The one-dimensional $\mathrm{SU}(n)$ Hubbard model is investigated numerically for $n=2$ , 3, 4, and 5 at half-filling and $1∕n$ filling using the density-matrix renormalization-group method. The energy gaps and various quantum information entropies are calculated. In the half-filled case, finite spin and charge gaps are found for arbitrary positive $U$ if $n>2$ . Furthermore, it is shown that the transition to the gapped phase at ${U}_{c}=0$ is of Kosterlitz-Thouless type and is accompanied by a bond dimerization both for even and odd $n$ . In the $1∕n$ -filled case, the transition has similar features as the metal-insulator transition in the half-filled SU(2) Hubbard model. The charge gap opens exponentially slowly for $U>{U}_{c}=0$ , the spin sector remains gapless, and the ground state is nondimerized.The one-dimensional $\mathrm{SU}(n)$ Hubbard model is investigated numerically for $n=2$, 3, 4, and 5 at half-filling and $1∕n$ filling using the density-matrix renormalization-group method. The energy gaps and various quantum information entropies are calculated. In the half-filled case, finite spin and charge gaps are found for arbitrary positive $U$ if $n>2$. Furthermore, it is shown that the transition to the gapped phase at ${U}_{c}=0$ is of Kosterlitz-Thouless type and is accompanied by a bond dimerization both for even and odd $n$. In the $1∕n$-filled case, the transition has similar features as the metal-insulator transition in the half-filled SU(2) Hubbard model. The charge gap opens exponentially slowly for $U>{U}_{c}=0$, the spin sector remains gapless, and the ground state is nondimerized.

arXiv:cond-mat/0607374Physical Review BApr 19, 200748 citations

Opportunities in quantum

Simon Andrews

Journal of The Foundation for Science and TechnologyMar 31, 20250 citations

Keeping quantum simple

III-Vs ReviewNov 1, 20030 citations

Spin-gap state and superconducting correlations in a one-dimensional dimerizedt-Jmodel

Masatoshi Imada

The phase diagram of one-dimensional dimerized t-J model is investigated by exact-diagonalization, quantum tranfer-matrix, and quantum Monte Carlo methods. The spin gap persists near but away from half-filling as well as in a strongly dimerized region, while the charge can be described as a Tomonaga-Luttinger liquid in the entire region. The spin-gap region extends to the weak-dimerization region as well as to the Haldane-gap region. Critical exponents of various correlation functions are discussed. The pairing correlation shows remarkable enhancement and by far dominates over other correlations near half-filling. At quarter filling, charge-gap formation is observed.The phase diagram of one-dimensional dimerized t-J model is investigated by exact-diagonalization, quantum tranfer-matrix, and quantum Monte Carlo methods. The spin gap persists near but away from half-filling as well as in a strongly dimerized region, while the charge can be described as a Tomonaga-Luttinger liquid in the entire region. The spin-gap region extends to the weak-dimerization region as well as to the Haldane-gap region. Critical exponents of various correlation functions are discussed. The pairing correlation shows remarkable enhancement and by far dominates over other correlations near half-filling. At quarter filling, charge-gap formation is observed.

Physical review. B, Condensed matterJul 1, 199333 citations

The Quantum Puzzle

Barry R. Clarke

WORLD SCIENTIFIC eBooksMay 14, 20151 citation

Topological phase transition without single particle gap closing in strongly correlated systems

Peizhi Mai, Jinchao Zhao, Thomas Maier +2 more

We show here two models where changing topology does not necessarily close the bulk insulating charge gap as demanded in the standard noninteracting picture. From extensive determinantal and dynamical cluster quantum Monte Carlo simulations of the half-filled and quarter-filled Kane-Mele-Hubbard model, we show that, for sufficiently strong interactions at either half- or quarter-filling, a transition between topological and trivial insulators occurs without the closing of a charge gap. To shed light on this behavior, we illustrate that an exactly solvable model reveals that while the single-particle gap remains, the many-body gap does, in fact, close. These two gaps are the same in the noninteracting system but depart from each other as the interaction turns on. We purport that for interacting systems, the proper probe of topological phase transitions is the closing of the many-body rather than the single-particle gap.We show here two models where changing topology does not necessarily close the bulk insulating charge gap as demanded in the standard noninteracting picture. From extensive determinantal and dynamical cluster quantum Monte Carlo simulations of the half-filled and quarter-filled Kane-Mele-Hubbard model, we show that, for sufficiently strong interactions at either half- or quarter-filling, a transition between topological and trivial insulators occurs without the closing of a charge gap. To shed light on this behavior, we illustrate that an exactly solvable model reveals that while the single-particle gap remains, the many-body gap does, in fact, close. These two gaps are the same in the noninteracting system but depart from each other as the interaction turns on. We purport that for interacting systems, the proper probe of topological phase transitions is the closing of the many-body rather than the single-particle gap.

arXiv:2401.01402Physical review. B./Physical review. BAug 5, 202410 citations

The one-dimensional

\mathrm{SU}(n)

Hubbard model is investigated numerically for

n=2

, 3, 4, and 5 at half-filling and

1∕n

filling using the density-matrix renormalization-group method. The energy gaps and various quantum information entropies are calculated. In the half-filled case, finite spin and charge gaps are found for arbitrary positive

U

n>2

. Furthermore, it is shown that the transition to the gapped phase at

{U}_{c}=0

is of Kosterlitz-Thouless type and is accompanied by a bond dimerization both for even and odd

n

. In the

1∕n

-filled case, the transition has similar features as the metal-insulator transition in the half-filled SU(2) Hubbard model. The charge gap opens exponentially slowly for

U>{U}_{c}=0

, the spin sector remains gapless, and the ground state is nondimerized.