PROJECTOR APPROXIMATION AND QUANTUM MONTE CARLO

1994 ◽  
Vol 05 (03) ◽  
pp. 483-488
Author(s):  
R.M. FYE
Keyword(s):  
Hilbert Space ◽  
Monte Carlo ◽  
Quantum Monte Carlo ◽  
Lattice Models ◽  
Quantum Spin ◽  
Spin Systems ◽  
Test Model ◽  
Exact Results ◽  
Quantum Spin Systems ◽  
Quantum Monte Carlo Simulations

We derive a general approximation for performing quantum Monte Carlo simulations within a desired subspace of the full Hilbert space. We analytically determine the form of the resulting systematic error, allowing controlled extrapolation to exact results. We discuss some numerical applications, including fermion impurity and lattice models with infinite on-site Colulomb repulsion U and quantum spin systems. We demonstrate the use of the approximation in simulations with a test model.

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

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.

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