scholarly journals Entanglement spreading in non-equilibrium integrable systems

2020 ◽  
Author(s):  
Pasquale Calabrese
Keyword(s):  
Summer School ◽  
Condensed Matter ◽  
Entanglement Entropy ◽  
Interaction Strength ◽  
Quantum Systems ◽  
Equilibrium Dynamics ◽  
Thermodynamic Entropy ◽  
Short Course ◽  
Quasiparticle Picture ◽  
Non Equilibrium

These are lecture notes for a short course given at the Les Houches Summer School on ``Integrability in Atomic and Condensed Matter Physics'', in summer 2018. Here, I pedagogically discuss recent advances in the study of the entanglement spreading during the non-equilibrium dynamics of isolated integrable quantum systems. I first introduce the idea that the stationary thermodynamic entropy is the entanglement accumulated during the non-equilibrium dynamics and then join such an idea with the quasiparticle picture for the entanglement spreading to provide quantitive predictions for the time evolution of the entanglement entropy in arbitrary integrable models, regardless of the interaction strength.

scholarly journals Transport in one-dimensional integrable quantum systems

2020 ◽  
Author(s):  
Jesko Sirker
Keyword(s):  
Transport Properties ◽  
Spin Chain ◽  
Linear Response ◽  
Summer School ◽  
Condensed Matter ◽  
Quantum Systems ◽  
Integrable Models ◽  
One Dimensional ◽  
Integrable Quantum ◽  
Linear Response Regime

These notes are based on a series of three lectures given at the Les Houches summer school on ’Integrability in Atomic and Condensed Matter Physics’ in August 2018. They provide an introduction into the unusual transport properties of integrable models in the linear response regime focussing, in particular, on the spin-1/21/2 XXZ spin chain.

scholarly journals Steady Floquet-Andreev States Probed by Tunnelling Spectroscopy

2021 ◽  
Author(s):  
Gil-Ho Lee ◽  
Sein Park ◽  
Wonjun Lee ◽  
Seong Jang ◽  
Yong-Bin Choi ◽  
...  
Keyword(s):  
Phase Difference ◽  
Theoretical Calculations ◽  
Condensed Matter ◽  
Spectral Characteristics ◽  
Interaction Strength ◽  
Microwave Frequency ◽  
Quantum States ◽  
New Paradigm ◽  
Non Equilibrium ◽  
Floquet States

Abstract Engineering quantum states through light-matter interaction has created a new paradigm in condensed matter physics. A representative example is the Floquet-Bloch state, which is generated by time-periodically driving the Bloch wavefunctions in crystals. Previous attempts to realise such states in condensed matter systems have been limited by the transient nature of the Floquet states produced by optical pulses, which masks the universal properties of non-equilibrium physics. Here, we report the generation of steady Floquet Andreev (F-A) states in graphene Josephson junctions by continuous microwave application and direct measurement of their spectra by superconducting tunnelling spectroscopy. We present quantitative analysis of the spectral characteristics of the F-A states while varying the phase difference of superconductors, temperature, microwave frequency and power. The oscillations of the F-A state spectrum with phase difference agreed with our theoretical calculations. Moreover, we confirmed the steady nature of the F-A states by establishing a sum rule of tunnelling conductance, and analysed the spectral density of Floquet states depending on Floquet interaction strength. This study provides a basis for understanding and engineering non-equilibrium quantum states in nano-devices.

scholarly journals Entanglement dynamics after quantum quenches in generic integrable systems

2018 ◽  
Vol 4 (3) ◽  
Author(s):  
Vincenzo Alba ◽  
Pasquale Calabrese
Keyword(s):  
Entanglement Entropy ◽  
Maximum Velocity ◽  
Quantum Systems ◽  
Analytic Description ◽  
One Dimensional ◽  
Quantum Quenches ◽  
Interacting Systems ◽  
Crucial Information ◽  
Quasiparticle Picture ◽  
Dependent State

The time evolution of the entanglement entropy in non-equilibrium quantum systems provides crucial information about the structure of the time-dependent state. For quantum quench protocols, by combining a quasiparticle picture for the entanglement spreading with the exact knowledge of the stationary state provided by Bethe ansatz, it is possible to obtain an exact and analytic description of the evolution of the entanglement entropy. Here we discuss the application of these ideas to several integrable models. First we show that for non-interacting systems, both bosonic and fermionic, the exact time-dependence of the entanglement entropy can be derived by elementary techniques and without solving the dynamics. We then provide exact results for interacting spin chains that are carefully tested against numerical simulations. Finally, we apply this method to integrable one-dimensional Bose gases (Lieb-Liniger model) both in the attractive and repulsive regimes. We highlight a peculiar behaviour of the entanglement entropy due to the absence of a maximum velocity of excitations.

scholarly journals Entanglement evolution and generalised hydrodynamics: interacting integrable systems

2019 ◽  
Vol 7 (1) ◽  
Author(s):  
Vincenzo Alba ◽  
Bruno Bertini ◽  
Maurizio Fagotti
Keyword(s):  
Integrable Systems ◽  
Entanglement Entropy ◽  
Integrable Models ◽  
Analytical Prediction ◽  
Bipartite Entanglement ◽  
Entanglement Evolution ◽  
Thermodynamic Entropy ◽  
Quasiparticle Picture

We investigate the dynamics of bipartite entanglement after the sudden junction of two leads in interacting integrable models. By combining the quasiparticle picture for the entanglement spreading with Generalised Hydrodynamics we derive an analytical prediction for the dynamics of the entanglement entropy between a finite subsystem and the rest. We find that the entanglement rate between the two leads depends only on the physics at the interface and differs from the rate of exchange of thermodynamic entropy. This contrasts with the behaviour in free or homogeneous interacting integrable systems, where the two rates coincide.

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