Monte Carlo simulation of the quantum transverse Ising model

Oliveira, Mário J. de; Chiappin, José Raymundo Novaes

doi:10.1016/s0378-4371(96)00461-x

Cited by 8 publications

(6 citation statements)

References 24 publications

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“…In one dimensional case, our numerical results fit Pfeuty's exact result [22] very good. Many numerical studies ablout 1D TFIM has been done, for example the Mote Carlo method was used in [23]. While in two dimension models, our results coincides with those from real space renormalization group analysis [36] [37].…”

Section: Key Observables Of the Tfim Ground Statesupporting

confidence: 81%

Neural-Network Quantum State of Transverse-Field Ising Model

Shi

Sun

Zeng

2019

Commun. Theor. Phys.

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Along the way initiated by Carleo and Troyer [1], we construct the neural-network quantum state of transverse-field Ising model(TFIM) by an unsupervised machine learning method. Such a wave function is a map from the spin-configuration space to the complex number field determined by an array of network parameters. To get the ground state of the system, values of the network parameters are calculated by a Stochastic Reconfiguration(SR) method. We provide for this SR method an understanding from action principle and information geometry aspects. With this quantum state, we calculate key observables of the system, the energy, correlation function, correlation length, magnetic moment and susceptibility. As innovations, we provide a high efficiency method and use it to calculate entanglement entropy (EE) of the system and get results consistent with previous work very well.

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Section: Key Observables Of the Tfim Ground Statesupporting

confidence: 81%

Neural-Network Quantum State of Transverse-Field Ising Model

Shi

Sun

Zeng

2019

Commun. Theor. Phys.

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“…for a given point on the trajectory (m, µ) at time t. To obtain the overlap function ( 16) and ( 17) (18), we used the concept of dynamical replica theory (the DRT) [21,22], namely, 'equipartitioning' and 'self-averaging' of the M during the evolution in time. As the derivation is a bit complicated, we shall show the detail in Appendix A.…”

Section: Disordered Systems: An Application For Statistical-mechanica...mentioning

confidence: 99%

“…This approach is very powerful and a lot of researches have succeeded in exploring the quantum phases in strongly correlated quantum systems. However, when we simulate the quantum system at zero temperature in which quantum effect is essential, we encounter some technical difficulties although several sophisticated algorithms were proposed [18]. From the view point of information science, it is very informative for us to evaluate the process of information processing and if one seeks to utilize the quantum fluctuation to solve the problems, we should use the 'zero-temperature dynamics'.…”

Section: Introductionmentioning

confidence: 99%

“…Obviously we find that the saddle point is obtained by the equations ( 17) and (18). Then, the overlap function is evaluated as…”

mentioning

confidence: 99%

“…This result is nothing but equation (16). As parameters m and μ are related to the order-parameters m and µ in equations (17) (18), overlap function M is influenced by quantum fluctuation through (17) (18) and the solution of equations (14) (15).…”

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confidence: 99%

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Deterministic flows of order-parameters in stochastic processes of quantum Monte Carlo method

Inoue

2010

J. Phys.: Conf. Ser.

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In terms of the stochastic process of quantum-mechanical version of Markov chain Monte Carlo method (the MCMC), we analytically derive macroscopically deterministic flow equations of order parameters such as spontaneous magnetization in infinite-range (d(= ∞)dimensional) quantum spin systems. By means of the Trotter decomposition, we consider the transition probability of Glauber-type dynamics of microscopic states for the corresponding (d + 1)-dimensional classical system. Under the static approximation, differential equations with respect to macroscopic order parameters are explicitly obtained from the master equation that describes the microscopic-law. In the steady state, we show that the equations are identical to the saddle point equations for the equilibrium state of the same system. The equation for the dynamical Ising model is recovered in the classical limit. We also check the validity of the static approximation by making use of computer simulations for finite size systems and discuss several possible extensions of our approach to disordered spin systems for statisticalmechanical informatics. Especially, we shall use our procedure to evaluate the decoding process of Bayesian image restoration. With the assistance of the concept of dynamical replica theory (the DRT), we derive the zero-temperature flow equation of image restoration measure showing some 'non-monotonic' behaviour in its time evolution.

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