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Anyons, namely particles obeying fractional quantum statistics that interpolate between bosons and fermions, possess a lot of new and exotic physical properties related to the particle exchange statistics. In this work, we explore the few-body quantum dynamics and quantum correlations of indistinguishable anyons with on-site interactions in onedimensional lattices within the scheme of three-body continuous-time quantum walks. By employing a time-evolving block decimation (TEBD) algorithm, we numerically calculate the dynamical evolution process of the local density distribution of anyons among the whole lattice. Numerical simulations shown in the main text mainly focus on a threebody initial state as ψ|(t=0)＞=â†-1â†0â†1|0＞, in which three particles are located on neighbouring sites at lattice centre. This choice of initial state features that the three particles influence one another most strongly, while we have also implemented numerical simulations on other choices of three-body initial states as are discussed in appendix. It is shown that the local density distribution of anyons is dramatically altered by fractional particle statistics with new dynamical structure showing up during the time evolution. For free anyons, an inner cone emerges as the statistical parameter increases, while the outer cone remains robust all along. When the on-site interaction joins in, the structure of the inner cone is further modified with new features. Specifically, for interaction of finite strength, an exotic dynamical asymmetry in real space, is clearly demonstrated during the time evolution of the local density distribution for particles within the fractional statistics regime. However, for boson limit and pseudofermion limit, the time evolution of the local density distribution keeps symmetric as the three-body initial state. And remarkably, the dynamical asymmetry is interactiondependent manifested as the local density distribution of anyons favors opposite side of the lattice for repulsive and attractive interaction, respectively. Moreover, when the on-site interaction is further increased to hard-core limit, the dynamical asymmetry will then be largely suppressed. We also calculate the density-density correlations for anyons before they reach the lattice boundary to reveal the interesting effect of fractional statistics on quantum correlations. It is shown that the inner cone corresponds to co-walking of anyons, while the outer cone is related to individual walking and is immune to the variation of statistical parameter. Furthermore, the exotic real-space asymmetry originated from the interplay of fractional statistics and finite interaction is also shown up in the density-density correlations.
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Keywords:
- indistinguishable anyons /
- fractional statistics /
- multi-particle quantum walk /
- dynamical asymmetry
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[1] Farhi E, Gutmann S 1998 Phys. Rev. A 58915
[2] Aharonov Y, Davidovich L, Zagury N 1993 Phys. Rev. A 481687
[3] Kempe J 2003 Contemp. Phys. 44307
[4] Manouchehri K, Wang J B 2013 Physical implementation of quantum walks (Berlin: Springer)
[5] Karski M, Förster L, Choi J M, Steffen A, Alt W, Meschede D, Widera A 2009 Science 325174
[6] Preiss P M, Ma R, Tai M E, Lukin A, Rispoli M, Zupancic P, Lahini Y, Islam R, Greiner M 2015 Science 3471229
