Faculté des sciences

Dynamical symmetry approach to path integrals of quantum spin systems

Ringel, Matouš ; Gritsev, Vladimir

In: Physical Review A, 2014, vol. 88, no. 6, p. 062105

We develop a dynamical symmetry approach to path integrals for general interacting quantum spin systems. The time-ordered exponential obtained after the Hubbard-Stratonovich transformation can be disentangled into the product of a finite number of the usual exponentials. This procedure leads to a set of stochastic differential equations on the group manifold, which can be further formulated in... More

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    Summary
    We develop a dynamical symmetry approach to path integrals for general interacting quantum spin systems. The time-ordered exponential obtained after the Hubbard-Stratonovich transformation can be disentangled into the product of a finite number of the usual exponentials. This procedure leads to a set of stochastic differential equations on the group manifold, which can be further formulated in terms of the supersymmetric effective action. This action has the form of the Witten topological field theory in the continuum limit. As a consequence, we show how it can be used to obtain the exact results for a specific quantum many-body system which can be otherwise solved only by the Bethe ansatz. This represents an example of a many-body system treated exactly using the path-integral formulation. Moreover, our method can deal with time-dependent parameters, which we demonstrate explicitly.