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arXiv:cond-mat/9504019 · Journal of Physics Condensed Matter

Pseudospin SU(2)-symmetry breaking, charge-density waves and superconductivity in the Hubbard model

Shun-Qing Shen, Xin Xie

Published Jun 24, 1996• 10 citations
arXivHTMLPDF

Abstract

In this paper, we discuss the physical consequences of pseudospin SU(2)-symmetry breaking in a negative-U Hubbard model at half-filling. If pseudospin symmetry is spontaneously broken while its unique subgroup U(1) remains invariant, this will lead to a charge-density-wave (CDW) ground state. Furthermore, if the U(1) symmetry is also broken, the ground state will have off-diagonal long-range order, signalling a superconductor. In this case, CDW and superconductivity coexist and form a supersolid. Finally, we show that CDW suppress, but do not destroy superconductivity.

DOI
10.1088/0953-8984/8/26/012

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In this paper, we discuss the physical consequences of pseudospin SU(2)-symmetry breaking in a negative-U Hubbard model at half-filling. If pseudospin symmetry is spontaneously broken while its unique subgroup U(1) remains invariant, this will lead to a charge-density-wave (CDW) ground state. Furthermore, if the U(1) symmetry is also broken, the ground state will have off-diagonal long-range order, signalling a superconductor. In this case, CDW and superconductivity coexist and form a supersolid. Finally, we show that CDW suppress, but do not destroy superconductivity.
The Hubbard model possesses a SU(2) pseudospin symmetry, which contains the U(1) phase symmetry as a subgroup. The existence of such symmetry leads to interesting experimental consequences if the U(1) phase symmetry is spontaneously broken, i.e., if the ground state is superconducting. In this case, there must exist a pair of massive collective modes which together with the usual Goldstone mode form a triplet representation of the psuedospin group. These collective modes are collisionless and couple directly to external charge disturbances with wave number \ensuremath{\pi} and can therefore be detected experimentally as sharp resonances.
We revisit the ground-state phase diagram of the one-dimensional half-filled extended Hubbard model with on-site (U) and nearest-neighbor (V) repulsive interactions. In the first half of the paper, using the weak-coupling renormalization-group approach (g(g(g-ology) including second-order corrections to the coupling constants, we show that bond-charge-density-wave (BCDW) phase exists for $U\ensuremath{\approx}2V$ in between charge-density-wave (CDW) and spin-density-wave (SDW) phases. We find that the umklapp scattering of parallel-spin electrons disfavors the BCDW state and leads to a bicritical point where the CDW-BCDW and SDW-BCDW continuous-transition lines merge into the CDW-SDW first-order transition line. In the second half of the paper, we investigate the phase diagram of the extended Hubbard model with either additional staggered site potential $\ensuremath{\Delta}$ or bond alternation $\ensuremath{\delta}.$ Although the alternating site potential $\ensuremath{\Delta}$ strongly favors the CDW state (that is, a band insulator), the BCDW state is not destroyed completely and occupies a finite region in the phase diagram. Our result is a natural generalization of the work by Fabrizio, Gogolin, and Nersesyan [Phys. Rev. Lett. 83,83,83, 2014 (1999)], who predicted the existence of a spontaneously dimerized insulating state between a band insulator and a Mott insulator in the phase diagram of the ionic Hubbard model. The bond alternation $\ensuremath{\delta}$ destroys the SDW state and changes it into the BCDW state (or Peierls insulating state). As a result the phase diagram of the model with $\ensuremath{\delta}$ contains only a single critical line separating the Peierls insulator phase and the CDW phase. The addition of $\ensuremath{\Delta}$ or $\ensuremath{\delta}$ changes the universality class of the CDW-BCDW transition from the Gaussian transition into the Ising transition.
We exhibit an additional SU(2) symmetry of the Hubbard model at half-filling, which suggests a simple physical manifestation of this symmetry in the presence of an applied magnetic field. The system governed by a negative-U Hubbard Hamiltonian will lose its superconductivity at an applied magnetic field well below the critical Hc{\mathit{H}}_{\mathit{c}}Hc​ associated with a conventional superconductor. Though departure from half-filling and the inclusion of a repulsive nearest-neighbor interaction break this symmetry, the above physical effect should still persist strongly and is indicative of a new type of SU(2) superconductor for the negative-U or attractive on-site Hubbard model.
The half-filled attractive Hubbard model exhibits a simultaneous charge-density wave and superconducting order in its ground state. In this paper we use approximation-free quantum Monte Carlo techniques to explore the effect of disorder in the site energies on this degeneracy. We find that superconducting order survives randomness out to a critical amount of disorder, but charge ordering is immediately destroyed. This settles the issue as to whether disordered site energies, which do not break time-reversal invariance, can destroy pairing correlations. We also locate the precise ratio of disorder to bandwidth required for the disorder-driven transition from the superconducting state. We explore the validity of a strong-coupling picture which maps the system onto a Heisenberg model in a random magnetic field.