Evolution of entanglement entropy following a quantum quench : Analytic results for the XY chain in a transverse magnetic field
By M. Fagotti, Pasquale Calabrese. 2008
271 citations recorded by the source corpus.
The non-equilibrium evolution of extended quantum systems is one of the most challenging problems of contemporary research in theoretical physics. The subject is in a renaissance era after the experimental realization [1] of cold atomic systems that can evolve out of equilibrium in the absence of any dissipation and with high degree of tunability of Hamiltonian parameters. A strongly limiting factor for a better understanding of these phenomena is the absence of effective numerical methods to simulate the dynamics of quantum systems. For methods like time dependent density matrix renormalization group (tDMRG) [2] this lack of efficiency has been traced back [3] to a too fast increasing of the entanglement entropy between parts of the whole system and the impossibility for a classical computer to store and manipulate such large amount of quantum information. This observation partially moved the interest from the study of local observables to the understanding of the evolution of the entanglement entropy and in particular to its growth with time [5, 6]. Based on early results from conformal field theory [6, 7] and on exact/numerical ones for simple solvable model [6, 8] it is widely accepted [3] that the entanglement entropy grows linearly with time for a so called global quench (i.e. when the initial state differs globally from the ground state and the excess of energy is extensive), while at most logarithmically for a local one (i.e. when the the initial state has only a local difference with the ground state and so a little excess of energy). As a consequence a local quench is simulable by means of tDMRG, while a global one is not. However, despite this fundamental interest and a large effort of the community, still analytic results are lacking. In this letter we fill this gap providing the analytic expression of the entanglement entropy at any time in the limit of a large block for the XY chain in a transverse magnetic field described by the Hamiltonian
Subfields: Atomic and Molecular Physics, and Optics
View Paper: https://www.semanticscholar.org/paper/b7a49516b2b6415f2ef8d92091c5ff75e7b78d0e
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In Atomic and Molecular Physics, and Optics
Citations in the corpus
- Entanglement in a fermion chain under continuous monitoring (2018, background): “, λ`, where ` = x2−x1 + 1, the entanglement entropy (8) is given by [43,65,69]”
- Quantum quenches in 1 + 1 dimensional conformal field theories (2016, methodology): “and in quantum simulations, such as in [63, 64, 67, 68, 69, 70, 71, 72, 73, 74] (but this list is far from being exhaustive).”
- Entanglement entropy of excited states (2009, background): “It is known that for a global quench, the entanglement entropy first increases linearly with the time and then saturates to a values proportional to the length of the block ` [23, 24, 25].”
- Entanglement entropy and conformal field theory (2009, methodology): “The exact form of f (p′, p′′) has been exactly calculated only for the XY model in a transverse field [124].”
- Entanglement entropy of two disjoint blocks in XY chains (2010, background): “This subleading term is present also for the single-interval case [34], and can be included in the asymptotic result [35].”
- Quantum quenches in the transverse field Ising chain: II. Stationary state properties (2012, background): “Longitudinal versus Transverse Correlators A global quantum quench of the transverse field in the Ising model is an essentially ideal testing ground for many ideas related to thermalization [49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61].”
- Quench dynamics and relaxation in isolated integrable quantum spin chains (2016, background): “A key result obtained in [48] is that after quenches to conformal field theories the von Neumann entropy of a subsystem of length increases linearly in time until it eventually saturates (see the review by Calabrese and Cardy [88] in this volume)”
- Random Quantum Circuits (2022, background): “Nature Reviews Physics, 2(8):411–425, 2020.”
- Entanglement dynamics after quantum quenches in generic integrable systems (2017, background): “For the Ising model our result agrees with the ab initio derivation in [69], providing a further benchmark of the ideas pursued in this paper and in [10].”