scholarly journals A New Monte Carlo Approach to Quantum Spin Systems: Direct Evaluation of the Partition Function

1987 ◽  
Vol 78 (2) ◽  
pp. 224-236 ◽  
Author(s):  
S. Kadowaki ◽  
A. Ueda
Keyword(s):  
Monte Carlo ◽  
Partition Function ◽  
Quantum Spin ◽  
Spin Systems ◽  
Quantum Spin Systems ◽  
Direct Evaluation ◽  
Monte Carlo Approach

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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