Fetching the paper…

Reading the bibliography…

Quantum MERA Channels · Around

2008

Quantum MERA Channels

Giovannetti, Vittorio, Montangero, Simone, Fazio, Rosario

Original
PDF
Post on X

Understand

Tensor networks representations of many-body quantum systems can be described in terms of quantum channels.

We focus on channels associated with the Multi-scale Entanglement Renormalization Ansatz (MERA) tensor network that has been recently introduced to efficiently describe critical systems.
Our approach allows us to compute the MERA correspondent to the thermodynamic limit of a critical system introducing a transfer matrix formalism, and to relate the system critical exponents to the convergence rates of the associated channels.

Built on

A. Royer, Phys. Rev. A 43
1991
Earlier work this paper cites.
M. Fannes, B. Nachtergaele, and R. F. Werner, Lett. Math. Phys. 25
1992
Earlier work this paper cites.
S. R. White, Phys. Rev. Lett. 69
1993
Earlier work this paper cites.
S. Ostlund and S. Rommer, Phys. Rev. Lett. 75
1995
Earlier work this paper cites.
B. M. Terhal and D. P. DiVincenzo, Phys. Rev. A 61
2000
Earlier work this paper cites.
M. Raginsky, Phys. Rev. A 65
2002
Earlier work this paper cites.
G. Vidal, Phys. Rev. Lett. 91
2003
Earlier work this paper cites.

Similar

F. Verstraete, D. Porras, and J. I. Cirac, Phys. Rev. Lett. 93
2004
Cited alongside, same era.
R. Gohm, Noncommutative Stationary Processes
2004
Cited alongside, same era.
U. Schollwöck, Rev. Mod. Phys. 77
2006
Cited alongside, same era.
W. Dür et al
2006
Cited alongside, same era.
I. Bengstsson and K. Życzkowski, Geometry of Quantum States
2006
Cited alongside, same era.
M. M. Wolf, et al
2006
Cited alongside, same era.
F. Verstraete, J. I. Cirac, Eprint arXiv:cond-mat/0407066; V. Murg, F. Verstraete, and J. I. Cirac, Phys. Rev. A 75
2007
Cited alongside, same era.

Then

D. Burgarth and V. Giovannetti, New J. Phys. 9
2007
Later among the works it cites.
G. Vidal, Phys. Rev. Lett. 99
2008
Closest in time.
M. Rizzi, S. Montangero, and G. Vidal, Phys. Rev. A 77
2008
Closest in time.
M. Aguado and G. Vidal, Phys. Rev. Lett. 100
2008
Closest in time.
G. Evenbly and G. Vidal, Eprint arXiv:quant-ph/0710.0692; L. Cincio, J. Dziarmaga, and M. M. Rams, Phys. Rev. Lett. 100
2008
Closest in time.
C. M. Dawson, J. Eisert, and T. J. Osborne, Phys. Rev. Lett. 100
2008
Closest in time.

Beyond the bibliography

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

Open on alphaXiv

alphaXiv is searching for related work…

G. Vidal, Eprint: arXiv:0707.1454

Cited in the paper.

For easy of notation we consider the dimension D D of the tensors χ \chi and λ \lambda to be equal to the physical dimension d d . However, the subsequent equations hold for any D D

Cited in the paper.

A necessary and sufficient condition [ 15 ] for Φ ( L ) = Φ ( R ) \Phi^{(L)}=\Phi^{(R)} is the existence of a unitary matrix U r , s U_{{r},{s}} , such that L ^ r = ∑ s U r , s R ^ s \hat{L}_{r}=\sum_{s}U_{{r},{s}}\;\hat{R}_{{s}} . This can then be easily casted into a necessary and sufficient condition for the tensor ℳ 5 {\cal M}_{5}

Cited in the paper.

M. Rizzi, et al

Cited in the paper.