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We review recent developments in the study of out-of-equilibrium topological states of matter in isolated systems.
Absence of diffusion in certain random lattices
P. W. Anderson · 1958
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Interactions and the anderson transition
L. Fleishman and P. Anderson · 1980
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Localization in a disordered elastic medium near two dimensions
S. John, H. Sompolinsky and M. J. Stephen · 1983
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Experimental evidence for the haldane gap in a spin-1 nearly isotropic, antiferromagnetic chain
W. J. L. Buyers, R. M. Morra, R. L. Armstrong, M. J. Hogan, P. Gerlach and K. Hirakawa · 1986
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Quantum statistical mechanics in a closed system
J. M. Deutsch · 1991
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Chaos and quantum thermalization
M. Srednicki · 1994
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Critical behavior of random transverse-field Ising spin chains
D. S. Fisher · 1995
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Nonstandard symmetry classes in mesoscopic normal-superconducting hybrid structures
A. Altland and M. R. Zirnbauer · 1997
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Bosonic excitations in random media
V. Gurarie and J. T. Chalker · 2003
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Fault-tolerant quantum computation by anyons
A. Kitaev · 2003
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Quantum Field Theory of Many-Body Systems: From the Origin of Sound to an Origin of Light and Electrons
X. Wen · 2004
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Interacting electrons in disordered wires: Anderson localization and low- t t transport
I. Gornyi, A. Mirlin and D. Polyakov · 2005
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Quantum spin hall effect in graphene
C. L. Kane and E. J. Mele · 2005
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Quantum glassiness in strongly correlated clean systems: An example of topological overprotection
C. Chamon · 2005
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Metal-insulator transition in a weakly interacting many-electron system with localized single-particle states
D. Basko, I. Aleiner and B. Altshuler · 2006
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Quantum spin hall effect and topological phase transition in hgte quantum wells
B. A. Bernevig, T. L. Hughes and S.-C. Zhang · 2006
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Anyons in an exactly solved model and beyond
A. Kitaev · 2006
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Topological entanglement entropy
A. Kitaev and J. Preskill · 2006
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Detecting topological order in a ground state wave function
M. Levin and X.-G. Wen · 2006
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Localization of interacting fermions at high temperature
V. Oganesyan and D. A. Huse · 2007
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Quantum spin hall insulator state in hgte quantum wells
M. Konig, S. Wiedmann, C. Brune, A. Roth, H. Buhmann, L. W. Molenkamp, X.-L. Qi and S.-C. Zhang · 2007
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Topological insulators in three dimensions
L. Fu, C. L. Kane and E. J. Mele · 2007
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Topological invariants of time-reversal-invariant band structures
J. E. Moore and L. Balents · 2007
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Interacting anyons in topological quantum liquids: The golden chain
A. Feiguin, S. Trebst, A. W. W. Ludwig, M. Troyer, A. Kitaev, Z. Wang and M. H. Freedman · 2007
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Many-body localization in the heisenberg xxz magnet in a random field
M. Žnidarič, T. c. v. Prosen and P. Prelovšek · 2008
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A topological dirac insulator in a quantum spin hall phase
D. Hsieh, D. Qian, L. Wray, Y. Xia, Y. S. Hor, R. J. Cava and M. Z. Hasan · 2008
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Classification of topological insulators and superconductors in three spatial dimensions
A. P. Schnyder, S. Ryu, A. Furusaki and A. W. W. Ludwig · 2008
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Non-Abelian anyons and topological quantum computation
C. Nayak, S. H. Simon, A. Stern, M. Freedman and S. Das Sarma · 2008
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Collective states of interacting fibonacci anyons
S. Trebst, E. Ardonne, A. Feiguin, D. A. Huse, A. W. W. Ludwig and M. Troyer · 2008
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Topological phases and the quantum spin hall effect in three dimensions
R. Roy · 2009
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Tensor-entanglement-filtering renormalization approach and symmetry-protected topological order
Z.-C. Gu and X.-G. Wen · 2009
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Periodic table for topological insulators and superconductors
A. Kitaev · 2009
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Topological phases and quantum computation
A. Kitaev and C. Laumann · 2009
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Sufficient symmetry conditions for topological quantum order
Z. Nussinov and G. Ortiz · 2009
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Colloquium: topological insulators
M. Z. Hasan and C. L. Kane · 2010
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The birth of topological insulators
J. E. Moore · 2010
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Many-body localization phase transition
A. Pal and D. A. Huse · 2010
