scholarly journals Ornstein-Zernike decay in the ground state of the quantum Ising model in a strong transverse field

1991 ◽  
Vol 137 (3) ◽  
pp. 599-615 ◽  
Author(s):  
Tom Kennedy
Keyword(s):  
Ising Model ◽  
Ground State ◽  
Transverse Field ◽  
Strong Transverse ◽  
Quantum Ising Model

scholarly journals Quantum Ising model in a period-2 modulated transverse field

2019 ◽  
Vol 100 (2) ◽  
Author(s):  
Adalberto D. Varizi ◽  
Raphael C. Drumond
Keyword(s):  
Ising Model ◽  
Transverse Field ◽  
Period 2 ◽  
Quantum Ising Model

scholarly journals Monte Carlo simulation of stoquastic Hamiltonians

2015 ◽  
Vol 15 (13&14) ◽  
pp. 1122-1140
Author(s):  
Sergey Bravyi
Keyword(s):  
Monte Carlo ◽  
Ising Model ◽  
Ground State ◽  
State Energy ◽  
Transverse Field ◽  
Variable Number ◽  
Monte Carlo Algorithm ◽  
Standard Product ◽  
Ferromagnetic Ising Model ◽  
Transverse Field Ising Model

Stoquastic Hamiltonians are characterized by the property that their off-diagonal matrix elements in the standard product basis are real and non-positive. Many interesting quantum models fall into this class including the Transverse field Ising Model (TIM), the Heisenberg model on bipartite graphs, and the bosonic Hubbard model. Here we consider the problem of estimating the ground state energy of a local stoquastic Hamiltonian $H$ with a promise that the ground state of $H$ has a non-negligible correlation with some `guiding' state that admits a concise classical description. A formalized version of this problem called Guided Stoquastic Hamiltonian is shown to be complete for the complexity class $\MA$ (a probabilistic analogue of $\NP$). To prove this result we employ the Projection Monte Carlo algorithm with a variable number of walkers. Secondly, we show that the ground state and thermal equilibrium properties of the ferromagnetic TIM can be simulated in polynomial time on a classical probabilistic computer. This result is based on the approximation algorithm for the classical ferromagnetic Ising model due to Jerrum and Sinclair (1993).

QUANTUM PHASE TRANSITION AND ENTANGLEMENT IN THE TRANSVERSE-FIELD ISING MODEL

2006 ◽  
Vol 04 (04) ◽  
pp. 705-713 ◽  
Author(s):  
JUNPENG CAO ◽  
GANG XIONG ◽  
YUPENG WANG ◽  
X. R. WANG
Keyword(s):  
Phase Transition ◽  
Ising Model ◽  
Quantum Phase Transition ◽  
Ground State ◽  
Transverse Field ◽  
Quantum Phase ◽  
Global Entanglement ◽  
Transverse Field Ising Model ◽  
Analytical Expressions ◽  
Number Of Particles

We present an exact calculation of the global entanglement for the ground state of the transverse-field Ising model. We obtain the analytical expressions for the correlation functions, concurrence and the global entanglement of the system for arbitrary number of particles in the ground state. We prove that the inflexion of the global entanglement exactly corresponds to the quantum phase transition point of the system.

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