Quantum thermodynamics for lattice gauge theories

Quantum computers hold promise for simulating gauge theories, which model fundamental forces, condensed matter, and more. Gauge theories obey Gauss’s laws—local constraints that restrict a system to an entanglement-rich subspace. This restriction prevents one from straightforwardly partitioning the system into independent, localized system-of-interest degrees of freedom (DOFs) and analogous environmental DOFs. Yet heat is often defined as the energy exchanged by a system and its environment. How, then, can one formulate a gauge theory’s thermodynamics? We do so by applying strong-coupling thermodynamics, a toolkit recently under development in the field of quantum thermodynamics. Using this toolkit, we define the work and heat exchanged within a lattice-gauge-theory (LGT) system during a quench protocol performable on quantum simulators. The heat and work, we show, obey the first and second laws of thermodynamics. Moreover, the quantities are expected to be experimentally measurable. We illustrate our framework by numerically simulating a Z₂ LGT coupled to matter in 1+1 dimensions. Our thermodynamic quantities evidence a phase transition. This work opens the door for a quantum thermodynamic theory of LGTs.