Built on

Q. Zhuang, T. Schuster, B. Yoshida, and N. Y. Yao, “Scrambling and complexity in phase space,” Phys. Rev
Original
1902
Earlier work this paper cites.
A. Blommaert, T. G. Mertens, and H. Verschelde, “Clocks and Rods in Jackiw-Teitelboim Quantum Gravity,” JHEP
Original
1902
Earlier work this paper cites.
P. Saad, S. H. Shenker, and D. Stanford, “JT gravity as a matrix integral,” arXiv:1903.11115 [hep-th]
Original
1903
Earlier work this paper cites.
J. Maldacena, G. J. Turiaci, and Z. Yang, “Two dimensional Nearly de Sitter gravity,” arXiv:1904.01911 [hep-th]
Original
1904
Earlier work this paper cites.
N. Hunter-Jones, “Unitary designs from statistical mechanics in random quantum circuits,” arXiv:1905.12053 [quant-ph]
Original
1905
Earlier work this paper cites.
J. Cotler, K. Jensen, and A. Maloney, “Low-dimensional de Sitter quantum gravity,” JHEP
Original
1905
Earlier work this paper cites.
D. Stanford and E. Witten, “JT Gravity and the Ensembles of Random Matrix Theory,” arXiv:1907.03363 [hep-th]
Original
1907
Earlier work this paper cites.
P. Saad, “Late Time Correlation Functions, Baby Universes, and ETH in JT Gravity,” arXiv:1910.10311 [hep-th]
Original
1910
Earlier work this paper cites.
A. W. Harrow and R. A. Low, “Random Quantum Circuits are Approximate 2-designs,” Commun. Math. Phys
Original
1919
Earlier work this paper cites.
F. J. Dyson, “The Threefold Way. Algebraic Structure of Symmetry Groups and Ensembles in Quantum Mechanics,” J. Math. Phys
1962
Earlier work this paper cites.
A. I. Larkin and Y. N. Ovchinnikov, “Quasiclassical Method in the Theory of Superconductivity,” JETP
1969
Earlier work this paper cites.
C. Teitelboim, “Gravitation and Hamiltonian Structure in Two Space-Time Dimensions,” Phys. Lett
1983
Earlier work this paper cites.
O. Bohigas, M. J. Giannoni, and C. Schmit, “Characterization of Chaotic Quantum Spectra and Universality of Level Fluctuation Laws,” Phys. Rev. Lett
1984
Earlier work this paper cites.
R. Jackiw, “Lower Dimensional Gravity,” Nucl. Phys
1985
Earlier work this paper cites.
R. Jackiw, “Gauge theories for gravity on a line,” Theor. Math. Phys
1992
Earlier work this paper cites.
S. Sachdev and J. Ye, “Gapless spin-fluid ground state in a random quantum Heisenberg magnet,” Phys. Rev. Lett
1993
Earlier work this paper cites.
E. Brézin and A. Zee, “Universality of the correlations between eigenvalues of large random matrices,” Nucl. Phys. B
1993
Earlier work this paper cites.
M. Srednicki, “Chaos and quantum thermalization,” Phys. Rev
1994
Earlier work this paper cites.
E. Brézin and S. Hikami, “Spectral form factor in a random matrix theory,” Phys. Rev
1997
Earlier work this paper cites.
A. Altland and M. R. Zirnbauer, “Nonstandard symmetry classes in mesoscopic normal- superconducting hybrid structures,” Phys. Rev
1997
Earlier work this paper cites.
R. E. Prange, “The Spectral Form Factor Is Not Self-Averaging,” Phys. Rev. Lett
1997
Earlier work this paper cites.
T. Guhr, A. Müller-Groeling, and H. A. Weidenmüller, “Random matrix theories in quantum physics: Common concepts,” Phys. Rept
1998
Earlier work this paper cites.
M. Srednicki, “The approach to thermal equilibrium in quantized chaotic systems,” J. Phys. A: Math. Gen
1999
Earlier work this paper cites.
B. Collins, “Moments and cumulants of polynomial random variables on unitary groups, the Itzykson-Zuber integral, and free probability,” Int. Math. Res. Not
2003
Earlier work this paper cites.
Pure and Applied Mathematics. Elsevier Science, 2004
M. Mehta, Random Matrices · 2004
Earlier work this paper cites.
B. Collins and P. Śniady, “Integration with Respect to the Haar Measure on Unitary, Orthogonal and Symplectic Group,” Commun. Math. Phys
2006
Earlier work this paper cites.
D. Gross, K. Audenaert, and J. Eisert, “Evenly distributed unitaries: On the structure of unitary designs,” J. Math. Phys
2007
Earlier work this paper cites.

