Built on

M. Fukuda, R. König, and I. Nechita, RTNI—A symbolic integrator for Haar-random tensor networks, J. Phys. A: Math. Theor. 52
Original
1902
Earlier work this paper cites.
S. Gopalakrishnan and A. Lamacraft, Unitary circuits of finite depth and infinite width from quantum channels, Phys. Rev. B 100
Original
1903
Earlier work this paper cites.
B. Bertini, P. Kos, and T. Prosen, Exact Correlation Functions for Dual-Unitary Lattice Models in 1 + 1 1+1 Dimensions, Phys. Rev. Lett. 123
Original
1904
Earlier work this paper cites.
C. Lancien and D. Pérez-García, Correlation Length in Random MPS and PEPS, Ann. Henri Poincaré 23
Original
1906
Earlier work this paper cites.
B. Bertini, P. Kos, and T. Prosen, Operator Entanglement in Local Quantum Circuits I: Chaotic Dual-Unitary Circuits, SciPost Phys. 8
Original
1909
Earlier work this paper cites.
R. Movassagh and J. Schenker, An Ergodic Theorem for Quantum Processes with Applications to Matrix Product States, Comm. Math. Phys. 395
Original
1909
Earlier work this paper cites.
L. Piroli, B. Bertini, J. I. Cirac, and T. Prosen, Exact dynamics in dual-unitary quantum circuits, Phys. Rev. B 101
Original
1911
Earlier work this paper cites.
F. G. S. L. Brandão, W. Chemissany, N. Hunter-Jones, R. Kueng, and J. Preskill, Models of Quantum Complexity Growth, PRX Quantum 2
Original
1912
Earlier work this paper cites.
M. C. Bañuls, M. B. Hastings, F. Verstraete, and J. I. Cirac, Matrix Product States for Dynamical Simulation of Infinite Chains, Phys. Rev. Lett. 102
Original
1926
Earlier work this paper cites.
P. W. Claeys and A. Lamacraft, Maximum velocity quantum circuits, Phys. Rev. Research 2
Original
2003
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
2003
Earlier work this paper cites.
A. J. Daley, C. Kollath, U. Schollwöck, and G. Vidal, Time-dependent density-matrix renormalization-group using adaptive effective Hilbert spaces, J. Stat. Mech. 2004
2004
Earlier work this paper cites.
S. R. White and A. E. Feiguin, Real-Time Evolution Using the Density Matrix Renormalization Group, Phys. Rev. Lett. 93
2004
Earlier work this paper cites.
B. Bertini and L. Piroli, Scrambling in random unitary circuits: Exact results, Phys. Rev. B 102
Original
2004
Earlier work this paper cites.
P. Calabrese and J. Cardy, Evolution of entanglement entropy in one-dimensional systems, J. Stat. Mech. 2005
2005
Earlier work this paper cites.

Similar

F. Verstraete and J. I. Cirac, Matrix product states represent ground states faithfully, Phys. Rev. B 73
2006
Cited alongside, same era.
B. Collins and P. Śniady, Integration with Respect to the Haar Measure on Unitary, Orthogonal and Symplectic Group, Comm. Math. Phys. 264
2006
Cited alongside, same era.
G. Vidal, Classical Simulation of Infinite-Size Quantum Lattice Systems in One Spatial Dimension, Phys. Rev. Lett. 98
2007
Cited alongside, same era.
D. Pérez-García, F. Verstraete, M. M. Wolf, and J. I. Cirac, Matrix product state representations, Quant. Inf. Comp. 7
2007
Cited alongside, same era.
D. Pérez-García, F. Verstraete, J. I. Cirac, and M. M. Wolf, PEPS as unique ground states of local Hamiltonians, Quant. Inf. Comp. 8
Original
2008
Cited alongside, same era.

Then

D. A. Roberts and B. Yoshida, Chaos and complexity by design, J. High Energ. Phys. 2017
Original
2017
Later among the works it cites.
C. W. von Keyserlingk, T. Rakovszky, F. Pollmann, and S. L. Sondhi, Operator Hydrodynamics, OTOCs, and Entanglement Growth in Systems without Conservation Laws, Phys. Rev. X 8
Original
2018
Later among the works it cites.
A. Chan, A. D. Luca, and J. T. Chalker, Solution of a Minimal Model for Many-Body Quantum Chaos, Phys. Rev. X 8
Original
2018
Later among the works it cites.
J. Watrous, The Theory of Quantum Information (Cambridge University Press, Cambridge, 2018)
2018
Later among the works it cites.
T. Prosen, Many-body quantum chaos and dual-unitarity round-a-face, Chaos 31
Original

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2023

Correlations in Disordered Solvable Tensor Network States

Haag, Daniel, Milbradt, Richard M., Mendl, Christian B.

