Integrable Trotterization: Local Conservation Laws and Boundary Driving.

Area of Science:

• Quantum mechanics
• Statistical mechanics
• Condensed matter physics

Background:

• Interacting lattice models are crucial in condensed matter physics.
• Simulating real-time dynamics and nonequilibrium states is computationally challenging.
• Integrable models offer exact solutions but are often limited to equilibrium or specific dynamics.

Purpose of the Study:

• To develop a general procedure for constructing integrable real-time Trotterizations of interacting lattice models.
• To analyze the application of this method to the spin-1/2 Heisenberg chain.
• To investigate nonequilibrium steady-state properties and propose conservation laws.

Main Methods:

• Construction of an integrable real-time Trotterization procedure.
• Derivation of local conservation laws using an inhomogeneous transfer matrix and boost operator for periodic boundary conditions.
• Examination of nonequilibrium dynamics using a Kraus representation and stochastic boundary driving.
• Development of a staggered matrix product ansatz for the nonequilibrium steady-state density matrix.

Main Results:

• The general Trotterization procedure is demonstrated on the spin-1/2 Heisenberg chain.
• Local charges in the continuous time limit reduce to known integrals of motion.
• An exact nonequilibrium steady-state density matrix is derived for the open system.
• Quasilocal conservation laws are proposed for the periodic boundary condition model.

Conclusions:

• The developed Trotterization scheme provides an integrable framework for real-time dynamics of lattice models.
• The method is particularly effective for studying nonequilibrium steady states in open systems.
• This approach holds promise for experimental simulations using trapped ion and atom optics setups.