Relaxation of dynamically prepared out-of-equilibrium initial states within and beyond linear response theory

Richter, Jonas; Lamann, Mats H.; Bartsch, Christian; Steinigeweg, Robin; Gemmer, Jochen

doi:10.1103/physreve.100.032124

Cited by 9 publications

(6 citation statements)

References 71 publications

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“…( 138) is a mathematically rigorous statement if |ψ is essentially drawn at random from a sufficiently large Hilbert space (Bartsch and Gemmer, 2009;Reimann, 2007). In fact, the idea of using random states |ψ has a long history (Alben et al, 1975;De Raedt and De Vries, 1989;Jaklič and Prelovšek, 1994) and is at the basis of various numerical approaches to the density of states (Hams and De Raedt, 2000), thermodynamic quantities (De Vries and De Raedt, 1993;Shimizu, 2012, 2013;Wietek et al, 2019), equilibrium correlation functions (Elsayed and Fine, 2013;Iitaka and Ebisuzaki, 2003;Rousochatzakis et al, 2019;Steinigeweg et al, 2014aSteinigeweg et al, , 2016b, non-equilibrium processes (Endo et al, 2018;Monnai and Sugita, 2014;Richter et al, 2019c), as well as ETH (Steinigeweg et al, 2014c). In this review, we focus on the case of equilibrium correlation functions.…”

Section: Dynamical Quantum Typicalitymentioning

confidence: 99%

Finite-temperature transport in one-dimensional quantum lattice models

et al. 2021

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Section: Dynamical Quantum Typicalitymentioning

confidence: 99%

Finite-temperature transport in one-dimensional quantum lattice models

et al. 2021

View full text Add to dashboard Cite

“…( 145) is a mathematically rigorous statement if |ψ is essentially drawn at random from a sufficiently large Hilbert space (Bartsch and Gemmer, 2009;Reimann, 2007). In fact, the idea of using random states |ψ has a long history (Alben et al, 1975;De Raedt and De Vries, 1989;Jaklič and Prelovšek, 1994) and is at the basis of various numerical approaches to the density of states (Hams and De Raedt, 2000), thermodynamic quantities (De Vries and De Raedt, 1993;Shimizu, 2012, 2013;Wietek et al, 2019), equilibrium correlation functions (Elsayed and Fine, 2013;Iitaka and Ebisuzaki, 2003;Rousochatzakis et al, 2019;Steinigeweg et al, 2014aSteinigeweg et al, , 2016b, non-equilibrium processes (Endo et al, 2018;Monnai and Sugita, 2014;Richter et al, 2019d), as well as ETH (Steinigeweg et al, 2014c). In this review, we focus on the case of equilibrium correlation functions.…”

Section: Dynamical Quantum Typicalitymentioning

confidence: 99%

Finite-temperature transport in one-dimensional quantum lattice models

Bertini,

Heidrich-Meisner,

Karrasch

et al. 2020

Preprint

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The last decade has witnessed an impressive progress in the theoretical understanding of transport properties of clean, one-dimensional quantum lattice systems. Many physically relevant models in one dimension are Bethe-ansatz integrable, including the anisotropic spin-1/2 Heisenberg (also called spin-1/2 XXZ chain) and the Fermi-Hubbard model. Nevertheless, practical computations of, for instance, correlation functions and transport coefficients pose hard problems from both the conceptual and technical point of view. Only due to recent progress in the theory of integrable systems on the one hand and due to the development of numerical methods on the other hand has it become possible to compute their finite temperature and nonequilibrium transport properties quantitatively. Most importantly, due to the discovery of a novel class of quasilocal conserved quantities, there is now a qualitative understanding of the origin of ballistic finite-temperature transport, and even diffusive or super-diffusive subleading corrections, in integrable lattice models. We shall review the current understanding of transport in one-dimensional lattice models, in particular, in the paradigmatic example of the spin-1/2 XXZ and Fermi-Hubbard models, and we elaborate on state-of-the-art theoretical methods, including both analytical and computational approaches. Among other novel techniques, we discuss matrix-product-states based simulation methods, dynamical typicality, and, in particular, generalized hydrodynamics. We will discuss the close and fruitful connection between theoretical models and recent experiments, with examples from both the realm of quantum magnets and ultracold quantum gases in optical lattices.

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“…The typicality approximation (4) has proven to be very useful to calculate equilibrium quantities of quantum many-body systems such as the specific heat, entropy, or magnetic susceptibility [33][34][35][36]40]. For the purpose of this review, however, it is most important to note that typicality is not just restricted to equilibrium properties, but also extends to the real-time dynamics of quantum expectation values [16,[26][27][28][41][42][43]. This dynamical version of typicality forms the basis of the numerical approach to time-dependent correlation functions and out-of-equilibrium dynamics more generally, which is discussed in Sec.…”

Section: What Is Typicality?mentioning

confidence: 99%

“…7 and Ref. [43] for a more detailed description of the protocol). Here, the accuracy of the DQT approach is demonstrated by comparing to data obtained by exact diagonalization.…”

Section: Applications To Far-from-equilibrium Dynamicsmentioning

confidence: 99%

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

Heitmann,

Richter,

Schubert

et al. 2020

Preprint

Self Cite

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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.

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Relaxation of dynamically prepared out-of-equilibrium initial states within and beyond linear response theory

Cited by 9 publications

References 71 publications

Finite-temperature transport in one-dimensional quantum lattice models

Finite-temperature transport in one-dimensional quantum lattice models

Finite-temperature transport in one-dimensional quantum lattice models

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

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