Onset of Random Matrix Behavior in Scrambling Systems

A. W. Harrow and R. A. Low, “Random quantum circuits are approximate 2-designs,” Comm.Math.Phys

Original

1919

Earlier work this paper cites.

F. J. Dyson, “Statistical theory of the energy levels of complex systems. I,” J. Math. Phys

1962

Earlier work this paper cites.

A. I. Larkin and Y. N. Ovchinnikov, “Quasiclassical method in the theory of superconductivity,” Sov. Phys. JETP

1969

Earlier work this paper cites.

E. H. Lieb and D. W. Robinson, “The finite group velocity of quantum spin systems,” Commun. Math. Phys

1972

Earlier work this paper cites.

T. Banks, L. Susskind and M. E. Peskin, “Difficulties for the Evolution of Pure States Into Mixed States,” Nucl. Phys. B

1984

Earlier work this paper cites.

B. Altshuler and B. Shklovskii, “Repulsion of energy levels and conductivity of small metal samples,” Sov. Phys. JETP

1986

Earlier work this paper cites.

S. Sachdev and J.-w. Ye, “Gapless spin fluid ground state in a random, quantum Heisenberg magnet,” Phys. Rev. Lett

1993

Earlier work this paper cites.

Lenhard Ng, “Heisenberg Model, Bethe Ansatz and Random Walks,” Thesis (1996)

1996

Earlier work this paper cites.

J. T. Chalker, I V. Lerner, and R. A. Smith, “Random Walks through the Ensemble: Linking Spectral Statistics with Wave-Function Correlations in Disordered Metals,” Phys. Rev. Lett

1996

Earlier work this paper cites.

E. Brézin and S. Hikami, “Spectral form factor in a random matrix theory,” Physical Review E

1997

Earlier work this paper cites.

E. Brezin and S. Hikami, “Extension of level-spacing universality,” Phys. Rev

1997

Earlier work this paper cites.

M. Karabach, G. Müller, H. Gould, and J. Tobochnik, “Introduction to the Bethe Ansatz I,” Comput. Phys

1997

Earlier work this paper cites.

T. Guhr, A. Muller-Groeling, and H. A. Weidenmuller, “Random matrix theories in quantum physics: Common concepts,” Phys. Rept

1998

Earlier work this paper cites.

F. Haake, H.-J. Sommers, and J. Weber, “Fluctuations and ergodicity of the form factor of quantum propagators and random unitary matrices,” J. Phys. A: Math. Gen. 32

1999

Earlier work this paper cites.

J. C. Flores, M. Horoi, M. Müller, and T. H. Seligman, “Spectral statistics of the two-body random ensemble revisited,” Phys. Rev. E

2001

Earlier work this paper cites.

P. Diaconis and S. N. Evans, “Linear Functionals of Eigenvalues of Random Matrices,” Trans. Am. Math. Soc

2001

Earlier work this paper cites.

J. Emerson, Y. S. Weinstein, M. Saraceno, S. Lloyd, and D. G. Cory, “ Pseudo-random unitary operators for quantum information processing,” Science

2003

Earlier work this paper cites.

Academic press, 2004

M. L. Mehta, Random matrices · 2004

Earlier work this paper cites.

J. Emerson, E. Livine, and S. Lloyd, “Convergence conditions for random quantum circuits,” Phys. Rev. A

2005

Earlier work this paper cites.

F. Haake, “Quantum Signatures of Chaos,” Springer-Verlag New York, Inc

2006

Earlier work this paper cites.

P. Hayden and J. Preskill, “Black holes as mirrors: Quantum information in random subsystems,” JHEP

Original

2007

Earlier work this paper cites.

R. Oliveira, O. C. O. Dahlsten, and M. B. Plenio, “Efficient Generation of Generic Entanglement,” Phys. Rev. Lett., 98(130502)

2007

Cited alongside, same era.

D. Gross, K. Audenaert, and J. Eisert, “Evenly distributed unitaries: On the structure of unitary designs,” J. Math. Phys

2007

Cited alongside, same era.

L. Arnaud and D. Braun, “Efficiency of producing random unitary matrices with quantum circuits,” Phys. Rev. A

Original

2008

Cited alongside, same era.

A. Harrow and R. Low. “Efficient quantum tensor product expanders and k k -designs,” Proc. of APPROX-RANDOM

Original

2009

Cited alongside, same era.

W. G. Brown and L. Viola, “Convergence rates for arbitrary statistical moments of random quantum circuits,” Phys. Rev. Lett

Original

D. J. Luitz, N. Laflorencie, and F. Alet, “Many-body localization edge in the random-field Heisenberg chain,” Phys. Rev. B

2015

Later among the works it cites.

M. Serbyn and J. E. Moore, “Spectral statistics across the many-body localization transition,” Phys. Rev. B

2016

Later among the works it cites.

A. M. García-García and J. J. M. Verbaarschot, “Spectral and thermodynamic properties of the Sachdev–Ye–Kitaev model,” Phys. Rev. D

Original

2016

Later among the works it cites.

J. Maldacena and D. Stanford, “Remarks on the Sachdev-Ye-Kitaev model,” Phys. Rev

Original

2016

Later among the works it cites.

J. Maldacena, S. H. Shenker, and D. Stanford, “A bound on chaos,” JHEP

Original

2016