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Models for non-unitary quantum dynamics, such as quantum circuits that include projective measurements, have been shown to exhibit rich quantum critical behavior.
1903
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Bernard Derrida, “Can disorder induce several phase transitions?” Physics Reports 103
1984
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1986
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J L Cardy, “Logarithmic corrections to finite-size scaling in strips,” Journal of Physics A: Mathematical and General 19
1986
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Andreas W. W. Ludwig, “Critical behavior of the two-dimensional random q-state potts model by expansion in (q - 2),” Nuclear Physics B 285
1987
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Andreas W. W. Ludwig and John L. Cardy, “Perturbative evaluation of the conformal anomaly at new critical points with applications to random systems,” Nuclear Physics B 285
1987
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J T Chalker and P D Coddington, “Percolation, quantum tunnelling and the integer hall effect,” Journal of Physics C: Solid State Physics 21
1988
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Franz Wegner, “Four-loop-order β \beta -function of nonlinear σ \sigma -models in symmetric spaces,” Nuclear Physics B 316
1989
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Andreas W. W. Ludwig, “Infinite hierarchies of exponents in a diluted ferromagnet and their interpretation,” Nuclear Physics B 330
1990
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Renate Gade and Franz Wegner, “The n = 0 replica limit of u(n) and u(n)/so(n) models,” Nuclear Physics B 360
1991
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Renate Gade, “Anderson localization for sublattice models,” Nuclear Physics B 398
1993
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1994
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Daniel S Fisher, “Random antiferromagnetic quantum spin chains,” Physical Review B 50
1994
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Andreas W. W. Ludwig, Matthew P. A. Fisher, R. Shankar, and G. Grinstein, “Integer quantum hall transition: An alternative approach and exact results,” Phys. Rev. B 50
1994
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Martin R. Zirnbauer, “Riemannian symmetric superspaces and their origin in random‐matrix theory,” Journal of Mathematical Physics 37
1996
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H. M. Wiseman, “Quantum trajectories and quantum measurement theory,” Quantum and Semiclassical Optics 8
1996
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K. Efetov, Supersymmetry in Disorder and Chaos (Cambridge University Press, 1996)
1996
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Alexander Altland and Martin R Zirnbauer, “Nonstandard symmetry classes in mesoscopic normal-superconducting hybrid structures,” Physical Review B 55
1997
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Shanhui Xiong, N. Read, and A. Douglas Stone, “Mesoscopic conductance and its fluctuations at a nonzero hall angle,” Phys. Rev. B 56
1997
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Martin Janssen, Marcus Metzler, and Martin R. Zirnbauer, “Point-contact conductances at the quantum hall transition,” Phys. Rev. B 59
1999
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Ilya A. Gruzberg, Andreas W. W. Ludwig, and N. Read, “Exact exponents for the spin quantum hall transition,” Phys. Rev. Lett. 82
1999
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Ian Affleck and Shaojin Qin, “Logarithmic corrections in quantum impurity problems,” Journal of Physics A: Mathematical and General 32
1999
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S. Guruswamy, A. LeClair, and A. W. W. Ludwig, “gl(n/n) super-current algebras for disordered dirac fermions in two dimensions,” Nuclear Physics B 583
2000
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Olexei Motrunich, Kedar Damle, and David A Huse, “Griffiths effects and quantum critical points in dirty superconductors without spin-rotation invariance: One-dimensional examples,” Physical Review B 63
2001
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J. T. Chalker, N. Read, V. Kagalovsky, B. Horovitz, Y. Avishai, and A. W. W. Ludwig, “Thermal metal in network models of a disordered two-dimensional superconductor,” Phys. Rev. B 65
2001
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Barbara M Terhal and David P DiVincenzo, “Classical simulation of noninteracting-fermion quantum circuits,” Physical Review A 65
2002
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Jean Zinn-Justin, Quantum field theory and critical phenomena , 4th ed., International series of monographs on physics (Oxford, England); 113 (Clarendon Press ; Oxford University Press, Oxford : New York, 2002)
2002
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Marc Bocquet and J. T. Chalker, “Network models for localization problems belonging to the chiral symmetry classes,” Phys. Rev. B 67
2003
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G. Vidal, J.I. Latorre, E. Rico, and A. Kitaev, “Entanglement in Quantum Critical Phenomena,” Phys. Rev. Lett. 90
2003
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2003
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Andreas W.W. Ludwig and Kay Jörg Wiese, “The 4-loop β \beta -function in the 2d non-abelian thirring model, and comparison with its conjectured “exact” form,” Nuclear Physics B 661
2003
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Sergey Bravyi, “Lagrangian representation for fermionic linear optics,” Preprint (2004), arXiv:quant-ph/0404180
2004
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Frank Verstraete and J Ignacio Cirac, “Renormalization algorithms for quantum-many body systems in two and higher dimensions,” arXiv preprint cond-mat/0407066 (2004)
2004
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Pasquale Calabrese and John Cardy, “Entanglement entropy and quantum field theory,” Journal of Statistical Mechanics: Theory and Experiment 2004
2004
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G. Refael and J. E. Moore, “Entanglement entropy of random quantum critical points in one dimension,” Phys. Rev. Lett. 93
2004
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2004
Cited alongside, same era.
2004
Cited alongside, same era.
Pasquale Calabrese and John Cardy, “Evolution of entanglement entropy in one-dimensional systems,” Journal of Statistical Mechanics: Theory and Experiment 2005
2005
Cited alongside, same era.
