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Bulletin of the American Physical Society

Improved cluster-effective-field study on frustrated quantum spin systems in 2D

Yoshihiko Nonomura

Published Mar 19, 2013• 0 citations
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Cluster-effective-field approximations in frustrated quantum spin systems: CAM analysis of Neel-dimer transition in the S= 1/2 frustrated XXZ chain at the ground state

Yoshihiko Nonomura, Masuo Suzuki

How to impose boundary conditions is crucial to finite-cluster calculations of quantum spin systems, but only open-boundary clusters have been used in cluster-effective-field approximations up to now. In the present paper, periodic-boundary clusters are also considered for the formulation of cluster-effective-field approximations in frustrated quantum spin systems. Namely, the open-boundary-condition double-cluster approximation (OBC-DCA) and the periodic-boundary-condition double-cluster approximation (PBC-DCA) are applied to the one-dimensional S= 1/2 frustrated XXZ model at the ground state. These two approximations are compared using the coherent-anomaly method (CAM). Within the limitation of cluster sizes in exact-diagonalization calculations, the PBC-DCA can reproduce the true phase boundary of the Neel-dimer transition. On the other hand, the OBC-DCA severely underestimates the existence of magnetic orders as quantum fluctuation is increased. These findings suggest that previous cluster-effective-field studies based on open-boundary clusters should be reconsidered.

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Path integrals, diffusion onSU(2) and the fully frustrated antiferromagnetic spin cluster

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We study the path-integral treatment of the quantum mechanics of a fully frustrated cluster of spins: a cluster in which every pair of spins is coupled equally by antiferromagnetic Heisenberg interactions. Such clusters are interesting partly because they are the building blocks of geometrically frustrated spin systems. Using a Hubbard–Stratonovich transformation to decouple the interactions, the Boltzmann factor for the spin cluster is written in terms of the time-evolution operator for a single spin in a stochastically varying magnetic field. The time-evolution operator follows a random walk in SU (2): by switching from a Langevin to a Fokker–Planck description of this walk and computing the probability distribution of its end-point, we arrive at an expression for the partition function as a finite sum of single integrals. The calculation provides an analytically tractable illustration of the auxiliary field approach, as used in quantum Monte Carlo calculations, and may potentially be extended to treat more complex frustrated spin systems.

Journal of Physics A Mathematical and General•Nov 25, 2004•18 citations
How to impose boundary conditions is crucial to finite-cluster calculations of quantum spin systems, but only open-boundary clusters have been used in cluster-effective-field approximations up to now. In the present paper, periodic-boundary clusters are also considered for the formulation of cluster-effective-field approximations in frustrated quantum spin systems. Namely, the open-boundary-condition double-cluster approximation (OBC-DCA) and the periodic-boundary-condition double-cluster approximation (PBC-DCA) are applied to the one-dimensional S= 1/2 frustrated XXZ model at the ground state. These two approximations are compared using the coherent-anomaly method (CAM). Within the limitation of cluster sizes in exact-diagonalization calculations, the PBC-DCA can reproduce the true phase boundary of the Neel-dimer transition. On the other hand, the OBC-DCA severely underestimates the existence of magnetic orders as quantum fluctuation is increased. These findings suggest that previous cluster-effective-field studies based on open-boundary clusters should be reconsidered.
We study the path-integral treatment of the quantum mechanics of a fully frustrated cluster of spins: a cluster in which every pair of spins is coupled equally by antiferromagnetic Heisenberg interactions. Such clusters are interesting partly because they are the building blocks of geometrically frustrated spin systems. Using a Hubbard–Stratonovich transformation to decouple the interactions, the Boltzmann factor for the spin cluster is written in terms of the time-evolution operator for a single spin in a stochastically varying magnetic field. The time-evolution operator follows a random walk in SU (2): by switching from a Langevin to a Fokker–Planck description of this walk and computing the probability distribution of its end-point, we arrive at an expression for the partition function as a finite sum of single integrals. The calculation provides an analytically tractable illustration of the auxiliary field approach, as used in quantum Monte Carlo calculations, and may potentially be extended to treat more complex frustrated spin systems.