Similar

P. Hayden and J. Preskill, “Black holes as mirrors: Quantum information in random subsystems,” JHEP
Original
2007
Cited alongside, same era.
A. J. Scott, “Optimizing quantum process tomography with unitary 2-designs,” J. Phys
Original
2008
Cited alongside, same era.
B. Collins and M. Stolz, “Borel theorems for random matrices from the classical compact symmetric spaces,” Ann. Probab
2008
Cited alongside, same era.
C. Dankert, R. Cleve, J. Emerson, and E. Livine, “Exact and approximate unitary 2-designs and their application to fidelity estimation,” Phys. Rev
2009
Cited alongside, same era.
B. Collins and S. Matsumoto, “On some properties of orthogonal Weingarten functions,” J. Math. Phys
Original
2009

Then

D. A. Roberts and B. Yoshida, “Chaos and complexity by design,” JHEP
Original
2017
Later among the works it cites.
Y. Nakata, C. Hirche, M. Koashi, and A. Winter, “Efficient Quantum Pseudorandomness with Nearly Time-Independent Hamiltonian Dynamics,” Phys. Rev
Original
2017
Later among the works it cites.
E. Onorati, O. Buerschaper, M. Kliesch, W. Brown, A. H. Werner, and J. Eisert, “Mixing properties of stochastic quantum Hamiltonians,” Commun. Math. Phys
Original
2017
Later among the works it cites.
A. Nahum, J. Ruhman, S. Vijay, and J. Haah, “Quantum Entanglement Growth Under Random Unitary Dynamics,” Phys. Rev
Original
2017
Later among the works it cites.
R. Mondaini and M. Rigol, “Eigenstate thermalization in the two-dimensional transverse field Ising model. II. Off-diagonal matrix elements of observables,” Phys. Rev

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2019

Spectral decoupling in many-body quantum chaos

Cotler, Jordan, Hunter-Jones, Nicholas

Understand

We argue that in a large class of disordered quantum many-body systems, the late time dynamics of time-dependent correlation functions is captured by random matrix theory, specifically the energy eigenvalue statistics of the corresponding ensemble of disordered Hamiltonians.

We find that late time correlation functions approximately factorize into a time-dependent piece, which only depends on spectral statistics of the Hamiltonian ensemble, and a time-independent piece, which only depends on the data of the constituent operators of the correlation function.
We call this phenomenon "spectral decoupling," which signifies a dynamical onset of random matrix theory in correlation functions.
A key diagnostic of spectral decoupling is $k$-invariance, which we refine and study in detail.

