Relation between far-from-equilibrium dynamics and equilibrium correlation functions for binary operators

Abstract

Linear response theory (LRT) is one of the main approaches to the dynamics of quantum manybody systems. However, this approach has limitations and requires, e.g., that the initial state is (i) mixed and (ii) close to equilibrium. In this paper, we discuss these limitations and study the nonequilibrium dynamics for a certain class of properly prepared initial states. Specifically, we consider thermal states of the quantum system in the presence of an additional static force which, however, become nonequilibrium states when this static force is eventually removed. While for weak forces the relaxation dynamics is well captured by LRT, much less is known in the case of strong forces, i.e., initial states far away from equilibrium. Summarizing our main results, we unveil that, for high temperatures, the nonequilibrium dynamics of so-called binary operators is always generated by an equilibrium correlation function. In particular, this statement holds true for states in the far-from-equilibrium limit, i.e., outside the linear response regime. In addition, we confirm our analytical results by numerically studying the dynamics of local fermionic occupation numbers and local energy densities in the spin-1/2 Heisenberg chain. Remarkably, these simulations also provide evidence that our results qualitatively apply in a more general setting, e.g., in the anisotropic XXZ model where the local energy is a non-binary operator, as well as for a wider range of temperature. Furthermore, exploiting the concept of quantum typicality, all of our findings are not restricted to mixed states, but are valid for pure initial states as well.

Quantum versus classical dynamics in spin models: Chains, ladders, and square lattices

“…( 19) is very accurate even for a single |ψ , and no averaging is required. In the high-temperature limit β → 0, the correlation function C(t ) can also be approximated on the basis of just one auxiliary pure state [79],…”

Quantum versus Classical Dynamics in Spin Models: Chains, Ladders, and Square Lattices

“…( 19) is very accurate even for a single |ψ , and no averaging is required. In the high-temperature limit β → 0, the correlation function C(t) can also be approximated on the basis of just one auxiliary pure state 77 ,…”

Selected applications of typicality to real-time dynamics of quantum many-body systems

“…The post-quench Hamiltonian can, for instance, be created by adding or removing a static (weak or strong) force of strength to the initial Hamiltonian, i.e., H 2 = H 1 ± A, where the operator A is conjugated to the force [12,57,80,81]. The resulting expectation value dynamics of, e.g., the operator A is given by…”

“…Generally, the theoretical analysis of quantum manybody dynamics is notoriously difficult. Given a quantum system H and an arbitrary nonequilibrium state ρ(0), universal concepts to describe the resulting dynamics are rare [10][11][12], and one is usually required to solve the microscopic equation of motion for the density matrix ρ(t), i.e., the von-Neumann equation…”