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Effects of interactions on the topological classification of free fermion systems
L. Fidkowski and A. Kitaev · 2010
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Complete classification of one-dimensional gapped quantum phases in interacting spin systems
X. Chen, Z.-C. Gu and X.-G. Wen · 2011
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Topological phases of one-dimensional fermions: An entanglement point of view
A. M. Turner, F. Pollmann and E. Berg · 2011
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Topological phases of fermions in one dimension
L. Fidkowski and A. Kitaev · 2011
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Two-dimensional symmetry-protected topological orders and their protected gapless edge excitations
X. Chen, Z.-X. Liu and X.-G. Wen · 2011
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Diagnosing deconfinement and topological order
K. Gregor, D. A. Huse, R. Moessner and S. L. Sondhi · 2011
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Floquet topological insulator in semiconductor quantum wells
N. H. Lindner, G. Refael and V. Galitski · 2011
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Topological order in an exactly solvable 3d spin model
S. Bravyi, B. Leemhuis and B. M. Terhal · 2011
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Local stabilizer codes in three dimensions without string logical operators
J. Haah · 2011
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Unbounded growth of entanglement in models of many-body localization
J. H. Bardarson, F. Pollmann and J. E. Moore · 2012
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Symmetry protection of topological phases in one-dimensional quantum spin systems
F. Pollmann, E. Berg, A. M. Turner and M. Oshikawa · 2012
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Theory and classification of interacting integer topological phases in two dimensions: A chern-simons approach
Y.-M. Lu and A. Vishwanath · 2012
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Braiding statistics approach to symmetry-protected topological phases
M. Levin and Z.-C. Gu · 2012
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Symmetry-protected topological orders in interacting bosonic systems
X. Chen, Z.-C. Gu, Z.-X. Liu and X.-G. Wen · 2012
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Parafermionic edge zero modes in 𝕫 n {\mathbb{z}}_{n} invariant spin chains
P. Fendley · 2012
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Superconducting proximity effect on the edge of fractional topological insulators
M. Cheng · 2012
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Topological quantum glassiness
C. Castelnovo and C. Chamon · 2012
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Orthogonal metals: The simplest non-fermi liquids
R. Nandkishore, M. A. Metlitski and T. Senthil · 2012
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Localization-protected quantum order
D. A. Huse, R. Nandkishore, V. Oganesyan, A. Pal and S. L. Sondhi · 2013
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Area laws in a many-body localized state and its implications for topological order
B. Bauer and C. Nayak · 2013
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Local conservation laws and the structure of the many-body localized states
M. Serbyn, Z. Papić and D. A. Abanin · 2013
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Many-body localization in one dimension as a dynamical renormalization group fixed point
R. Vosk and E. Altman · 2013
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Symmetry protected topological orders and the group cohomology of their symmetry group
X. Chen, Z.-C. Gu, Z.-X. Liu and X.-G. Wen · 2013
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Many-body localization in a quasiperiodic system
S. Iyer, V. Oganesyan, G. Refael and D. A. Huse · 2013
Earlier work this paper cites.
Exotic non-abelian anyons from conventional fractional quantum hall states
D. J. Clarke, J. Alicea and K. Shtengel · 2013
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Observation of floquet-bloch states on the surface of a topological insulator
Y. H. Wang, H. Steinberg, P. Jarillo-Herrero and N. Gedik · 2013
Cited alongside, same era.
Photonic Floquet topological insulators
M. C. Rechtsman, J. M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev and A. Szameit · 2013
Cited alongside, same era.
Quantum self-correction in the 3d cubic code model
S. Bravyi and J. Haah · 2013
Cited alongside, same era.
Exotic topological order in fractal spin liquids
B. Yoshida · 2013
Cited alongside, same era.
Many-body localization and symmetry-protected topological order
A. Chandran, V. Khemani, C. R. Laumann and S. L. Sondhi · 2014
Cited alongside, same era.
On Many-Body Localization for Quantum Spin Chains
J. Z. Imbrie · 2014
Cited alongside, same era.
Abelian floquet symmetry-protected topological phases in one dimension
R. Roy and F. Harper · 2016
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A bound on chaos
J. Maldacena, S. H. Shenker and D. Stanford · 2016
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Fractal symmetries: Ungauging the cubic code
D. J. Williamson · 2016
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Robustness of many-body localization in the presence of dissipation
E. Levi, M. Heyl, I. Lesanovsky and J. P. Garrahan · 2016
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Dynamics of a many-body-localized system coupled to a bath
M. H. Fischer, M. Maksymenko and E. Altman · 2016
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Influence of dephasing on many-body localization
M. V. Medvedyeva, T. c. v. Prosen and M. Žnidarič · 2016
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Phenomenology of fully many-body-localized systems
D. A. Huse, R. Nandkishore and V. Oganesyan · 2014
Cited alongside, same era.
