We consider a general one-dimensional tight-binding electron model which has a period $P$ . For any filling factor $ν$ such that $Pν$ is non-integral, we prove that the model in the infinite volume limit has either a symmetry breaking or a unique ground state with gapless excitations. The proof is based on the idea of Yamanaka, Oshikawa and Affleck (cond-mat/9701141), who extended the Lieb-Schultz-Mattis argument to electron systems.We consider a general one-dimensional tight-binding electron model which has a period $P$. For any filling factor $ν$ such that $Pν$ is non-integral, we prove that the model in the infinite volume limit has either a symmetry breaking or a unique ground state with gapless excitations. The proof is based on the idea of Yamanaka, Oshikawa and Affleck (cond-mat/9701141), who extended the Lieb-Schultz-Mattis argument to electron systems.

arXiv:cond-mat/0407616Jul 23, 20044 citations

Dynamical properties of one-dimensional quantum systems

Yasuhiro Saiga, Yusuke S. Kato, Yoshio Kuramoto +3 more

Jan 1, 19960 citations

Dynamical properties and elementary excitations of one-dimensional quantum systems

Yasuhiro Saiga, Shinji Watanabe, Yoshio Kuramoto +3 more

Jan 1, 19980 citations

Few-fermion systems in one dimension: Ground- and excited-state energies and contacts

Lukas Rammelmüller, William J. Porter, Andrew C. Loheac +1 more

Using the lattice Monte Carlo method, we compute the energy and Tan's contact in the ground state as well as the first excited state of few- to many-fermion systems in a one-dimensional periodic box. We focus on unpolarized systems of $N=4,6,...,12$ particles, with a zero-range interaction, and a wide range of attractive couplings. In addition, we provide extrapolations to the infinite-volume and thermodynamic limits.Using the lattice Monte Carlo method, we compute the energy and Tan's contact in the ground state as well as the first excited state of few- to many-fermion systems in a one-dimensional periodic box. We focus on unpolarized systems of $N=4,6,...,12$ particles, with a zero-range interaction, and a wide range of attractive couplings. In addition, we provide extrapolations to the infinite-volume and thermodynamic limits.

arXiv:1505.02131Physical Review AJul 27, 201528 citations

Quasi time crystal

Xintian Wu

We discuss the possibility of making a quasi time crystal. A simple two-state model is studied to clarify our definition. In a superposition of the ground state and the excited state and the probability of observation varies periodically in time during the lifetime of the excited state. The quasi time crystal is also discussed around the first order quantum phase transition, which is characterized by the degeneracy and crossing of the two lowest-energy states in the infinite-volume limit. Our results have broad validity. As an example, the one-dimensional transverse field Ising model with surface fields is shown to have similar behavior. The oscillating magnetization profile is solved exactly.We discuss the possibility of making a quasi time crystal. A simple two-state model is studied to clarify our definition. In a superposition of the ground state and the excited state and the probability of observation varies periodically in time during the lifetime of the excited state. The quasi time crystal is also discussed around the first order quantum phase transition, which is characterized by the degeneracy and crossing of the two lowest-energy states in the infinite-volume limit. Our results have broad validity. As an example, the one-dimensional transverse field Ising model with surface fields is shown to have similar behavior. The oscillating magnetization profile is solved exactly.

arXiv:2203.01468Mar 3, 20220 citations

New method for the quantum ground states in one dimension

S. G. Chung

arXiv:1008.0366Physics Letters ASep 29, 20069 citations

We consider a general one-dimensional tight-binding electron model which has a period

P

. For any filling factor

ν

such that

Pν

is non-integral, we prove that the model in the infinite volume limit has either a symmetry breaking or a unique ground state with gapless excitations. The proof is based on the idea of Yamanaka, Oshikawa and Affleck (cond-mat/9701141), who extended the Lieb-Schultz-Mattis argument to electron systems.

N=4,6,...,12

particles, with a zero-range interaction, and a wide range of attractive couplings. In addition, we provide extrapolations to the infinite-volume and thermodynamic limits.