Here we study zero temperature quantum phase transition driven by the transverse field for random $\pm J$ Ising model on chain and square lattice. We present some analytical results for one dimension and some numerical results for very small square lattice under periodic boundary condition. The numerical results are obtained employing exact diagonalization technique following Lanczos method.Here we study zero temperature quantum phase transition driven by the transverse field for random $\pm J$ Ising model on chain and square lattice. We present some analytical results for one dimension and some numerical results for very small square lattice under periodic boundary condition. The numerical results are obtained employing exact diagonalization technique following Lanczos method.

arXiv:cond-mat/0310381Oct 16, 20030 citations

Entanglement in the Quantum Ising Model

Geoffrey R. Grimmett, Tobias J. Osborne, Petra F. Scudo

arXiv:0704.2981Journal of Statistical PhysicsMar 3, 200822 citations

Renormalization of quantum coherence and quantum phase transition in the Ising model

Meng Qin

arXiv:2001.10714Physica A Statistical Mechanics and its ApplicationsSep 1, 202013 citations

Classical model emerges in quantum entanglement: Quantum Monte Carlo study for an Ising-Heisenberg bilayer

Siying Wu, Xiaoxue Ran, Binbin Yin +4 more

By developing a cluster sampling of the stochastic series expansion quantum Monte Carlo method, we investigate a spin- $\frac{1}{2}$ model on a bilayer square lattice with intralayer ferromagnetic (FM) Ising coupling and interlayer antiferromagnetic Heisenberg interaction. The continuous quantum phase transition which occurs at ${g}_{c}=3.045(2)$ between the FM Ising phase and the dimerized phase is studied via large-scale simulations. From analysis of the critical exponents we show that this phase transition belongs to the ( $2+1$ )-dimensional Ising universality class. In addition, the quantum entanglement is strong between the two layers, especially in the dimerized phase. The effective Hamiltonian of a single layer seems like a transverse-field Ising model. However, we found that the quantum entanglement Hamiltonian is a pure classical Ising model without any quantum fluctuations. Furthermore, we give a more general explanation about how a classical entanglement Hamiltonian emerges.By developing a cluster sampling of the stochastic series expansion quantum Monte Carlo method, we investigate a spin-$\frac{1}{2}$ model on a bilayer square lattice with intralayer ferromagnetic (FM) Ising coupling and interlayer antiferromagnetic Heisenberg interaction. The continuous quantum phase transition which occurs at ${g}_{c}=3.045(2)$ between the FM Ising phase and the dimerized phase is studied via large-scale simulations. From analysis of the critical exponents we show that this phase transition belongs to the ($2+1$)-dimensional Ising universality class. In addition, the quantum entanglement is strong between the two layers, especially in the dimerized phase. The effective Hamiltonian of a single layer seems like a transverse-field Ising model. However, we found that the quantum entanglement Hamiltonian is a pure classical Ising model without any quantum fluctuations. Furthermore, we give a more general explanation about how a classical entanglement Hamiltonian emerges.

arXiv:2210.06764Physical review. B./Physical review. BApr 10, 202315 citations

Entanglement and Quantum Phase Transition in Quantum Spin Systems

Synge Todo

Jan 1, 20150 citations

Here we study zero temperature quantum phase transition driven by the transverse field for random

\pm J

Ising model on chain and square lattice. We present some analytical results for one dimension and some numerical results for very small square lattice under periodic boundary condition. The numerical results are obtained employing exact diagonalization technique following Lanczos method.

By developing a cluster sampling of the stochastic series expansion quantum Monte Carlo method, we investigate a spin-

\frac{1}{2}

model on a bilayer square lattice with intralayer ferromagnetic (FM) Ising coupling and interlayer antiferromagnetic Heisenberg interaction. The continuous quantum phase transition which occurs at

{g}_{c}=3.045(2)

between the FM Ising phase and the dimerized phase is studied via large-scale simulations. From analysis of the critical exponents we show that this phase transition belongs to the (

2+1

)-dimensional Ising universality class. In addition, the quantum entanglement is strong between the two layers, especially in the dimerized phase. The effective Hamiltonian of a single layer seems like a transverse-field Ising model. However, we found that the quantum entanglement Hamiltonian is a pure classical Ising model without any quantum fluctuations. Furthermore, we give a more general explanation about how a classical entanglement Hamiltonian emerges.