Interferometric probes of many-body localization
M. Serbyn, M. Knap, S. Gopalakrishnan, Z. Papić, N. Y. Yao, C. R. Laumann, D. A. Abanin, M. D. Lukin and E. A. Demler · 2014
Cited alongside, same era.
Quantum quenches in the many-body localized phase
M. Serbyn, Z. Papić and D. A. Abanin · 2014
Cited alongside, same era.
Hilbert-Glass Transition: New Universality of Temperature-Tuned Many-Body Dynamical Quantum Criticality
D. Pekker, G. Refael, E. Altman, E. Demler and V. Oganesyan · 2014
Cited alongside, same era.
Many-body localization in a disordered quantum ising chain
J. A. Kjäll, J. H. Bardarson and F. Pollmann · 2014
Cited alongside, same era.
Dynamical quantum phase transitions in random spin chains
R. Vosk and E. Altman · 2014
Cited alongside, same era.
Obtaining highly excited eigenstates of many-body localized hamiltonians by the density matrix renormalization group approach
V. Khemani, F. Pollmann and S. L. Sondhi · 2016
Later among the works it cites.
Many-body localization and transition by density matrix renormalization group and exact diagonalization studies
S. P. Lim and D. N. Sheng · 2016
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Entanglement scaling of excited states in large one-dimensional many-body localized systems
D. M. Kennes and C. Karrasch · 2016
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Power-law entanglement spectrum in many-body localized phases
M. Serbyn, A. A. Michailidis, D. A. Abanin and Z. Papić · 2016
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Recent progress in many-body localization
D. A. Abanin and Z. Papić · 2017
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Many-body localization: an introduction and selected topics
F. Alet and N. Laflorencie · 2017
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Slow scrambling in disordered quantum systems
B. Swingle and D. Chowdhury · 2017
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Out-of-time-ordered correlators in many-body localized systems
Y. Huang, Y.-L. Zhang and X. Chen · 2017
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Eigenstate phase transitions and the emergence of universal dynamics in highly excited states
S. A. Parameswaran, A. C. Potter and R. Vasseur · 2017
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Machine learning out-of-equilibrium phases of matter
J. Venderley, V. Khemani and E.-A. Kim · 2017
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Private communication (2017)
V. Khemani and D. Huse · 2017
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Private communication (2017)
S. Sondhi · 2017
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Effect of su(2) symmetry on many-body localization and thermalization
I. V. Protopopov, W. W. Ho and D. A. Abanin · 2017
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Localization-protected order in spin chains with non-Abelian discrete symmetries
A. J. Friedman, R. Vasseur, A. C. Potter and S. A. Parameswaran · 2017
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Eigenstate phases with finite on-site non-abelian symmetry
A. Prakash, S. Ganeshan, L. Fidkowski and T.-C. Wei · 2017
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Floquet topological order in interacting systems of bosons and fermions
F. Harper and R. Roy · 2017
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Stability and instability towards delocalization in many-body localization systems
W. De Roeck and F. Huveneers · 2017
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Thermal inclusions: how one spin can destroy a many-body localized phase
P. Ponte, C. R. Laumann, D. A. Huse and A. Chandran · 2017
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Rare-region effects and dynamics near the many-body localization transition
K. Agarwal, E. Altman, E. Demler, S. Gopalakrishnan, D. A. Huse and M. Knap · 2017
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Solvable model for a dynamical quantum phase transition from fast to slow scrambling
S. Banerjee and E. Altman · 2017
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Private communication (2017)
E. Altman · 2017
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How a small quantum bath can thermalize long localized chains
D. J. Luitz, F. m. c. Huveneers and W. De Roeck · 2017
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Signatures of many-body localization in a controlled open quantum system
H. P. Lüschen, P. Bordia, S. S. Hodgman, M. Schreiber, S. Sarkar, A. J. Daley, M. H. Fischer, E. Altman, I. Bloch and U. Schneider · 2017
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How does a locally constrained quantum system localize?
