Built on

P. W. Anderson, Absence of diffusion in certain random lattices . Phys. Rev. 109, 1492 (1958)
1958
Earlier work this paper cites.
F. J. Wegner, Duality in generalized Ising models and phase transitions without local order parameters . Journal of Mathematical Physics 12, 2259 (1971)
1971
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M. P. A. Fisher, Vortex-Glass Superconductivity: A Possible New Phase in Bulk High- T c T_{c} Oxides . Phys. Rev. Lett. 62, 1415 (1989)
1989
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J. M. Deutsch, Quantum statistical mechanics in a closed system . Physical Review A. 43 (4): 2046 (1991)
1991
Earlier work this paper cites.
D. S. Fisher, M. P. A. Fisher, and D. A. Huse, Thermal fluctuations, quenched disorder, phase transitions, and transport in type-II superconductors . Phys. Rev. B 43, 130 (1991)
1991
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A. Pal and D. A. Huse, Many-body localization phase transition . Phys. Rev. B 82, 174411 (2010), arXiv:1010.1992
Original
1992
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M. Srednicki, Chaos and quantum thermalization . Phys Rev E 50, 888 (1994), arXiv:cond-mat/9403051v2
1994
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O. Motrunich et al., Infinite-randomness quantum Ising critical fixed points . Phys. Rev. B 61, 1160 (2000), arXiv:cond-mat/9906322
2000
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N. Laflorencie and H. Rieger, Scaling of the spin stiffness in random spin-1/2 chains: Crossover from pure-metallic behavior to random singlet-localized regime . Eur. Phys. J. B 40, 201 (2004), arXiv:cond-mat/0402198v3
2004
Earlier work this paper cites.
T.H. Hansson, V. Oganesyan and S.L. Sondhi, Superconductors are topologically ordered , Annals Of Physics vol. 313, 497 (2004), arXiv:cond-mat/0404327
2004
Earlier work this paper cites.
I. V. Gornyi, A. D. Mirlin, and D. G. Polyakov, Interacting electrons in disordered wires: Anderson localization and low-T transport . Phys. Rev. Lett. 95, 206603 (2005), arXiv:cond-mat/0506411
2005
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J. Polchinski, String Theory: Volume I . Cambridge University Press (2005)
2005
Earlier work this paper cites.
D. Basko, I. Aleiner, and B. Altshuler, Metal–insulator transition in a weakly interacting many-electron system with localized single-particle states . Annals of Physics 321, 5 1126 (2006), arXiv:cond-mat/0506617v2
2006
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D. Basko, I. Aleiner, and B. Altshuler, On the problem of many-body localization . arXiv:cond-mat/0602510 (2006)
2006
Earlier work this paper cites.
V. Oganesyan and D. A. Huse, Localization of interacting fermions at high temperature . Phys. Rev. B 75, 155111 (2007), arXiv:cond-mat/0610854
2007
Earlier work this paper cites.
M. Rigol, V. Dunjko and M. Olshanii, Thermalization and its mechanism for generic isolated quantum systems Nature 452, 854 (2008)
2008
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M. Znidaric, T. Prosen, and P. Prelovsek, Many-body localization in the Heisenberg XXZ magnet in a random field . Phys. Rev. B 77, 064426 (2008), arXiv:0706.2539v2
Original
2008
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C. Castelnovo and C. Chamon, Topological order in a 3d toric code at finite temperature . Phys. Rev. B 78, 155120 (2008), arXiv:0804.3591v2
Original
2008
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J.M. Martinis, M. Ansmann and J. Aumentado, Energy decay in superconducting Josephson junction qubits from non-equilibrium quasiparticle excitations . Phys. Rev. Lett. 103, 097002 (2009), arXiv:0904.2171v2
Original
2009
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J. H. Bardarson, F. Pollman, and J. E. Moore, Unbounded growth of entanglement in models of many-body localization . Phys. Rev. Lett. 109, 017202 (2012), arXiv:1202.5532v2
Original
2012
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D. A. Huse et al., Localization protected quantum order . Phys. Rev. B 88, 014206 (2013), arXiv:1304.1158
Original
2013
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B. Bauer and C. Nayak, Area laws in a many-body localized state and its implications for topological order . J. Stat. Mech. P09005 (2013), arXiv:1306.5753v2
Original
2013
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M. Serbyn, Z. Papic, and D. A. Abanin, Local conservation laws and the structure of the many-body localized states . Phys. Rev. Lett. 111, 127201 (2013), arXiv:1305.5554v2
Original
2013
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B. Swingle, A simple model of many-body localization . arXiv:1307.0507 (2013)
Original
2013
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M. Serbyn, Z. Papic, and D. A. Abanin, Universal slow growth of entanglement in interacting strongly disordered systems . Phys. Rev. Lett. 110, 260601 (2013), arXiv:1304.4605v3
Original
2013
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B. Bauer and C. Nayak, Area laws in a many-body localized state and its implications for topological order . J. Stat. Mech. P09005 (2013), arXiv:1306.5753v2
Original
2013
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A. Chandran et al., Many-body localization and symmetry protected topological order . Phys. Rev. B. 89, 144201 (2014), arXiv:1310.1096v2
Original
2014
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D. A. Huse, R. Nandkishore, and V. Oganesyan, Phenomenology of fully many-body-localized systems . Phys. Rev. B 90, 174202 (2014), arXiv:1408.4297v2
Original
2014
Earlier work this paper cites.

