Quantum Spin Systems

Hal Tasaki

Hans A. De Raedt, V. V. Dobrovitski

Computer simulations of decoherence in quantum spin systems require the solution of the time-dependent Schrodinger equation for interacting quantum spin systems over extended periods of time. We use exact diagonalization, Chebyshev polynomial technique, four Suzuki-formula algorithms, and the short-iterative-Lanczos method to solve a simple model for decoherence of a quantum spin system by an environment consisting of quantum spins, and compare advantages and limitations of different algorithms.

Hans A. De Raedt, V. V. Dobrovitski

Abstract. Computer simulations of decoherence in quantum spin systems require the solution of the time-dependent Schrödinger equation for interacting quantum spin systems over extended periods of time. We use exact diagonalization, Chebyshev polynomial technique, four Suzukiformula algorithms, and the short-iterative-Lanczos method to solve a simple model for decoherence of a quantum spin system by an environment consisting of quantum spins, and compare advantages and limitations of different algorithms. 1

Stefanie Czischek

Ola Bratteli, Akitaka Kishimoto, Derek W. Robinson

Jan Krieg, Peter Kopietz

We show that the diagrammatic approach to quantum spin systems developed in a seminal work by Vaks, Larkin, and Pikin [Sov. Phys. JETP 26, 188 (1968)] can be embedded in the framework of the functional renormalization group. The crucial insight is that the generating functional of the time-ordered connected spin correlation functions of an arbitrary quantum spin system satisfies an exact renormalization group flow equation which resembles the corresponding flow equation of interacting bosons. The $SU(2)$ spin algebra is implemented via a nontrivial initial condition for the renormalization group flow. Our method is rather general and offers a different nonperturbative approach to quantum spin systems.