2000 character limit reached
Entanglement detection in postquench nonequilibrium states: thermal Gibbs vs. generalized Gibbs ensemble
Published 20 Feb 2024 in quant-ph and cond-mat.stat-mech | (2403.07897v1)
Abstract: We use entanglement witnesses related to the entanglement negativity of the state to detect entanglement in the $XY$ chain in the postquench states in the thermodynamic limit after a quench when the parameters of the Hamiltonian are changed suddenly. The entanglement negativity is related to correlations, which in the postquench stationary state are described by a generalized Gibbs ensemble, in the ideal case. If, however, integrability breaking perturbations are present, the system is expected to thermalize. Here we compare the nearest-neighbor entanglement in the two circumstances.
- O. Gühne and G. Tóth, Entanglement detection, Phys. Rep. 474, 1 (2009).
- A. Peres, Separability criterion for density matrices, Phys. Rev. Lett. 77, 1413 (1996).
- P. Horodecki, Separability criterion and inseparable mixed states with positive partial transposition, Phys. Lett. A 232, 333 (1997).
- M. Horodecki, P. Horodecki, and R. Horodecki, Separability of mixed states: necessary and sufficient conditions, Phys. Lett. A 223, 1 (1996).
- B. M. Terhal, Bell inequalities and the separability criterion, Phys. Lett. A 271, 319 (2000).
- G. Tóth, Entanglement witnesses in spin models, Phys. Rev. A 71, 010301(R) (2005).
- G. Tóth and O. Gühne, Detection of multipartite entanglement with two-body correlations, Appl. Phys. B 82, 237 (2006).
- O. Gühne and G. Tóth, Energy and multipartite entanglement in multidimensional and frustrated spin models, Phys. Rev. A 73, 052319 (2006).
- O. Gühne, G. Tóth, and H. J. Briegel, Multipartite entanglement in spin chains, New J. Phys. 7, 229 (2005).
- C. Brukner and V. Vedral, Macroscopic Thermodynamical Witnesses of Quantum Entanglement, arXiv: quant-ph/0406040 (2004).
- M. R. Dowling, A. C. Doherty, and S. D. Bartlett, Energy as an entanglement witness for quantum many-body systems, Phys. Rev. A 70, 062113 (2004).
- T. Vértesi and E. Bene, Thermal entanglement in the nanotubular system Na2V3O7subscriptNa2subscriptV3subscriptO7{\mathrm{Na}}_{2}{\mathrm{V}}_{3}{\mathrm{O}}_{7}roman_Na start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT roman_V start_POSTSUBSCRIPT 3 end_POSTSUBSCRIPT roman_O start_POSTSUBSCRIPT 7 end_POSTSUBSCRIPT, Phys. Rev. B 73, 134404 (2006).
- I. Siloi and F. Troiani, Towards the chemical tuning of entanglement in molecular nanomagnets, Phys. Rev. B 86, 224404 (2012).
- I. Siloi and F. Troiani, Quantum entanglement in heterometallic wheels, Eur. Phys. J. B 86, 71 (2013).
- F. Troiani and I. Siloi, Energy as a witness of multipartite entanglement in chains of arbitrary spins, Phys. Rev. A 86, 032330 (2012).
- T. Homayoun and K. Aghayar, Energy as an entanglement witnesses for one dimensional XYZ Heisenberg lattice: Optimization approach, J. Stat. Phys. 176, 85 (2019).
- F. Troiani, S. Carretta, and P. Santini, Detection of entanglement between collective spins, Phys. Rev. B 88, 195421 (2013).
- G. Vidal and R. F. Werner, Computable measure of entanglement, Phys. Rev. A 65, 032314 (2002).
- E. Barouch, B. M. McCoy, and M. Dresden, Statistical mechanics of the XYXY\mathrm{XY}roman_XY model. I, Phys. Rev. A 2, 1075 (1970).
