Efficient computations of quantum canonical Gibbs state in phase space

TL;DR

This paper introduces a highly accurate and efficient method for computing the quantum canonical Gibbs state in phase space by directly solving the Bloch equation, enabling advanced nonequilibrium quantum simulations.

Contribution

It presents a novel numerical approach to compute the Gibbs state Wigner function with near machine precision, addressing a longstanding computational challenge.

Findings

Achieved nearly machine accuracy in Gibbs state Wigner function calculations.

Provided algorithms for high-quality Wigner distributions of various quantum states.

Enabled efficient quantum simulations directly in phase space.

Abstract

The Gibbs canonical state, as a maximum entropy density matrix, represents a quantum system in equilibrium with a thermostat. This state plays an essential role in thermodynamics and serves as the initial condition for nonequilibrium dynamical simulations. We solve a long standing problem for computing the Gibbs state Wigner function with nearly machine accuracy by solving the Bloch equation directly in the phase space. Furthermore, the algorithms are provided yielding high quality Wigner distributions for pure stationary states as well as for Thomas-Fermi and Bose-Einstein distributions. The developed numerical methods furnish a long-sought efficient computation framework for nonequilibrium quantum simulations directly in the Wigner representation.