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arXiv:0705.1611 · Physical Review B

Bosonization study of quantum phase transitions in the one-dimensional asymmetric Hubbard model

Z. G. Wang, Yong-Gui Chen, S. J. Gu

Published Apr 17, 2007• 19 citations
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Abstract

The quantum phase transitions in the one-dimensional asymmetric Hubbard model are investigated with the bosonization approach. The conditions for the phase transition from density wave to phase separation, the correlation functions, and their exponents are obtained analytically. Our results show that the difference between the hopping integrals for up- and down-spin electrons is crucial for the occurrence of the phase separation. When the difference is large enough, the phase separation will appear even if the on-site interaction is small.

DOI
10.1103/physrevb.75.165111

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The quantum phase transitions in the one-dimensional asymmetric Hubbard model are investigated with the bosonization approach. The conditions for the phase transition from density wave to phase separation, the correlation functions, and their exponents are obtained analytically. Our results show that the difference between the hopping integrals for up- and down-spin electrons is crucial for the occurrence of the phase separation. When the difference is large enough, the phase separation will appear even if the on-site interaction is small.
We address some open questions regarding the phase diagram of the one-dimensional Hubbard model with asymmetric hopping coefficients and balanced species. In the attractive regime we present a numerical study of the passage from on-site pairing dominant correlations at small asymmetries to charge-density waves in the region with markedly different hopping coefficients. In the repulsive regime we exploit two analytical treatments in the strong- and weak-coupling regimes in order to locate the onset of phase separation at small and large asymmetries, respectively.
We use the correlated-random-field approximation and a conditional coherent-potential approximation to study the ground-state phase diagram of the one-band Hubbard model. Our approach incorporates both spin and electron correlations. It has been found that for certain values of the parameters of the model, in addition to paramagnetic, ferromagnetic, antiferromagnetic, and spin-glass or spin-liquid phases found in our earlier studies, a phase-separated phase is found to be favored for 0.7\ensuremath{\le}n\ensuremath{\le}1.0 and U/B\ensuremath{\ge}2 in good agreement with results obtained in the t-J model using the technique of the 1/N expansion. The present approach also allows one to watch the dependence of the electron density of states on the number of electrons per site and gives a single physical picture for the occurrence of a metal-insulator transition. Implications of these results for the existence of superconducting ground state as well as comparison to other studies will be briefly discussed.
The ground-state phase diagram of the asymmetric Hubbard model is studied in one and two dimensions by a well-controlled numerical method. The method allows us to calculate directly the probabilities of particular phases in the approximate ground state and thus to specify the stability domains corresponding to phases with the highest probabilities. Depending on the electron filling nnn and the magnitude of the asymmetry tf∕td{t}_{f}∕{t}_{d}tf​∕td​ between the hopping integrals of fff and ddd electrons two different scenarios in formation of ground states are observed. At low electron fillings $(n\ensuremath{\leqslant}1∕3)$ the ground states are always phase segregated in the limit of strong asymmetry (td⪢tf)({t}_{d}⪢{t}_{f})(td​⪢tf​). With decreasing asymmetry the system undergoes a transition to the phase-separated state and then to the homogeneous state. For electron fillings n>1∕3n>1∕3n>1∕3 and weak Coulomb interactions the ground state is homogeneous for all values of asymmetry, while for intermediate and strong interactions the system exhibits the same sequence of phase transitions as for nnn small. Moreover, it is shown that the segregated phase is significantly stabilized with increasing electron filling, while the separated phases disappear gradually from the ground-state phase diagrams.
We study the zero-temperature phase diagram of the half-filled one-dimensional ionic Hubbard model. This model is governed by the interplay of the on-site Coulomb repulsion and an alternating one-particle potential. Various many-body energy gaps, the charge-density-wave and bond-order parameters, the electric as well as the bond-order susceptibilities, and the density-density correlation function are calculated using the density-matrix renormalization group method. In order to obtain a comprehensive picture, we investigate systems with open as well as periodic boundary conditions and study the physical properties in different sectors of the phase diagram. A careful finite-size scaling analysis leads to results which give evidence in favor of a scenario with two quantum critical points and an intermediate spontaneously dimerized phase. Our results indicate that the phase transitions are continuous. Using a scaling ansatz we are able to read off critical exponents at the first critical point. In contrast to a bosonization approach, we do not find Ising critical exponents. We show that the low-energy physics of the strong-coupling phase can only partly be understood in terms of the strong-coupling behavior of the ordinary Hubbard model.
We study the one-dimensional two-orbital Hubbard model with general local interactions including a pair-hopping term. The model might be realized in one-dimensional transition-metal nanowires. Phase diagrams at T=0T=0T=0 are obtained by numerical integration of renormalization group equations and bosonization. Particular attention is paid to the effects of orbital degeneracy (or near degeneracy), interactions favoring locally high-spin configurations, and velocity differences. Dynamical symmetry enlargement and duality approaches are employed to determine ground states and to understand quantum phase transitions between them. An important result is that the pair-hopping term and associated orbital symmetry can lead to new insulating states. The ground state for the spin-polarized case is also discussed.
We examine the phase diagram of the half-filled one-dimensional extended Hubbard model using quantum information entropies within the density-matrix renormalization group. It is well known that there is a charge-density-wave phase at large nearest-neighbor and a small on-site Coulomb repulsion and a spin-density wave at small nearest-neighbor and large on-site Coulomb repulsion. At intermediate Coulomb interaction strength, we find an additional narrow region of a bond-order phase between these two phases. The phase transition line for the transition out of the charge-density-wave phase changes from first order at strong coupling to second order in a parameter regime where all three phases are present. We present evidence that the additional phase-transition line between the spin-density-wave and bond-order phases is infinite order. While these results are in agreement with recent numerical work, our study provides an independent unbiased means of determining the phase boundaries by using quantum information analysis, yields values for the location of some of the phase boundaries that differ from those previously found, and provides insight into the limitations of numerical methods in determining phase boundaries, especially those of infinite-order transitions.