For the one-dimensional Ising chain with spin- $1/2$ and exchange couple $J$ in a steady transverse field(TF), an analytical theory has well been developed in terms of some topological order parameters such as Berry phase(BP). For a TF Ising chain, the nonzero BP which depends on the exchange couple and the field strength characterizes the corresponding symmetry breaking of parity and time reversal(PT). However, there apparently exists a topological phase transition for the one-dimensional infinite Ising chain in a longitudinal field(LF). If the LF is added at zero temperature, researchers believe that the LF also could influence the PT-symmetry and there exists the discontinuous BP. But the theoretic characterization has not been well founded. This paper tries to aim at this problem. With the Jordan-Wigner transformation, we give the four-fermion interaction form of the Hamiltonian in the one-dimensional Ising chain with a LF. And by the method of the mean-field theory, four-fermion interaction is well dealt with. We solve the ground state energy and the ground wave function in the momentum space. We discuss the nonzero BP and suggest that there exist topological transitions in the paramagnetic and diamagnetic cases.For the one-dimensional Ising chain with spin-$1/2$ and exchange couple $J$ in a steady transverse field(TF), an analytical theory has well been developed in terms of some topological order parameters such as Berry phase(BP). For a TF Ising chain, the nonzero BP which depends on the exchange couple and the field strength characterizes the corresponding symmetry breaking of parity and time reversal(PT). However, there apparently exists a topological phase transition for the one-dimensional infinite Ising chain in a longitudinal field(LF). If the LF is added at zero temperature, researchers believe that the LF also could influence the PT-symmetry and there exists the discontinuous BP. But the theoretic characterization has not been well founded. This paper tries to aim at this problem. With the Jordan-Wigner transformation, we give the four-fermion interaction form of the Hamiltonian in the one-dimensional Ising chain with a LF. And by the method of the mean-field theory, four-fermion interaction is well dealt with. We solve the ground state energy and the ground wave function in the momentum space. We discuss the nonzero BP and suggest that there exist topological transitions in the paramagnetic and diamagnetic cases.

Sep 9, 20180 citations

The Ising Chain in a Transverse Field

Subir Sachdev A

Cambridge University Press eBooksJan 13, 20000 citations

Magnetic Quantum Phases of Ultracold Dipolar Gases in an Optical Superlattice

Xiang-Guo Yin, Lushuai Cao, Peter Schmelcher

We propose an effective Ising spin chain constructed with dipolar quantum gases confined in a one-dimensional optical superlattice. Mapping the motional degrees of freedom of a single particle in the lattice onto a pseudo-spin results in effective transverse and longitudinal magnetic fields. This effective Ising spin chain exhibits a quantum phase transition from a paramagnetic to a single-kink phase as the dipolar interaction increases. Particularly in the single-kink phase,a magnetic kink arises in the effective spin chain and behaves as a quasi-particle in a pinning potential exerted by the longitudinal magnetic field. Being realizable with current experimental techniques, this effective Ising chain presents a unique platform for emulating the quantum phase transition as well as the magnetic kink effects in the Ising-spin chain and enriches the toolbox for quantum emulation of spin models by ultracold quantum gases.We propose an effective Ising spin chain constructed with dipolar quantum gases confined in a one-dimensional optical superlattice. Mapping the motional degrees of freedom of a single particle in the lattice onto a pseudo-spin results in effective transverse and longitudinal magnetic fields. This effective Ising spin chain exhibits a quantum phase transition from a paramagnetic to a single-kink phase as the dipolar interaction increases. Particularly in the single-kink phase,a magnetic kink arises in the effective spin chain and behaves as a quasi-particle in a pinning potential exerted by the longitudinal magnetic field. Being realizable with current experimental techniques, this effective Ising chain presents a unique platform for emulating the quantum phase transition as well as the magnetic kink effects in the Ising-spin chain and enriches the toolbox for quantum emulation of spin models by ultracold quantum gases.

arXiv:1411.4154Nov 15, 20140 citations

The one dimensional Ising model with a transverse field

Annals of PhysicsFeb 1, 197063 citations

For the one-dimensional Ising chain with spin-

1/2

and exchange couple

J

in a steady transverse field(TF), an analytical theory has well been developed in terms of some topological order parameters such as Berry phase(BP). For a TF Ising chain, the nonzero BP which depends on the exchange couple and the field strength characterizes the corresponding symmetry breaking of parity and time reversal(PT). However, there apparently exists a topological phase transition for the one-dimensional infinite Ising chain in a longitudinal field(LF). If the LF is added at zero temperature, researchers believe that the LF also could influence the PT-symmetry and there exists the discontinuous BP. But the theoretic characterization has not been well founded. This paper tries to aim at this problem. With the Jordan-Wigner transformation, we give the four-fermion interaction form of the Hamiltonian in the one-dimensional Ising chain with a LF. And by the method of the mean-field theory, four-fermion interaction is well dealt with. We solve the ground state energy and the ground wave function in the momentum space. We discuss the nonzero BP and suggest that there exist topological transitions in the paramagnetic and diamagnetic cases.