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2017

Localization of Extended Quantum Objects

Pretko, Michael, Nandkishore, Rahul M.

Understand

A quantum system of particles can exist in a localized phase, exhibiting ergodicity breaking and maintaining forever a local memory of its initial conditions.

We generalize this concept to a system of extended objects, such as strings and membranes, arguing that such a system can also exhibit localization in the presence of sufficiently strong disorder (randomness) in the Hamiltonian.
We show that localization of large extended objects can be mapped to a lower-dimensional many-body localization problem.
For example, motion of a string involves propagation of point-like signals down its length to keep the different segments in causal contact.

Built on

P. W. Anderson, Absence of diffusion in certain random lattices . Phys. Rev. 109, 1492 (1958)
1958
Earlier work this paper cites.
F. J. Wegner, Duality in generalized Ising models and phase transitions without local order parameters . Journal of Mathematical Physics 12, 2259 (1971)
1971
Earlier work this paper cites.
M. P. A. Fisher, Vortex-Glass Superconductivity: A Possible New Phase in Bulk High- T c T_{c} Oxides . Phys. Rev. Lett. 62, 1415 (1989)
1989
Earlier work this paper cites.
J. M. Deutsch, Quantum statistical mechanics in a closed system . Physical Review A. 43 (4): 2046 (1991)
1991
Earlier work this paper cites.
D. S. Fisher, M. P. A. Fisher, and D. A. Huse, Thermal fluctuations, quenched disorder, phase transitions, and transport in type-II superconductors . Phys. Rev. B 43, 130 (1991)
1991
Earlier work this paper cites.
A. Pal and D. A. Huse, Many-body localization phase transition . Phys. Rev. B 82, 174411 (2010), arXiv:1010.1992
Original
1992
Earlier work this paper cites.
M. Srednicki, Chaos and quantum thermalization . Phys Rev E 50, 888 (1994), arXiv:cond-mat/9403051v2
1994
Earlier work this paper cites.
O. Motrunich et al., Infinite-randomness quantum Ising critical fixed points . Phys. Rev. B 61, 1160 (2000), arXiv:cond-mat/9906322
2000
Earlier work this paper cites.
N. Laflorencie and H. Rieger, Scaling of the spin stiffness in random spin-1/2 chains: Crossover from pure-metallic behavior to random singlet-localized regime . Eur. Phys. J. B 40, 201 (2004), arXiv:cond-mat/0402198v3
2004
Earlier work this paper cites.
T.H. Hansson, V. Oganesyan and S.L. Sondhi, Superconductors are topologically ordered , Annals Of Physics vol. 313, 497 (2004), arXiv:cond-mat/0404327
2004
Earlier work this paper cites.
I. V. Gornyi, A. D. Mirlin, and D. G. Polyakov, Interacting electrons in disordered wires: Anderson localization and low-T transport . Phys. Rev. Lett. 95, 206603 (2005), arXiv:cond-mat/0506411
2005
Earlier work this paper cites.
J. Polchinski, String Theory: Volume I . Cambridge University Press (2005)
2005
Earlier work this paper cites.
D. Basko, I. Aleiner, and B. Altshuler, Metal–insulator transition in a weakly interacting many-electron system with localized single-particle states . Annals of Physics 321, 5 1126 (2006), arXiv:cond-mat/0506617v2
2006
Earlier work this paper cites.
