Quantum thermodynamics of nonequilibrium processes in lattice gauge theories (2404.02965v2)

Abstract: A key objective in nuclear and high-energy physics is to describe nonequilibrium dynamics of matter, e.g., in the early universe and in particle colliders, starting from the Standard Model. Classical-computing methods, via the framework of lattice gauge theory, have experienced limited success in this mission. Quantum simulation of lattice gauge theories holds promise for overcoming computational limitations. Because of local constraints (Gauss's laws), lattice gauge theories have an intricate Hilbert-space structure. This structure complicates the definition of thermodynamic properties of systems coupled to reservoirs during equilibrium and nonequilibrium processes. We show how to define thermodynamic quantities such as work and heat using strong-coupling thermodynamics, a framework that has recently burgeoned within the field of quantum thermodynamics. Our definitions suit instantaneous quenches, simple nonequilibrium processes undertaken in quantum simulators. To illustrate our framework, we compute the work and heat exchanged during a quench in a $\mathbb{Z}_2$ lattice gauge theory coupled to matter in 1+1 dimensions. The thermodynamic quantities, as functions of the quench parameter, evidence a phase transition. For general thermal states, we derive a simple relation between a quantum many-body system's entanglement Hamiltonian, measurable with quantum-information-processing tools, and the Hamiltonian of mean force, used to define strong-coupling thermodynamic quantities.

• The paper introduces a quantum thermodynamic framework to analyze nonequilibrium processes in lattice gauge theories (LGTs), providing methods to define and compute quantities like work and heat applicable to strong-coupling regimes and feasible for quantum simulation.
• Key theoretical developments include adapting thermodynamic quantity definitions for LGTs and establishing a link between the measurable entanglement Hamiltonian and the Hamiltonian of mean force, enabling computation from partial system observations.
• Numerical exploration demonstrates that thermodynamic signatures, such as dissipated work, can reliably signal phase transitions in a $Z_2$ LGT model, highlighting the potential of using quantum simulation to study complex LGT phenomena beyond classical methods.

Quantum Thermodynamics of Nonequilibrium Processes in Lattice Gauge Theories

The paper "Quantum Thermodynamics of Nonequilibrium Processes in Lattice Gauge Theories" presents a theoretical framework for analyzing nonequilibrium thermodynamic processes within the field of lattice gauge theories (LGTs). Authored by Zohreh Davoudi et al., this work situates itself at the intersection of nuclear and high-energy physics, condensed matter, and quantum information science. It aims to overcome the computational limitations of classical simulation methods in studying the nonequilibrium dynamics of strongly interacting gauge theories, as are prominent in the early universe and particle collider environments.

Summary and Core Contributions

This research introduces a quantum thermodynamic perspective to LGTs, focusing on strong-coupling regimes. Traditional approaches to LGT have been impeded by significant challenges, such as the sign problem in Monte-Carlo methods when applied to finite density systems and out-of-equilibrium processes. The authors argue for the applicability of quantum simulators, which do not suffer from such computational problems and are adept at studying thermodynamics within the quantum domain.

The paper achieves the following:

1. Thermodynamic Definitions in LGT: The authors develop a framework to define thermodynamic quantities like work and heat in systems governed by LGTs. These definitions are adapted to the context of strong-coupling thermodynamics, essential due to the non-negligible contributions of interaction energies between subsystems.
2. Instantaneous Quenches: The work describes methods to compute work and heat exchanges during instantaneous quenches—a nonequilibrium protocol feasible in quantum simulators. Such quenches are explored through a specific LGT model using a $Z_2$ gauge theory coupled with matter in one spatial dimension.
3. Hamiltonian of Mean Force: A pivotal theoretical development relates the entanglement Hamiltonian—a tool that can be practically measured in experimental setups—to the Hamiltonian of mean force. This connection facilitates the computation of thermodynamic quantities from partial observations of the whole system.

Theoretical and Practical Implications

The implications of this research reach both theoretical expansions of quantum thermodynamics and practical applications in quantum simulations:

• Theoretical Expansion: By systematically applying quantum thermodynamic concepts to LGTs, this work bridges quantum statistical mechanics and gauge theory, enabling a new layer of analysis for gauge-theoretic models. This bridging is crucial for studying scenarios like quantum chromodynamics (QCD) under nonequilibrium conditions, which are relevant to high-energy physics contexts such as particle collisions.
• Practical Simulation: The framework provides a pathway for efficiently studying work and heat in LGTs using quantum simulators. This capability is especially promising for simulating early universe phenomena and complex nonequilibrium processes, potentially offering insights unreachable by classical methods.

Numerical Results and Future Directions

A noteworthy element of the paper is its numerical exploration of a model quench in a $Z_2$ LGT. The authors demonstrate that thermodynamic signatures, such as the dissipated work and changes in entropy, robustly signal phase transitions. These results underline the effectiveness of their proposed measurement protocols.

Future research directions are abundant and can include:

• Scaling up to more complex non-Abelian gauge theories or higher dimensional settings.
• Investigating whether the proposed thermodynamic measures can detect topological or dynamical phase transitions.
• Extending this framework to simulate realistic scattering processes pertinent to nuclear and particle physics.

The presented framework thus serves both as a proof-of-concept for the application of quantum thermodynamics to LGTs and as a springboard for future experimental and theoretical work in the field. This paper marks a significant step in employing quantum simulation as a tool to address complex problems in gauge theory, with profound implications for understanding the fundamental forces of nature.