New Quantum Monte Carlo Approach to Ground-State Phase Transitions in Quantum Spin Systems

1998 ◽  
Vol 67 (1) ◽  
pp. 5-7 ◽  
Author(s):  
Yoshihiko Nonomura
Keyword(s):  
Monte Carlo ◽  
Phase Transitions ◽  
Ground State ◽  
Quantum Monte Carlo ◽  
Quantum Spin ◽  
Spin Systems ◽  
Quantum Spin Systems ◽  
Monte Carlo Approach

scholarly journals Unconventional phase transitions in strongly anisotropic 2D (pseudo)spin systems

2018 ◽  
Vol 185 ◽  
pp. 08006
Author(s):  
Vitaly Konev ◽  
Evgeny Vasinovich ◽  
Vasily Ulitko ◽  
Yury Panov ◽  
Alexander Moskvin
Keyword(s):  
Magnetic Field ◽  
Monte Carlo ◽  
Phase Transitions ◽  
Ground State ◽  
Quantum Monte Carlo ◽  
Mean Field ◽  
Spin Systems ◽  
Field Approach ◽  
Generalized Mean

We have applied a generalized mean-field approach and quantum Monte-Carlo technique for the model 2D S = 1 (pseudo)spin system to find the ground state phase with its evolution under application of the (pseudo)magnetic field. The comparison of the two methods allows us to clearly demonstrate the role of quantum effects. Special attention is given to the role played by an effective single-ion anisotropy ("on-site correlation").

An Efficient Monte Carlo Approach to Low-Lying Excitations of Quantum Spin Chains

1997 ◽  
Vol 08 (03) ◽  
pp. 609-634 ◽  
Author(s):  
Shoji Yamamoto
Keyword(s):  
Monte Carlo ◽  
Quantum Monte Carlo ◽  
Central Charge ◽  
Quantum Spin ◽  
Spin Chains ◽  
Full Description ◽  
Energy Structure ◽  
Quantum Spin Chains ◽  
Quantum Spin Systems ◽  
Monte Carlo Approach

We give a full description of a recently developed efficient Monte Carlo Approach to low-lying excitations of one-dimensional quantum spin systems. The idea is in a word expressed as extracting the lower edge of the excitation spectrum from imaginary-time quantum Monte Carlo data at a sufficiently low temperature. First, the method is applied to the antiferromagnetic Heisenberg chains of S=1/2, 1, 3/2, and 2. In the cases of S=1/2 and S=1, comparing the present results with the previous findings, we discuss the reliability of the method. The spectra for S=3/2 and S=2 turn out to be massless and massive, respectively. In order to demonstrate that our method is very good at treating long chains, we calculate the S=2 chain with length up to 512 spins and give a precise estimate of the Haldane gap. Second, we show its fruitful use in studying quantum critical phenomena of bond-alternating spin chains. Using the conformal invariance of the system as well, we calculate the central charge of the critical S=1 chain, which results in the Gaussian universality class. Third, we study an alternating-spin system composed of two kinds of spins S=1 and 1/2, which shows the ferrimagnetic behavior. We find a quadratic dispersion relation in the small-momentum region. The numerical findings are qualitatively explained well in terms of the spin-wave theory. Finally, we argue a possibility of applying the method to the higher excitations, where we again deal with the S=1 Heisenberg antiferromagnet and inquire further into its unique low-energy structure. All the applications demonstrate the wide applicability of the method and its own advantages.

NUMERICAL STOCHASTIC METHODS IN STATISTICAL MECHANICS

1996 ◽  
Vol 10 (11) ◽  
pp. 1313-1327 ◽  
Author(s):  
MÁRIO J. DE OLIVEIRA
Keyword(s):  
Monte Carlo ◽  
Statistical Mechanics ◽  
Ground State ◽  
Stochastic Dynamics ◽  
Quantum Spin ◽  
Spin Systems ◽  
Stochastic Methods ◽  
Quantum Spin Systems ◽  
Microscopic Reversibility

We review the numerical stochastic methods used in statistical mechanics with emphasis on the Langevin and Monte Carlo methods. We point out the role of microscopic reversibility in setting up the stochastic dynamics associated to the methods. We also present a Monte Carlo method which allows the calculation of the ground state properties of quantum spin systems.

Quantum Monte Carlo Study of Entanglement in Quantum Spin Systems

2005 ◽  
Vol 140 (3-4) ◽  
pp. 293-302 ◽  
Author(s):  
Tommaso Roscilde ◽  
Paola Verrucchi ◽  
Andrea Fubini ◽  
Stephan Haas ◽  
Valerio Tognetti
Keyword(s):  
Monte Carlo ◽  
Quantum Monte Carlo ◽  
Monte Carlo Study ◽  
Quantum Spin ◽  
Spin Systems ◽  
Quantum Spin Systems
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