- E. Barouch and B. M. McCoy, Statistical mechanics of the XYXY\mathrm{XY}roman_XY model. III, Phys. Rev. A 3, 2137 (1971).
- F. Iglói and H. Rieger, Long-range correlations in the nonequilibrium quantum relaxation of a spin chain, Phys. Rev. Lett. 85, 3233 (2000).
- K. Sengupta, S. Powell, and S. Sachdev, Quench dynamics across quantum critical points, Phys. Rev. A 69, 053616 (2004).
- S. Sotiriadis, D. Fioretto, and G. Mussardo, Zamolodchikov–Faddeev algebra and quantum quenches in integrable field theories, J. Stat. Mech.: Theory Exp. 2012 (02), P02017.
- G. Roux, Quenches in quantum many-body systems: One-dimensional bose-hubbard model reexamined, Phys. Rev. A 79, 021608 (2009).
- S. Sotiriadis, P. Calabrese, and J. Cardy, Quantum quench from a thermal initial state, Europhysics Letters 87, 20002 (2009).
- M. Kollar and M. Eckstein, Relaxation of a one-dimensional mott insulator after an interaction quench, Phys. Rev. A 78, 013626 (2008).
- T. Barthel and U. Schollwöck, Dephasing and the steady state in quantum many-particle systems, Phys. Rev. Lett. 100, 100601 (2008).
- M. A. Cazalilla, Effect of suddenly turning on interactions in the Luttinger model, Phys. Rev. Lett. 97, 156403 (2006).
- P. Calabrese and J. Cardy, Time dependence of correlation functions following a quantum quench, Phys. Rev. Lett. 96, 136801 (2006).
- R. Hamazaki, T. N. Ikeda, and M. Ueda, Generalized Gibbs ensemble in a nonintegrable system with an extensive number of local symmetries, Phys. Rev. E 93, 032116 (2016).
- J. Larson, Integrability versus quantum thermalization, J. Phys. B: At. Mol. Opt. Phys. 46, 224016 (2013).
- V. A. Yurovsky and M. Olshanii, Memory of the initial conditions in an incompletely chaotic quantum system: Universal predictions with application to cold atoms, Phys. Rev. Lett. 106, 025303 (2011).
- L. Vidmar and M. Rigol, Generalized Gibbs ensemble in integrable lattice models, J. Stat. Mech.: Theory Exp. 2016 (6), 064007.
- F. H. L. Essler, G. Mussardo, and M. Panfil, Generalized Gibbs ensembles for quantum field theories, Phys. Rev. A 91, 051602 (2015).
- B. Pozsgay, Quantum quenches and generalized Gibbs ensemble in a bethe ansatz solvable lattice model of interacting bosons, J. Stat. Mech.: Theory Exp. 2014 (10), P10045.
- B. Pozsgay, Failure of the generalized eigenstate thermalization hypothesis in integrable models with multiple particle species, J. Stat. Mech.: Theory Exp. 2014 (9), P09026.
- G. Goldstein and N. Andrei, Failure of the local generalized Gibbs ensemble for integrable models with bound states, Phys. Rev. A 90, 043625 (2014).
- P. Calabrese, F. H. L. Essler, and M. Fagotti, Quantum quench in the transverse field ising chain: I. time evolution of order parameter correlators, J. Stat. Mech.: Theory Exp. 2012 (07), P07016.
- B. Blass, H. Rieger, and F. Iglói, Quantum relaxation and finite-size effects in the XY chain in a transverse field after global quenches, EPL (Europhysics Letters) 99, 30004 (2012).
- J. Berges, S. Borsányi, and C. Wetterich, Prethermalization, Phys. Rev. Lett. 93, 142002 (2004).
- M. Kollar, F. A. Wolf, and M. Eckstein, Generalized gibbs ensemble prediction of prethermalization plateaus and their relation to nonthermal steady states in integrable systems, Phys. Rev. B 84, 054304 (2011).