Understand

Solvable matrix product and projected entangled pair states evolved by dual and ternary-unitary quantum circuits have analytically accessible correlation functions.

Here, we investigate the influence of disorder.
Specifically, we compute the average behavior of a physically motivated two-point equal-time correlation function with respect to random disordered solvable tensor network states arising from the Haar measure on the unitary group.
By employing the Weingarten calculus, we provide an exact analytical expression for the average of the $k$th moment of the correlation function.

Built on

M. Fukuda, R. König, and I. Nechita, RTNI—A symbolic integrator for Haar-random tensor networks, J. Phys. A: Math. Theor. 52
Original
1902
Earlier work this paper cites.
S. Gopalakrishnan and A. Lamacraft, Unitary circuits of finite depth and infinite width from quantum channels, Phys. Rev. B 100
Original
1903
Earlier work this paper cites.
B. Bertini, P. Kos, and T. Prosen, Exact Correlation Functions for Dual-Unitary Lattice Models in 1 + 1 1+1 Dimensions, Phys. Rev. Lett. 123
Original
1904
Earlier work this paper cites.
C. Lancien and D. Pérez-García, Correlation Length in Random MPS and PEPS, Ann. Henri Poincaré 23
Original
1906
Earlier work this paper cites.
B. Bertini, P. Kos, and T. Prosen, Operator Entanglement in Local Quantum Circuits I: Chaotic Dual-Unitary Circuits, SciPost Phys. 8
Original
1909
Earlier work this paper cites.
R. Movassagh and J. Schenker, An Ergodic Theorem for Quantum Processes with Applications to Matrix Product States, Comm. Math. Phys. 395
Original
1909
Earlier work this paper cites.
L. Piroli, B. Bertini, J. I. Cirac, and T. Prosen, Exact dynamics in dual-unitary quantum circuits, Phys. Rev. B 101
Original
1911
Earlier work this paper cites.
F. G. S. L. Brandão, W. Chemissany, N. Hunter-Jones, R. Kueng, and J. Preskill, Models of Quantum Complexity Growth, PRX Quantum 2
Original
1912
Earlier work this paper cites.
M. C. Bañuls, M. B. Hastings, F. Verstraete, and J. I. Cirac, Matrix Product States for Dynamical Simulation of Infinite Chains, Phys. Rev. Lett. 102
Original
1926
Earlier work this paper cites.
P. W. Claeys and A. Lamacraft, Maximum velocity quantum circuits, Phys. Rev. Research 2
Original
2003
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
2003
Earlier work this paper cites.
A. J. Daley, C. Kollath, U. Schollwöck, and G. Vidal, Time-dependent density-matrix renormalization-group using adaptive effective Hilbert spaces, J. Stat. Mech. 2004
2004
Earlier work this paper cites.
S. R. White and A. E. Feiguin, Real-Time Evolution Using the Density Matrix Renormalization Group, Phys. Rev. Lett. 93
2004
Earlier work this paper cites.
B. Bertini and L. Piroli, Scrambling in random unitary circuits: Exact results, Phys. Rev. B 102
Original
2004
Earlier work this paper cites.
P. Calabrese and J. Cardy, Evolution of entanglement entropy in one-dimensional systems, J. Stat. Mech. 2005
2005
Earlier work this paper cites.

Similar

F. Verstraete and J. I. Cirac, Matrix product states represent ground states faithfully, Phys. Rev. B 73
2006
Cited alongside, same era.
B. Collins and P. Śniady, Integration with Respect to the Haar Measure on Unitary, Orthogonal and Symplectic Group, Comm. Math. Phys. 264
2006
Cited alongside, same era.
G. Vidal, Classical Simulation of Infinite-Size Quantum Lattice Systems in One Spatial Dimension, Phys. Rev. Lett. 98
2007
Cited alongside, same era.
D. Pérez-García, F. Verstraete, M. M. Wolf, and J. I. Cirac, Matrix product state representations, Quant. Inf. Comp. 7
2007
Cited alongside, same era.
D. Pérez-García, F. Verstraete, J. I. Cirac, and M. M. Wolf, PEPS as unique ground states of local Hamiltonians, Quant. Inf. Comp. 8
Original
2008
Cited alongside, same era.