Quantum quenches in extended systems

By Pasquale Calabrese, J. Cardy. 2007

557 citations recorded by the source corpus.

We study in general the time evolution of correlation functions in a extended quantum system after the quench of a parameter in the Hamiltonian. We show that correlation functions in d dimensions can be extracted using methods of boundary critical phenomena in d+1 dimensions. For d = 1 this allows us to use the powerful tools of conformal field theory in the case of critical evolution. Several results are obtained in generic dimension in the Gaussian (mean field) approximation. These predictions are checked against the real time evolution of some solvable models that allow us also to understand which features are valid beyond the critical evolution. All our findings may be explained in terms of a picture generally valid, whereby quasiparticles, entangled over regions of the order of the correlation length in the initial state, then propagate with a finite speed through the system. Furthermore we show that the long time results can be interpreted in terms of a generalized Gibbs ensemble. We discuss some open questions and possible future developments.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics

View Paper: https://www.semanticscholar.org/paper/ead99ec024a1a1892133aafdd168a8d1054352b1

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

1. Pasquale Calabrese
2. R. Myers
3. T. Takayanagi
4. J. Cardy
5. T. Nishioka
6. V. Hubeny
7. E. Tonni
8. M. Fagotti

In Condensed Matter Physics

1. Pasquale Calabrese
2. J. Cardy
3. E. Tonni
4. T. Takayanagi
5. T. Nishioka
6. A. Allais
7. R. Myers
8. M. Fagotti

Citations in the corpus

• Entanglement and correlation functions following a local quench: a conformal field theory approach (2007, background): “A careful analysis [19, 12] shows that in fact it corresponds to the correlation length in the initial state and so it is not only a useful tool, but a physical important parameter.”
• Holographic evolution of the mutual information (2011, methodology): “These situations have been studied for two dimensional systems by employing conformal field theory techniques and spin chains models [25, 26, 27, 28, 29].”
• Entanglement temperature and entanglement entropy of excited states (2013, methodology): “Entanglement spectrum also holds a direct relation to the gluing function as well as the gapless edge modes in topological insulators [7, 8].”
• Information flow in black hole evaporation (2019, methodology): “The calculation of the entanglement entropy can then be carried out using replica techniques [44–46].”
• Quantum quenches in the transverse field Ising chain: II. Stationary state properties (2012, background): “[11, 12] it has been shown that for conformal field theories the long time limit of correlation functions after a quantum quench described by a conformally invariant boundary state is described by a thermal (Gibbs) ensemble.”
• The AdS/CFT correspondence (2014, background): “a particular form of global ‘quantum quench’ [88]: namely a sudden disturbance of the system”
• Entanglement entropy and conformal field theory (2009, methodology): “Using the conformal mapping (9), analytically continuing and taking t, one finally gets [120]”
• Measurement-driven entanglement transition in hybrid quantum circuits (2019, background): “Quantum many-body systems under unitary dynamics will generally thermalize [1–7].”
• Spreading of correlations and entanglement after a quench in the one-dimensional Bose–Hubbard model (2008, background): “Further the finding of the spreading of correlations with a finite velocity after a global quench has been verified in specific integrable models [5, 6, 7, 8, 9], as well as for critical systems which can be described by conformal field theory [10, 11].”
• Holographic evolution of entanglement entropy (2010, background): “An analogous conclusion is derived from the evaluation of correlation functions [27, 28].”
• Quench dynamics and relaxation in isolated integrable quantum spin chains (2016, background): “93 J. Cardy, Quantum quenches to a critical point in one dimension: some further results, J. Stat.”
• Entanglement dynamics after quantum quenches in generic integrable systems (2017, methodology): “(25) we just need to fix the conserved value nk = 〈ψ0|n̂k|ψ0〉 which is obtained by elementary methods [12] nk = 〈ψ0|n̂k|ψ0〉 = 〈ψ0|akak|ψ0〉 = 1 4 ( k k + k k ) − 1 2 .”