MONTE CARLO STUDIES ON FRUSTRATED QUANTUM SPIN SYSTEMS BY A NEW APPROACH TO THE NEGATIVE-SIGN PROBLEM: TRANSFER-MATRIX MONTE CARLO METHOD

1996 ◽  
Vol 07 (03) ◽  
pp. 425-431
Author(s):  
Seiji MIYASHITA ◽  
Tota NAKAMURA
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Transfer Matrix ◽  
Quantum Monte Carlo ◽  
Quantum Spin ◽  
Kondo Lattice ◽  
Negative Sign ◽  
Quantum Spin Systems ◽  
Sign Problem ◽  
Monte Carlo Studies

A new technique for the negative sign problem in the quantum Monte Carlo method using the Suzuki-Trotter decomposition is introduced. In order to reduce the cancellation between between samples with positive and negative weights, we make use of the transfer matrix method, which has been named the Transfer-Matrix Monte Carlo method. Applications to the Heisenberg antiferromagnet on the ∆-chain and on the kagome lattice, and also to the Kondo lattice system also are given.

PARALLELIZATION OF THE WORLDLINE QUANTUM MONTE CARLO METHOD

1992 ◽  
Vol 03 (01) ◽  
pp. 61-78 ◽  
Author(s):  
J.E. GUBERNATIS ◽  
W.R. SOMSKY
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Quantum Monte Carlo ◽  
Data Representation ◽  
Quantum Spin ◽  
Computational Technique ◽  
Interprocessor Communication ◽  
Quantum Spin Systems ◽  
Spinless Fermion ◽  
Quantum Monte Carlo Method

The worldline quantum Monte Carlo method is a computational technique for studying the properties of many-electron and quantum-spin systems. In this paper, we describe our efforts in developing an efficient implementation of this method for the massively-parallel Connection Machine CM-2. We discuss why one must look beyond the obvious parallelism in the method in order to reduce interprocessor communication and increase processor utilization, and how these goals may be achieved using a plaquette-based data representation. We also present performance statistics for our implementation and sample calculations for the spinless fermion model.

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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