C. Chen, F. Burnell and A. Chandran · 2017
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Emergent local integrals of motion without a complete set of localized eigenstates
S. D. Geraedts, R. N. Bhatt and R. Nandkishore · 2017
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Prethermal phases of matter protected by time-translation symmetry
D. V. Else, B. Bauer and C. Nayak · 2017
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Discrete time crystals: Rigidity, criticality, and realizations
N. Y. Yao, A. C. Potter, I.-D. Potirniche and A. Vishwanath · 2017
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Observation of a discrete time crystal
J. Zhang, P. W. Hess, A. Kyprianidis, P. Becker, A. Lee, J. Smith, G. Pagano, I. D. Potirniche, A. C. Potter, A. Vishwanath, N. Y. Yao and C. Monroe · 2017
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Observation of discrete time-crystalline order in a disordered dipolar many-body system
S. Choi, J. Choi, R. Landig, G. Kucsko, H. Zhou, J. Isoya, F. Jelezko, S. Onoda, H. Sumiya, V. Khemani, C. von Keyserlingk, N. Y. Yao, E. Demler and M. D. Lukin · 2017
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Floquet topological phases with symmetry in all dimensions
R. Roy and F. Harper · 2017
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An infinite family of 3d Floquet topological paramagnets
A. C. Potter, A. Vishwanath and L. Fidkowski · 2017
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Quantum entanglement growth under random unitary dynamics
A. Nahum, J. Ruhman, S. Vijay and J. Haah · 2017
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Dynamics of entanglement and transport in 1D systems with quenched randomness
A. Nahum, J. Ruhman and D. A. Huse · 2017
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Operator Spreading in Random Unitary Circuits
A. Nahum, S. Vijay and J. Haah · 2017
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Operator spreading and the emergence of dissipation in unitary dynamics with conservation laws
V. Khemani, A. Vishwanath and D. A. Huse · 2017
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Operator hydrodynamics, OTOCs, and entanglement growth in systems without conservation laws
C. von Keyserlingk, T. Rakovszky, F. Pollmann and S. Sondhi · 2017
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Diffusive hydrodynamics of out-of-time-ordered correlators with charge conservation
T. Rakovszky, F. Pollmann and C. W. von Keyserlingk · 2017
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Solution of a minimal model for many-body quantum chaos
A. Chan, A. De Luca and J. T. Chalker · 2017
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Prethermal strong zero modes and topological qubits
D. V. Else, P. Fendley, J. Kemp and C. Nayak · 2017
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Long coherence times for edge spins
J. Kemp, N. Y. Yao, C. R. Laumann and P. Fendley · 2017
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Localization of Extended Quantum Objects
M. Pretko and R. M. Nandkishore · 2017
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Fracton topological order via coupled layers
H. Ma, E. Lake, X. Chen and M. Hermele · 2017
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Isotropic Layer Construction and Phase Diagram for Fracton Topological Phases
S. Vijay · 2017
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Fracton topological phases from strongly coupled spin chains
G. B. Halász, T. H. Hsieh and L. Balents · 2017
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Emergent Phases of Fractonic Matter
A. Prem, M. Pretko and R. Nandkishore · 2017
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Recoverable Information and Emergent Conservation Laws in Fracton Stabilizer Codes
A. T. Schmitz, H. Ma, R. M. Nandkishore and S. A. Parameswaran · 2017
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Glassy quantum dynamics in translation invariant fracton models
A. Prem, J. Haah and R. Nandkishore · 2017
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Decipher the nonlocal entanglement entropy of fracton topological orders
B. Shi and Y.-M. Lu · 2017
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Topological Entanglement Entropy of Fracton Stabilizer Codes
H. Ma, A. T. Schmitz, S. A. Parameswaran, M. Hermele and R. M. Nandkishore · 2017
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Many body localized systems weakly coupled to baths
R. Nandkishore and S. Gopalakrishnan · 2017
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Spin-catalyzed hopping conductivity in disordered strongly interacting quantum wires
S. A. Parameswaran and S. Gopalakrishnan · 2017
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Finding matrix product state representations of highly excited eigenstates of many-body localized hamiltonians
X. Yu, D. Pekker and B. K. Clark · 2017
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Efficient representation of fully many-body localized systems using tensor networks
T. B. Wahl, A. Pal and S. H. Simon · 2017
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Non-fermi glasses: Localized descendants of fractionalized metals
S. A. Parameswaran and S. Gopalakrishnan · 2017
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Correlation function diagnostics for type-i fracton phases
T. Devakul, S. A. Parameswaran and S. L. Sondhi · 2018
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