Mainz 2026 – scientific programme

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Q: Fachverband Quantenoptik und Photonik

Q 43: Poster – Quantum Systems

Q 43.6: Poster

Wednesday, March 4, 2026, 17:00–19:00, Philo 2. OG

Imaginary-Time Truncated Wigner Approximation for the simulation of many-body spin-1/2 systems — •Tom Schlegel, Jens Hartmann, Dennis Breu, and Michael Fleischhauer — RPTU Kaiserslautern, Kaiserslautern, Germany

The recently developed Truncated Wigner Approximation (TWA) for spins [1] is a semiclassical method to describe interacting spin-1/2-systems including dephasing and decay. Instead of finding exact solutions in the exponentially growing Hilbert space, the method employs a mapping from the equation of motion of many-body density matrix to stochastic differential equations of classical variables in a continuous phase space. The method, which improves on a mean-field description by including leading order quantum corrections, was successfully employed to simulate the real-time dynamics of several models.

We here further develop the TWA method to an imaginary-time evolution, i.e. for the simulation of finite-temperature states and ground states of interacting spin systems. Specifically we derive the imaginary-time TWA for spin-1/2-systems, highlight emerging problems and discuss how to deal with them. We then benchmark the method for single-particle Hamiltonians. In order to assess the ability of the TWA method to faithfully describe quantum phase transitions, we analyze the one and two-dimensional transverse-field Ising model finding rather good agreement of the critical behavior simulated by TWA with exact results.

[1] C. Mink et al., PhysRevResearch.4.043136

Keywords: Truncated Wigner Approximation; Imaginary Time Evolution; Phase Space Methods; Ising model; Spin systems