Entanglement in quantum critical phenomena.

By Guifré Vidal, José I. Latorre, E. Rico, A. Kitaev. Physical Review Letters, 2002

2,155 citations recorded by the source corpus.

Entanglement, one of the most intriguing features of quantum theory and a main resource in quantum information science, is expected to play a crucial role also in the study of quantum phase transitions, where it is responsible for the appearance of long-range correlations. We investigate, through a microscopic calculation, the scaling properties of entanglement in spin chain systems, both near and at a quantum critical point. Our results establish a precise connection between concepts of quantum information, condensed matter physics, and quantum field theory, by showing that the behavior of critical entanglement in spin systems is analogous to that of entropy in conformal field theories. We explore some of the implications of this connection.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/4dcee3be43c2d9b785f36939fd4cf4462639b375

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Citations in the corpus

Entanglement entropy of two disjoint intervals in conformal field theory (2009, background): “Away from the critical point, SA saturates to a constant value [6] proportional to the logarithm of the correlation length [7].”
Efficient numerical simulations with Tensor Networks: Tensor Network Python (TeNPy) (2018, background): “Moreover, the canonical form discussed above is preserved if the transformations are unitary [57].”
Entanglement entropy of excited states (2009, methodology): “where θk is the Bogolioubov angle of the transformation that diagonalizes the Hamiltonian in equation (7) and Γ (GS) l is the corresponding matrix in the ground state [7, 13].”
Matrix product simulations of non-equilibrium steady states of quantum spin chains (2008, background): “Later, it has been shown [16, 17], using the arguments of conformal field theory, that ground state entanglement entropy of a finite block of size n in any non-critical (gaped) system in 1D saturates with n, whereas for critical (non-gaped) systems the growth of entanglement entropy is at most logar”
Entanglement entropy: Holography and renormalization group (2018, background): “…by their symmetries (Kitaev and Preskill, 2006; Levin and Wen, 2006), and to diagnose quantum critical phenomena (Calabrese and Cardy, 2004; Jin and Korepin, 2004; Vidal et al., 2003) and dynamics of strongly-correlated quantum systems (Calabrese and Cardy, 2007, 2005; Eisler and Peschel, 2007).”
Quantum Information Meets Quantum Matter (2015, background): “‘local Clifford equivalence’), and similarly every stabilizer state is equivalent to a graph state [20].”
Adiabatic Quantum Computing (2016, background): “…connection between entanglement entropy and gaps is not nearly as clear in higher dimensional systems, even though entanglement close to quantum phase transitions is a well developed subject (Amico et al., 2008; Osborne and Nielsen, 2002; Osterloh et al., 2002; Vidal et al., 2003; Wu et al., 2004).”
Entanglement in many-body systems (2007, background): “In particular, there has been an extensive analysis of entanglement in quantum critical models (Osborne and Nielsen, 2002; Osterloh et al., 2002; Vidal et al., 2003).”