[7] Broome M A, Fedrizzi A, Lanyon B P, Kassal I, Aspuru-Guzik A, White A G 2010 Phys. Rev. Lett.104153602
[8] Xue P, Zhang R, Qin H, Zhan X, Bian Z H, Li J, Sanders B C 2015 Phys. Rev. Lett. 114140502
[9] Ramasesh V V, Flurin E, Rudner M, Siddiqi I, Yao N Y 2017 Phys. Rev. Lett. 118130501
[10] Yan Z, Zhang Y R, Gong M, Wu Y, Zheng Y, Li S, Wang C, Liang F, Lin J, Xu Y, Guo C, Sun L,Peng C Z, Xia K, Deng H, Rong H, You J Q, Nori F, Fan H, Zhu X, Pan J W 2019 Science 364753
[11] Ye Y S, Ge Z Y, Wu Y L, Wang S Y, Gong M, Zhang Y R, Zhu Q L, Yang R, Li S W, Liang F T, Lin J, Xu Y, Guo C, Sun L H, Cheng C, Ma N, Meng Z Y, Deng H, Rong H, Lu C Y, Peng C Z, Fan H, Zhu X B, Pan J W 2019 Phys. Rev. Lett. 123050502
[12] Sansoni L, Sciarrino F, Vallone G, Mataloni P, Crespi A, Ramponi R, Osellame R 2012 Phys. Rev. Lett. 108010502
[13] Du J F, Li H, Xu X D, Shi M J, Wu J H, Zhou X Y, Han R D 2003 Phys. Rev. A 67042316
[14] Schmitz H, Matjeschk R, Schneider C, Glueckert J, Enderlein M, Huber T, Schaetz T 2009 Phys. Rev. Lett. 103090504
[15] Ambainis A 2003 Int. J. Quantum Inf. 1507
[16] Childs A M, Gosset D, Webb Z 2013 Science 339791
[17] Zatelli F, Benedetti C, Paris M G A 2020 Entropy 221321
[18] Venegas-Andraca S E 2012 Quantum Inf. Process. 111015
[19] Kitagawa T, Broome M A, Fedrizzi A, Rudner M S, Berg E, Kassal I, Aspuru-Guzik A, Demler E, White A G 2012 Nat. Commun. 3882
[20] Ramasesh V V, Flurin E, Rudner M, Siddiqi I, Yao N Y 2017 Phys. Rev. Lett. 118130501
[21] Wang K K, Li T Y, Xiao L, Han Y W, Yi W, Xue P 2021 Phys. Rev. Lett. 127270602
[22] Liu W J, Ke Y G, Zhang L, Lee C H 2019 Phys. Rev. A 99063614
[23] Tarallo M G, Mazzoni T, Poli N, Sutyrin D V, Zhang X, Tino G M 2014 Phys. Rev. Lett. 113023005
[24] Yin Y, Katsanos D E, Evangelou S N 2008 Phys. Rev. A 77022302
[25] Beggi A, Buscemi F, Bordone P 2016 Quantum Inf. Process. 153711
[26] Li Z J, Wang J B 2015 Sci. Rep. 513585
[27] Wang L M, Wang L, Zhang Y B 2014 Phys. Rev. A 90063618
[28] Qin X Z, Ke Y G, Guan X W, Li Z B, Andrei N, Lee C H 2014 Phys. Rev. A 90062301
[29] Wang L, Hao Y J, Chen S 2010 Phys. Rev. A 81063637
[30] Ganahl M, Rabel E, Essler F H L, Evertz H G 2012 Phys. Rev. Lett. 108077206
[31] Sarkar S, Sowiński T 2020 Phys. Rev. A 102043326
[32] Wang L, Hao Y J, Chen S 2008 Eur. Phys. J. D 48229
[33] Kraus Y E, Lahini Y, Ringel Z, Verbin M, Zilberberg O 2012 Phys. Rev. Lett. 109106402
[34] Wang L, Liu N, Chen S, Zhang Y B 2015 Phys. Rev. A 92053606
[35] Wang L, Liu N, Chen S, Zhang Y B 2017 Phys. Rev. A 95013619
[36] Cai X M, Yang H T, Shi H L, Lee C H, Andrei N, Guan X W 2021 Phys. Rev. Lett. 127100406
[37] Wilczek F 1982 Phys. Rev. Lett. 49957
[38] Halperin B I 1984 Phys. Rev. Lett. 521583
[39] Haldane F D M 1991 Phys. Rev. Lett. 67937
[40] Stern A 2008 Ann. Phys. 323204
[41] Bartolomei H, Kumar M, Bisognin R, Marguerite A, Berroir J M, Bocquillon E, Plaçais B, Cavanna A, Dong Q, Gennser U, Jin Y, Fève G 2020 Science 368173
[42] Nakamura J, Liang S, Gardner G C, Manfra M J 2020 Nat. Phys. 16931
[43] Nayak C, Simon S H, Stern A, Freedman M, Das Sarma S 2008 Rev. Mod. Phys. 801083
[44] Batchelor M T, Guan X W, Oelkers N 2006 Phys. Rev. Lett. 96210402
[45] Kundu A 1999 Phys. Rev. Lett. 831275
[46] Girardeau M D 2006 Phys. Rev. Lett. 97100402
[47] Keilmann T, Lanzmich S, McCulloch I, Roncaglia M 2011 Nat. Commun. 2361
[48] Greschner S, Santos L 2015 Phys. Rev. Lett. 115053002
[49] Vidal G 2003 Phys. Rev. Lett. 91147902
[50] Hao Y J, Zhang Y B, Chen S 2008 Phys. Rev. A 78023631
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