A variational approach for many-body systems at finite temperature

Abstract

We introduce a non-linear differential flow equation for density matrices that provides a monotonic decrease of the free energy and reaches a fixed point at the Gibbs thermal state. We use this equation to build a variational approach for analyzing equilibrium states of many-body systems and demonstrate that it can be applied to a broad class of states, including all bosonic and fermionic Gaussian states, as well as their generalizations obtained by unitary transformations, such as polaron transformations, in electron-phonon systems. We benchmark this method with a BCS lattice Hamiltonian and apply it to the Holstein model in two dimensions. For the latter, our approach reproduces the transition between the BCS pairing regime at weak interactions and the polaronic regime at stronger interactions, displaying phase separation between superconducting and charge-density wave phases.

arXiv comment5 pages, 3 figures, Supplemental Material 6 pages

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• Gaussian time-dependent variational principle for the finite-temperature anharmonic lattice dynamics
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• Emergence of a sharp quantum collective mode in a one-dimensional Fermi polaron
• Chemistry of a light impurity in a Bose-Einstein condensate
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• A Hybrid Quantum-Classical Method for Electron-Phonon Systems
• Rényi free energy and variational approximations to thermal states
• Particle zoo in a doped spin chain: Correlated states of mesons and magnons
• Variational Neural and Tensor Network Approximations of Thermal States
• Spin-deformation coupling in two-dimensional polar materials
• Thermal Tensor Network Simulations of Lattice Fermions with Fixed Filling
• Excitations of Quantum Many-Body Systems via Purified Ensembles: A Unitary-Coupled-Cluster-based Approach
• Attractive and repulsive angulons in superfluid environments