- T. Langen, T. Gasenzer, and J. Schmiedmayer, Prethermalization and universal dynamics in near-integrable quantum systems, Journal of Statistical Mechanics: Theory and Experiment 2016, 064009 (2016).
- K. Mallayya, M. Rigol, and W. De Roeck, Prethermalization and thermalization in isolated quantum systems, Phys. Rev. X 9, 021027 (2019).
- F. M. Surace and O. Motrunich, Weak integrability breaking perturbations of integrable models (2023), arXiv:2302.12804 [cond-mat.stat-mech] .
- T. J. Osborne and M. A. Nielsen, Entanglement in a simple quantum phase transition, Phys. Rev. A 66, 032110 (2002).
- D. Patanè, R. Fazio, and L. Amico, Bound entanglement in the XY model, New J. Phys. 9, 322 (2007).
- M. Hofmann, A. Osterloh, and O. Gühne, Scaling of genuine multiparticle entanglement close to a quantum phase transition, Phys. Rev. B 89, 134101 (2014).
- S. M. Giampaolo and B. C. Hiesmayr, Genuine multipartite entanglement in the xy𝑥𝑦xyitalic_x italic_y model, Phys. Rev. A 88, 052305 (2013).
- F. Iglói and G. Tóth, Entanglement witnesses in the xy𝑥𝑦xyitalic_x italic_y chain: Thermal equilibrium and postquench nonequilibrium states, Phys. Rev. Res. 5, 013158 (2023).
- E. Lieb, T. Schultz, and D. Mattis, Two soluble models of an antiferromagnetic chain, Ann. Phys 16, 407 (1961).
- P. Pfeuty, The one-dimensional ising model with a transverse field, Ann. Phys. 57, 79 (1970).
- M. Rigol, Quantum quenches and thermalization in one-dimensional fermionic systems, Phys. Rev. A 80, 053607 (2009).
- L. Foini, L. F. Cugliandolo, and A. Gambassi, Fluctuation-dissipation relations and critical quenches in the transverse field ising chain, Phys. Rev. B 84, 212404 (2011).
- B. M. Terhal, Detecting quantum entanglement, Theor. Comput. Sci. 287, 313 (2002).
- E. B. Fel’dman and A. N. Pyrkov, Evolution of spin entanglement and an entanglement witness in multiple-quantum nmr experiments, JETP Letters 88, 398 (2008).
- M. Gärttner, P. Hauke, and A. M. Rey, Relating out-of-time-order correlations to entanglement via multiple-quantum coherences, Phys. Rev. Lett. 120, 040402 (2018).
- M. Horodecki, P. Horodecki, and R. Horodecki, Mixed-state entanglement and distillation: Is there a “bound” entanglement in nature?, Phys. Rev. Lett. 80, 5239 (1998).
- A. Sanpera, R. Tarrach, and G. Vidal, Local description of quantum inseparability, Phys. Rev. A 58, 826 (1998).
- S. Rana, Negative eigenvalues of partial transposition of arbitrary bipartite states, Phys. Rev. A 87, 054301 (2013).
- A. Lamacraft, Quantum quenches in a spinor condensate, Phys. Rev. Lett. 98, 160404 (2007).
- T. Kinoshita, T. Wenger, and D. S. Weiss, A quantum newton’s cradle, Nature (London) 440, 900 (2006).
- I. Bloch, J. Dalibard, and W. Zwerger, Many-body physics with ultracold gases, Rev. Mod. Phys. 80, 885 (2008).
- S. Paul, P. Titum, and M. F. Maghrebi, Hidden quantum criticality and entanglement in quench dynamics, arXiv:2202.04654 (2022).
- V. Eisler and Z. Zimborás, On the partial transpose of fermionic gaussian states, New J. Phys. 17, 053048 (2015).
- J. Eisert, V. Eisler, and Z. Zimborás, Entanglement negativity bounds for fermionic gaussian states, Phys. Rev. B 97, 165123 (2018).
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.
