Dynamical thermalization in Bose-Hubbard systems

Schlagheck, Peter; Shepelyansky, Dima L.

doi:10.1103/physreve.93.012126

Cited by 9 publications

(11 citation statements)

References 41 publications

(51 reference statements)

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“…On the experimental side, an extreme degree of isolation and control has been achieved, such as in the case of ultracold quantum gases [60], trapped ions [61] and also NMR [62]. On the theoretical side, the use of the Hubbard model [53] has proven useful to address the dynamics of strongly-interacting many-body systems [63][64][65]. In addition, for spin systems, numerical studies have provided evidence indicating that the competence between disorder and interactions may lead to highly non-trivial dynamical phase diagrams [115,116].…”

Section: Closed Quantum Systems: To Equilibrate or To Localize?mentioning

confidence: 99%

Loschmidt echo in many-spin systems: a quest for intrinsic decoherence and emergent irreversibility

Zangara¹,

Pastawski²

2017

Phys. Scr.

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If a magnetic polarization excess is locally injected in a crystal of interacting spins in thermal equilibrium, this "excitation" would spread as consequence of spin-spin interactions. Such an apparently irreversible process is known as spin diffusion and it can lead the system back to "equilibrium". Even so, a unitary quantum dynamics would ensure a precise memory of the non-equilibrium initial condition. Then, if at certain time, say t/2, an experimental protocol reverses the many-body dynamics by changing the sign of the effective Hamiltonian, it would drive the system back to the initial non-equilibrium state at time t. As a matter of fact, the reversal is always perturbed by small experimental imperfections and/or uncontrolled internal or environmental degrees of freedom. This limits the amount of signal M (t) recovered locally at time t. The degradation of M (t) accounts for these perturbations, which can also be seen as the sources of decoherence. This general idea defines the Loschmidt echo (LE), which embodies the various time-reversal procedures implemented in nuclear magnetic resonance. Here, we present an invitation to the study of the LE following the pathway induced by the experiments. With such a purpose, we provide a historical and conceptual overview that briefly revisits selected phenomena that underlie the LE dynamics including chaos, decoherence, localization and equilibration. This guiding thread ultimately leads us to the discussion of decoherence and irreversibility as an emergent phenomenon. In addition, we introduce the LE formalism by means of spin-spin correlation functions in a manner suitable for presentation in a broad scope physics journal. Last, but not least, we present new results that could trigger new experiments and theoretical ideas. In particular, we propose to transform an initially localized excitation into a more complex initial state, enabling a dynamically prepared LE. This induces a global definition of the LE in terms of the raw overlap between many-body wave functions. Our results show that as the complexity of the prepared state increases, it becomes more fragile towards small perturbations.

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Section: Closed Quantum Systems: To Equilibrate or To Localize?mentioning

confidence: 99%

Loschmidt echo in many-spin systems: a quest for intrinsic decoherence and emergent irreversibility

Zangara¹,

Pastawski²

2017

Phys. Scr.

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“…These studies demonstrated the stability and efficiency of S(E)-computations confirming validity of the DTC for many-body interacting quantum systems. The dynamical thermalization of an individual eigenstate was also demonstrated in [33,34]. At present the interest of many-body interacting quantum systems is also growing in the context of many-body localization (MBL) and the eigenstate thermalization hypothesis (ETH) (see e.g.…”

Section: Introductionmentioning

confidence: 99%

Dynamical decoherence of a qubit coupled to a quantum dot or the SYK black hole

Frahm

Shepelyansky

2018

Eur. Phys. J. B

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We study the dynamical decoherence of a qubit weakly coupled to a two-body random interaction model (TBRIM) describing a quantum dot of interacting fermions or the Sachdev-Ye-Kitaev (SYK) black hole model. We determine the rates of qubit relaxation and dephasing for regimes of dynamical thermalization of the quantum dot or of quantum chaos in the SYK model. These rates are found to correspond to the Fermi golden rule and quantum Zeno regimes depending on the qubit-fermion coupling strength. An unusual regime is found where these rates are practically independent of TBRIM parameters. We push forward an analogy between TBRIM and quantum small-world networks with an explosive spreading over exponentially large number of states in a finite time being similar to six degrees of separation in small-world social networks. We find that the SYK model has approximately two-three degrees of separation.

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“…The knowledge of the spectral characteristics in a many-body system can be exploited to understand, engineer and control the system's dynamics, making such models and their experimental realizations interesting for the study of quantum thermalization and non-equilibrium transport phenomena, see e.g. [5,11,[13][14][15][16].…”

Section: Introductionmentioning

confidence: 99%

Spectral analysis of two-dimensional Bose-Hubbard models

Fischer¹,

Hoffmann²,

Wimberger³

2016

Phys. Rev. A

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One-dimensional Bose-Hubbard models are well known to obey a transition from regular to quantum-chaotic spectral statistics. We are extending this concept to relatively simple twodimensional many-body models. Also in two dimensions a transition from regular to chaotic spectral statistics is found and discussed. In particular, we analyze the dependence of the spectral properties on the bond number of the two-dimensional lattices and the applied boundary conditions. For maximal connectivity, the systems behave most regularly in agreement with the applicability of mean-field approaches in the limit of many nearest neighbor couplings at each site.

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Dynamical thermalization in Bose-Hubbard systems

Cited by 9 publications

References 41 publications

Loschmidt echo in many-spin systems: a quest for intrinsic decoherence and emergent irreversibility

Loschmidt echo in many-spin systems: a quest for intrinsic decoherence and emergent irreversibility

Dynamical decoherence of a qubit coupled to a quantum dot or the SYK black hole

Spectral analysis of two-dimensional Bose-Hubbard models

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