A quantum Monte Carlo algorithm realizing an intrinsic relaxation

Abstract

We propose a new quantum Monte Carlo algorithm which realizes a relaxation intrinsic to the original quantum system. The Monte Carlo dynamics satisfies the dynamic scaling relation $\tau \sim {\xi }^z$ and is independent of the Trotter number. Finiteness of the Trotter number just appears as the finite-size effect. An infinite Trotter number version of the algorithm is also formulated, which enables us to observe a true relaxation of the original system. The strategy of the algorithm is a compromise between the conventional worldline local flip and the modern cluster loop flip. It is a local flip in the real-space direction and is a cluster flip in the Trotter direction. The new algorithm is tested by the transverse-field Ising model in two dimensions. An accurate phase diagram is obtained.

9 pages, 4 figures

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• Infinitesimal incommensurate stripe phase in an axial next-nearest-neighbor Ising model in two dimensions
• The antiferromagnetic order in an F-AF random alternating quantum spin chain : (CH_3)_2 CHNH_3 Cu(Cl_x Br_{1-x})_3

Cited by in corpus (11)

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• New Nonequilibrium-to-Equilibrium Dynamical Scaling and Stretched-Exponential Critical Relaxation in Cluster Algorithms
• Quantum-thermal annealing with cluster-flip algorithm
• Nonequilibrium-relaxation approach to quantum phase transitions: Nontrivial critical relaxation in cluster-update quantum Monte Carlo
• Stationarity of quantum statistical ensembles at first-order phase transition points
• Bulk and Boundary Quantum Phase Transitions in a Square Rydberg Atom Array
• Statistical ensembles for phase coexistence states specified by noncommutative additive observables