Vladislav Popkov and Mario Salerno, “Logarithmic divergence of the block entanglement entropy for the ferromagnetic heisenberg model,” Phys. Rev. A 71
2005
Cited alongside, same era.
Andreas W. W. Ludwig, Hermann Schulz-Baldes, and Michael Stolz, “Lyapunov spectra for all ten symmetry classes of quasi-one-dimensional disordered systems of non-interacting fermions,” Journal of Statistical Physics 152
2013
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Y. Y. Atas, E. Bogomolny, O. Giraud, and G. Roux, “Distribution of the ratio of consecutive level spacings in random matrix ensembles,” Phys. Rev. Lett. 110
2013
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Chong Wang and T. Senthil, “Interacting fermionic topological insulators/superconductors in three dimensions,” Physical Review B 89
2014
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J. Dubail and N. Read, “Tensor network trial states for chiral topological phases in two dimensions and a no-go theorem in any dimension,” Phys. Rev. B 92
2015
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2005
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Michael M. Wolf, “Violation of the Entropic Area Law for Fermions,” Phys. Rev. Lett. 96
2006
Cited alongside, same era.
Eduardo Fradkin and Joel E. Moore, “Entanglement entropy of 2d conformal quantum critical points: Hearing the shape of a quantum drum,” Phys. Rev. Lett. 97
2006
Cited alongside, same era.
V. Oganesyan and D. A. Huse, “Localization of interacting fermions at high temperature,” Phys. Rev. B 75
2007
Cited alongside, same era.
Veronika E Hubeny, Mukund Rangamani, and Tadashi Takayanagi, “A covariant holographic entanglement entropy proposal,” Journal of High Energy Physics 2007
2007
Cited alongside, same era.
Viktor Eisler and Ingo Peschel, “Evolution of entanglement after a local quench,” Journal of Statistical Mechanics: Theory and Experiment 2007
2007
Cited alongside, same era.
Maurizio Fagotti and Pasquale Calabrese, “Evolution of entanglement entropy following a quantum quench: Analytic results for the x y xy chain in a transverse magnetic field,” Phys. Rev. A 78
2008
Cited alongside, same era.
2008
Cited alongside, same era.
2015
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Andreas W W Ludwig, “Topological phases: classification of topological insulators and superconductors of non-interacting fermions, and beyond,” Physica Scripta T168
2015
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Glen Evenbly and Steven R. White, “Entanglement renormalization and wavelets,” Phys. Rev. Lett. 116
2016
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Adam Nahum, Jonathan Ruhman, Sagar Vijay, and Jeongwan Haah, “Quantum entanglement growth under random unitary dynamics,” Physical Review X 7
2017
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Sergey Bravyi and David Gosset, “Complexity of quantum impurity problems,” Communications in Mathematical Physics 356
2017
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Adam Nahum, Sagar Vijay, and Jeongwan Haah, “Operator spreading in random unitary circuits,” Physical Review X 8
2018
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Yaodong Li, Xiao Chen, and Matthew PA Fisher, “Quantum zeno effect and the many-body entanglement transition,” Physical Review B 98
2018
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Jutho Haegeman, Brian Swingle, Michael Walter, Jordan Cotler, Glen Evenbly, and Volkher B. Scholz, “Rigorous free-fermion entanglement renormalization from wavelet theory,” Phys. Rev. X 8
2018
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2018
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John Watrous, The theory of quantum information (Cambridge University Press, 2018)
2018
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Tianci Zhou and Adam Nahum, “Emergent statistical mechanics of entanglement in random unitary circuits,” Physical Review B 99
2019
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Brian Skinner, Jonathan Ruhman, and Adam Nahum, “Measurement-induced phase transitions in the dynamics of entanglement,” Phys. Rev. X 9
2019
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Yaodong Li, Xiao Chen, and Matthew PA Fisher, “Measurement-driven entanglement transition in hybrid quantum circuits,” Physical Review B 100
2019
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Shriya Pai, Michael Pretko, and Rahul M Nandkishore, “Localization in fractonic random circuits,” Physical Review X 9
2019
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Amos Chan, Rahul M Nandkishore, Michael Pretko, and Graeme Smith, “Unitary-projective entanglement dynamics,” Physical Review B 99
2019
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Romain Vasseur, Andrew C. Potter, Yi-Zhuang You, and Andreas W. W. Ludwig, “Entanglement transitions from holographic random tensor networks,” Phys. Rev. B 100
2019
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Alexander Jahn, Marek Gluza, Fernando Pastawski, and Jens Eisert, “Holography and criticality in matchgate tensor networks,” Science Advances 5
2019
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Norbert Schuch and Bela Bauer, “Matrix product state algorithms for gaussian fermionic states,” Phys. Rev. B 100
2019
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Román Orús, “Tensor networks for complex quantum systems,” Nature Reviews Physics 1
2019
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Chao-Ming Jian, Yi-Zhuang You, Romain Vasseur, and Andreas W. W. Ludwig, “Measurement-induced criticality in random quantum circuits,” Phys. Rev. B 101
2020
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2020
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Yimu Bao, Soonwon Choi, and Ehud Altman, “Theory of the phase transition in random unitary circuits with measurements,” Phys. Rev. B 101
2020
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Nicolai Lang and Hans Peter Büchler, “Entanglement transition in the projective transverse field ising model,” Phys. Rev. B 102
2020
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2020
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