D. Basko, I. Aleiner, and B. Altshuler, On the problem of many-body localization . arXiv:cond-mat/0602510 (2006)
2006
Earlier work this paper cites.
V. Oganesyan and D. A. Huse, Localization of interacting fermions at high temperature . Phys. Rev. B 75, 155111 (2007), arXiv:cond-mat/0610854
2007
Earlier work this paper cites.
M. Rigol, V. Dunjko and M. Olshanii, Thermalization and its mechanism for generic isolated quantum systems Nature 452, 854 (2008)
2008
Earlier work this paper cites.
M. Znidaric, T. Prosen, and P. Prelovsek, Many-body localization in the Heisenberg XXZ magnet in a random field . Phys. Rev. B 77, 064426 (2008), arXiv:0706.2539v2
Original
2008
Earlier work this paper cites.
C. Castelnovo and C. Chamon, Topological order in a 3d toric code at finite temperature . Phys. Rev. B 78, 155120 (2008), arXiv:0804.3591v2
Original
2008
Earlier work this paper cites.
J.M. Martinis, M. Ansmann and J. Aumentado, Energy decay in superconducting Josephson junction qubits from non-equilibrium quasiparticle excitations . Phys. Rev. Lett. 103, 097002 (2009), arXiv:0904.2171v2
Original
2009
Earlier work this paper cites.
K. Gregor et al., Diagnosing deconfinement and topological order . New J. Phys. 13:025009 (2011), arXiv:1011.4187
Original
2011
Earlier work this paper cites.
M. Lenander et al
Original
2011
Earlier work this paper cites.
P.J. de Visser et al
Original
2011
Earlier work this paper cites.
J. H. Bardarson, F. Pollman, and J. E. Moore, Unbounded growth of entanglement in models of many-body localization . Phys. Rev. Lett. 109, 017202 (2012), arXiv:1202.5532v2
Original
2012
Earlier work this paper cites.
D. A. Huse et al., Localization protected quantum order . Phys. Rev. B 88, 014206 (2013), arXiv:1304.1158
Original
2013
Earlier work this paper cites.
B. Bauer and C. Nayak, Area laws in a many-body localized state and its implications for topological order . J. Stat. Mech. P09005 (2013), arXiv:1306.5753v2
Original
2013
Earlier work this paper cites.
M. Serbyn, Z. Papic, and D. A. Abanin, Local conservation laws and the structure of the many-body localized states . Phys. Rev. Lett. 111, 127201 (2013), arXiv:1305.5554v2
Original
2013
Earlier work this paper cites.
B. Swingle, A simple model of many-body localization . arXiv:1307.0507 (2013)
Original
2013
Earlier work this paper cites.
M. Serbyn, Z. Papic, and D. A. Abanin, Universal slow growth of entanglement in interacting strongly disordered systems . Phys. Rev. Lett. 110, 260601 (2013), arXiv:1304.4605v3
Original
2013
Earlier work this paper cites.
B. Bauer and C. Nayak, Area laws in a many-body localized state and its implications for topological order . J. Stat. Mech. P09005 (2013), arXiv:1306.5753v2
Original
2013
Earlier work this paper cites.
J. Wenner et al
Original
2013
Earlier work this paper cites.
D. Riste et al
Original
2013
Earlier work this paper cites.
A. Chandran et al., Many-body localization and symmetry protected topological order . Phys. Rev. B. 89, 144201 (2014), arXiv:1310.1096v2
Original
2014
Earlier work this paper cites.
D. A. Huse, R. Nandkishore, and V. Oganesyan, Phenomenology of fully many-body-localized systems . Phys. Rev. B 90, 174202 (2014), arXiv:1408.4297v2
Original
2014
Earlier work this paper cites.