Built on

Q. Zhuang, T. Schuster, B. Yoshida, and N. Y. Yao, “Scrambling and complexity in phase space,” Phys. Rev
Original
1902
Earlier work this paper cites.
A. Blommaert, T. G. Mertens, and H. Verschelde, “Clocks and Rods in Jackiw-Teitelboim Quantum Gravity,” JHEP
Original
1902
Earlier work this paper cites.
P. Saad, S. H. Shenker, and D. Stanford, “JT gravity as a matrix integral,” arXiv:1903.11115 [hep-th]
Original
1903
Earlier work this paper cites.
J. Maldacena, G. J. Turiaci, and Z. Yang, “Two dimensional Nearly de Sitter gravity,” arXiv:1904.01911 [hep-th]
Original
1904
Earlier work this paper cites.
N. Hunter-Jones, “Unitary designs from statistical mechanics in random quantum circuits,” arXiv:1905.12053 [quant-ph]
Original
1905
Earlier work this paper cites.
J. Cotler, K. Jensen, and A. Maloney, “Low-dimensional de Sitter quantum gravity,” JHEP
Original
1905
Earlier work this paper cites.
D. Stanford and E. Witten, “JT Gravity and the Ensembles of Random Matrix Theory,” arXiv:1907.03363 [hep-th]
Original
1907
Earlier work this paper cites.
P. Saad, “Late Time Correlation Functions, Baby Universes, and ETH in JT Gravity,” arXiv:1910.10311 [hep-th]
Original
1910
Earlier work this paper cites.
A. W. Harrow and R. A. Low, “Random Quantum Circuits are Approximate 2-designs,” Commun. Math. Phys
Original
1919
Earlier work this paper cites.
F. J. Dyson, “The Threefold Way. Algebraic Structure of Symmetry Groups and Ensembles in Quantum Mechanics,” J. Math. Phys
1962
Earlier work this paper cites.
A. I. Larkin and Y. N. Ovchinnikov, “Quasiclassical Method in the Theory of Superconductivity,” JETP
1969
Earlier work this paper cites.
C. Teitelboim, “Gravitation and Hamiltonian Structure in Two Space-Time Dimensions,” Phys. Lett
1983
Earlier work this paper cites.
O. Bohigas, M. J. Giannoni, and C. Schmit, “Characterization of Chaotic Quantum Spectra and Universality of Level Fluctuation Laws,” Phys. Rev. Lett
1984
Earlier work this paper cites.
R. Jackiw, “Lower Dimensional Gravity,” Nucl. Phys
1985
Earlier work this paper cites.
R. Jackiw, “Gauge theories for gravity on a line,” Theor. Math. Phys
1992
Earlier work this paper cites.
S. Sachdev and J. Ye, “Gapless spin-fluid ground state in a random quantum Heisenberg magnet,” Phys. Rev. Lett
1993
Earlier work this paper cites.
E. Brézin and A. Zee, “Universality of the correlations between eigenvalues of large random matrices,” Nucl. Phys. B
1993
Earlier work this paper cites.
M. Srednicki, “Chaos and quantum thermalization,” Phys. Rev
1994
Earlier work this paper cites.
E. Brézin and S. Hikami, “Spectral form factor in a random matrix theory,” Phys. Rev
1997
Earlier work this paper cites.
A. Altland and M. R. Zirnbauer, “Nonstandard symmetry classes in mesoscopic normal- superconducting hybrid structures,” Phys. Rev
1997
Earlier work this paper cites.
R. E. Prange, “The Spectral Form Factor Is Not Self-Averaging,” Phys. Rev. Lett
1997
Earlier work this paper cites.
T. Guhr, A. Müller-Groeling, and H. A. Weidenmüller, “Random matrix theories in quantum physics: Common concepts,” Phys. Rept
1998
Earlier work this paper cites.
M. Srednicki, “The approach to thermal equilibrium in quantized chaotic systems,” J. Phys. A: Math. Gen
1999
Earlier work this paper cites.
B. Collins, “Moments and cumulants of polynomial random variables on unitary groups, the Itzykson-Zuber integral, and free probability,” Int. Math. Res. Not
2003
Earlier work this paper cites.
Pure and Applied Mathematics. Elsevier Science, 2004
M. Mehta, Random Matrices · 2004
Earlier work this paper cites.
B. Collins and P. Śniady, “Integration with Respect to the Haar Measure on Unitary, Orthogonal and Symplectic Group,” Commun. Math. Phys
2006
Earlier work this paper cites.
D. Gross, K. Audenaert, and J. Eisert, “Evenly distributed unitaries: On the structure of unitary designs,” J. Math. Phys
2007
Earlier work this paper cites.

Similar

P. Hayden and J. Preskill, “Black holes as mirrors: Quantum information in random subsystems,” JHEP
Original
2007
Cited alongside, same era.
A. J. Scott, “Optimizing quantum process tomography with unitary 2-designs,” J. Phys
Original
2008
Cited alongside, same era.
B. Collins and M. Stolz, “Borel theorems for random matrices from the classical compact symmetric spaces,” Ann. Probab
2008
Cited alongside, same era.
C. Dankert, R. Cleve, J. Emerson, and E. Livine, “Exact and approximate unitary 2-designs and their application to fidelity estimation,” Phys. Rev
2009
Cited alongside, same era.
B. Collins and S. Matsumoto, “On some properties of orthogonal Weingarten functions,” J. Math. Phys
Original
2009

Then

D. A. Roberts and B. Yoshida, “Chaos and complexity by design,” JHEP
Original
2017
Later among the works it cites.
Y. Nakata, C. Hirche, M. Koashi, and A. Winter, “Efficient Quantum Pseudorandomness with Nearly Time-Independent Hamiltonian Dynamics,” Phys. Rev
Original
2017
Later among the works it cites.
E. Onorati, O. Buerschaper, M. Kliesch, W. Brown, A. H. Werner, and J. Eisert, “Mixing properties of stochastic quantum Hamiltonians,” Commun. Math. Phys
Original
2017
Later among the works it cites.
A. Nahum, J. Ruhman, S. Vijay, and J. Haah, “Quantum Entanglement Growth Under Random Unitary Dynamics,” Phys. Rev
Original
2017
Later among the works it cites.
R. Mondaini and M. Rigol, “Eigenstate thermalization in the two-dimensional transverse field Ising model. II. Off-diagonal matrix elements of observables,” Phys. Rev

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

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Cited alongside, same era.

Springer, 2010

F. Haake, Quantum Signatures of Chaos · 2010

Cited alongside, same era.

R. A. Low, “Pseudo-randomness and Learning in Quantum Computation,” arXiv:1006.5227 [quant-ph] . PhD Thesis, 2010