 20 strongly suggests that the ground state is many-fold degenerate( 1 A 1 + , 1 B 1 + , 3 A 2 - , and 3 B 2 - states) in the SDW region while it is doubly degenerate( 1 A 1 + and 1 B 2 - states) in the CDW region. Only the 1 A 1 + state makes a continuous phase transition from the SDW state to the CDW one. The 1 B 1 + , 3 A 2 - , and 3 B 2 - states cross the 1 B 2 - state around the phase boundary. We show that the continuous phase transition in the 1 A 1 + state is brought about by defects connecting the SDW-CDW domains called halfons. The correlation structures of these states are shown to clarify the origin of the degeneracies of the ground states.