Utilizing the Truncated Wigner Approximation for real and imaginary time evolution of spins

The simulation of large-scale quantum systems faces exponential complexity and becomes intractable in most higher-dimensional settings. The recently developed Truncated Wigner Approximation (TWA) for spins [1, 2] provides a powerful approach for simulating dissipative, interacting spin systems with a large number of spins, incorporating leading-order quantum effects. We further developed the method to not only real time but also imaginary time evolution and are therefore able to calculate thermal and ground states of large interacting spin systems [3]. With these tools we study the quantum contact process in one and two dimensions as well as ground state quantum phase transitions of the transverse field Ising model.

[1] C. Mink, M. Fleischhauer, SciPost Phys. 15, 233 (2023)

[2] J. Hartmann, T. Schlegel, C. Mink, M. Fleischhauer, Truncated Wigner Approximation for unitary and open many-body spin systems (in preparation)

[3] T. Schlegel, D. Breu, M. Fleischhauer, Imaginary-time evolution of interacting spin systems in the truncated Wigner approximation (in preparation)