Melting a Hubbard dimer: benchmarks of `ALDA' for quantum thermodynamics

Abstract

The competition between evolution time, interaction strength, and temperature challenges our understanding of many-body quantum systems out-of-equilibrium. Here we consider a benchmark system, the Hubbard dimer, which allows us to explore all the relevant regimes and calculate exactly the related average quantum work. At difference with previous studies, we focus on the effect of increasing temperature, and show how this can turn competition between many-body interactions and driving field into synergy. We then turn to use recently proposed protocols inspired by density functional theory to explore if these effects could be reproduced by using simple approximations. We find that, up to and including intermediate temperatures, a method which borrows from ground-state adiabatic local density approximation improves dramatically the estimate for the average quantum work, including, in the adiabatic regime, when correlations are strong. However at high temperature and at least when based on the pseudo-LDA, this method fails to capture the counterintuitive qualitative dependence of the quantum work with interaction strength, albeit getting the quantitative estimates relatively close to the exact results.

References in corpus (30)

• Density functional method for nonequilibrium electron transport
• Perspective on density functional theory
• Quantum many-body systems out of equilibrium
• Progress in Time-Dependent Density-Functional Theory
• Time-dependent density functional theory: Past, present, and future
• Quantum Thermodynamics
• The role of quantum information in thermodynamics --- a topical review
• Fluctuation theorems: Work is not an observable
• The Nonequilibrium Thermodynamics of Small Systems
• Experimental Test of Quantum Jarzynski Equality with a Trapped Ion System
• Experimental reconstruction of work distribution and verification of fluctuation relations at the full quantum level
• The Statistics of the Work Done on a Quantum Critical System by Quenching a Control Parameter
• Time-dependent quantum transport: A practical scheme using density functional theory
• Two Fermions in a double well: Exploring a fundamental building block of the Hubbard model
• Perspective: Quantum Thermodynamics
• Experimental rectification of entropy production by a Maxwell's Demon in a quantum system
• Density-functionals not based on the electron gas: Local-density approximation for a Luttinger liquid
• Irreversibility and the arrow of time in a quenched quantum system
• Experimental demonstration of information to energy conversion in a quantum system at the Landauer Limit
• The Hubbard Dimer: A density functional case study of a many-body problem
• Entanglement and density-functional theory: testing approximations on Hooke's atom
• Thermal density functional theory: Time-dependent linear response and approximate functionals from the fluctuation-dissipation theorem
• Work and Quantum Phase Transitions: Is there Quantum Latency?
• Time Dependent Density Functional Theory meets Dynamical Mean Field Theory: Real-Time Dynamics for the 3D Hubbard model
• Challenging Adiabatic Time-dependent Density Functional Theory with a Hubbard Dimer: The Case of Time-Resolved Long-Range Charge Transfer
• The Hubbard model as an approximation to the entanglement in nanostructures
• DFT-inspired methods for quantum thermodynamics
• Theory of Entropy Production in Quantum Many-Body Systems
• Quantum work distribution for a driven diatomic molecule
• Towards Quantum Cybernetics

Cited by in corpus (7)

• Many-body effects on the thermodynamics of closed quantum systems
• Density functionals and Kohn-Sham potentials with minimal wavefunction preparations on a quantum computer
• (Spin-)density-functional theory for open-shell systems: exact magnetization density functional for the half-filled Hubbard trimer
• Easy access to energy fluctuations in non-equilibrium quantum many-body systems
• Characterizing Adiabaticity in Quantum Many-Body Systems at Finite Temperature
• Approximating quantum thermodynamic properties using DFT
• Full Quantum Work Statistics for Non-Homogeneous Many-Body Systems