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

Abstract

Loosely speaking, the concept of quantum typicality refers to the fact that a single pure state can imitate the full statistical ensemble. This fact has given rise to a rather simple but remarkably useful numerical approach to simulate the dynamics of quantum many-body systems, called dynamical quantum typicality (DQT). In this paper, we give a brief overview of selected applications of DQT, where particular emphasis is given to questions on transport and thermalization in low-dimensional lattice systems like chains or ladders of interacting spins or fermions. For these systems, we discuss that DQT provides an efficient means to obtain time-dependent equilibrium correlation functions for comparatively large Hilbert-space dimensions and long time scales, allowing the quantitative extraction of transport coefficients within the framework of, e.g., linear response theory. Furthermore, it is discussed that DQT can also be used to study the far-from-equilibrium dynamics resulting from sudden quench scenarios, where the initial state is a thermal Gibbs state of the pre-quench Hamiltonian. Eventually, we summarize a few combinations of DQT with other approaches such as numerical linked cluster expansions or projection operator techniques. In this way, we demonstrate the versatility of DQT.

11 pages, 9 figures

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Cited by in corpus (37)

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• Estimation of equilibration time scales from nested fraction approximations
• Precursors to Anderson Localization in the Holstein Model: Quantum and Quantum-Classical Solutions
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• Real-time broadening of bath-induced density profiles from closed-system correlation functions
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• Spatiotemporal dynamics of classical and quantum density profiles in low-dimensional spin systems
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• Lanczos-Pascal approach to correlation functions in chaotic quantum systems
• Nontrivial damping of quantum many-body dynamics
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• Investigating Stark many-body localization with continuous unitary transformation flows
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• Typical Positivity of Nonequilibrium Entropy Production for Pure States
• Lindblad quantum dynamics from correlation functions of classical spin chains
• Nontrivial damping of magnetization currents in perturbed spin chains
• Quantum typicality approach to energy flow between two spin-chain domains at different temperatures
• Boundary-driven magnetization transport in the spin-$1/2$ XXZ chain: Role of the system-bath coupling strength and timescales