Physical review. B, Condensed matter

Symmetry breaking in the Hubbard model at zero temperature

Gang Su

Published Feb 1, 1993• 0 citations

Abstract

It is shown within the pseudospin framework that the U(1) phase symmetry and the pseudospin SU(2) symmetry in the Hubbard model at zero temperature are spontaneously broken away from half filling, which implies that the Hubbard model probably possesses some massless Goldstone bosons in its ground state.

DOI: 10.1103/physrevb.47.2901

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Investigation on the Ground State of the Hubbard Model

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Physical review. B, Condensed matter

Symmetry breaking in the Hubbard model at zero temperature

Gang Su

Published Feb 1, 1993• 0 citations

Publisher

Abstract

DOI: 10.1103/physrevb.47.2901

Related papers

Investigation on the Ground State of the Hubbard Model

Gang Su, Mo‐Lin Ge

Communications in Theoretical PhysicsJan 1, 19923 citations

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

Shun-Qing Shen, Xin Xie

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.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.

arXiv:cond-mat/9504019Journal of Physics Condensed MatterJun 24, 199610 citations

Pseudospin symmetry and new collective modes of the Hubbard model

Shoucheng Zhang

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.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.

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Yu-Min Hu, Biao Lian

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Akihisa Koga, Hiromasa Yanatori

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Symmetry and spontaneous symmetry breaking of the Hubbard model on a square lattice ground state

J. M. P. Carmelo

In this paper we consider the simplified form that a recently introduced general operator description of the Hubbard model on the square lattice with $N_a^2\gg 1$ sites, effective transfer integral $t$ , and onsite repulsion $U$ has in a suitable one- and two-electron subspace. Such an operator description is that consistent with the model exact global symmetry recently extended to $SO(3)\times SO(3)\times U(1)$ . There is a large consensus that in the thermodynamic limit $N_a^2\rightarrow\infty$ long-range antiferromagnetic order occurs in the spin-density $m=0$ ground state of the half-filled Hubbard model on the square lattice. Here we find that the corresponding spontaneous symmetry breaking lowers the symmetry of such a state from $SO(3)\times SO(3)\times U(1)$ for $N_a^2\gg 1$ large but finite to $[U(2)\times U(1)]/Z_2^2 \equiv [SO(3)\times U(1)\times U(1)]/Z_2$ for $N_a^2\rightarrow\infty$ . Moreover, we argue that the spin effective lattice being identical to the original lattice is a necessary condition for the occurrence of ground-state long-range antiferromagnetic order in the limit $N_a^2\rightarrow\infty$ . Consistently, strong evidence is provided that for very small hole concentration $0In this paper we consider the simplified form that a recently introduced general operator description of the Hubbard model on the square lattice with $N_a^2\gg 1$ sites, effective transfer integral $t$, and onsite repulsion $U$ has in a suitable one- and two-electron subspace. Such an operator description is that consistent with the model exact global symmetry recently extended to $SO(3)\times SO(3)\times U(1)$. There is a large consensus that in the thermodynamic limit $N_a^2\rightarrow\infty$ long-range antiferromagnetic order occurs in the spin-density $m=0$ ground state of the half-filled Hubbard model on the square lattice. Here we find that the corresponding spontaneous symmetry breaking lowers the symmetry of such a state from $SO(3)\times SO(3)\times U(1)$ for $N_a^2\gg 1$ large but finite to $[U(2)\times U(1)]/Z_2^2 \equiv [SO(3)\times U(1)\times U(1)]/Z_2$ for $N_a^2\rightarrow\infty$. Moreover, we argue that the spin effective lattice being identical to the original lattice is a necessary condition for the occurrence of ground-state long-range antiferromagnetic order in the limit $N_a^2\rightarrow\infty$. Consistently, strong evidence is provided that for very small hole concentration $0

arXiv:1003.4619Mar 24, 20100 citations

We investigate spontaneously symmetry breaking states in the attractive SU(

N

) Hubbard model at half filling. Combining dynamical mean-field theory with the continuous-time quantum Monte Carlo method, we obtain the finite temperature phase diagrams for the superfluid state. When

N>2

, the second-order phase transition occurs in the weak coupling region, while the first-order phase transition with the hysteresis appears in the strong coupling region. We also discuss the stability of the density wave state and clarify the component dependence of the maximum critical temperature.

In this paper we consider the simplified form that a recently introduced general operator description of the Hubbard model on the square lattice with

N_a^2\gg 1

sites, effective transfer integral

t

, and onsite repulsion

U

has in a suitable one- and two-electron subspace. Such an operator description is that consistent with the model exact global symmetry recently extended to

SO(3)\times SO(3)\times U(1)

. There is a large consensus that in the thermodynamic limit

N_a^2\rightarrow\infty

long-range antiferromagnetic order occurs in the spin-density

m=0

ground state of the half-filled Hubbard model on the square lattice. Here we find that the corresponding spontaneous symmetry breaking lowers the symmetry of such a state from

SO(3)\times SO(3)\times U(1)

for

N_a^2\gg 1

large but finite to

[U(2)\times U(1)]/Z_2^2 \equiv [SO(3)\times U(1)\times U(1)]/Z_2

for

N_a^2\rightarrow\infty

. Moreover, we argue that the spin effective lattice being identical to the original lattice is a necessary condition for the occurrence of ground-state long-range antiferromagnetic order in the limit

N_a^2\rightarrow\infty

. Consistently, strong evidence is provided that for very small hole concentration $0