Operator space entanglement entropy in a transverse Ising chain

By Tomaz Prosen, Iztok Pižorn. 2007

164 citations recorded by the source corpus.

The efficiency of time-dependent density matrix renormalization group methods is intrinsically connected to the rate of entanglement growth. We introduce a measure of entanglement in the space of operators and show, for a transverse Ising spin-$1∕2$ chain, that the simulation of observables, contrary to the simulation of typical pure quantum states, is efficient for initial local operators. For initial operators with a finite index in Majorana representation, the operator space entanglement entropy saturates with time to a level which is calculated analytically, while for initial operators with infinite index the growth of operator space entanglement entropy is shown to be logarithmic.

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

View Paper: https://www.semanticscholar.org/paper/5b3fe4f332a015bf043301fa2e6a7808af2621d3

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. A. Nahum
2. V. Khemani
3. S. Vijay
4. D. Huse
5. S. Gopalakrishnan
6. B. Skinner
7. J. Ruhman
8. Austen Lamacraft

In Atomic and Molecular Physics, and Optics

1. A. Nahum
2. V. Khemani
3. D. Huse
4. S. Gopalakrishnan
5. S. Vijay
6. Matthew Fisher
7. B. Skinner
8. Austen Lamacraft

Citations in the corpus

• Operator Spreading in Random Unitary Circuits (2017, methodology): “We note that the OTOC is not the only tool for characterizing operator spreading: The operator entanglement entropy of a spreading operator is also of interest [116,117].”
• Unitary circuits of finite depth and infinite width from quantum channels (2019, background): “The ancilla-space density matrices for these “dual-unitary” circuits are proportional to the identity and thus have no operator entanglement [44] at any time; they can be represented as matrix-product operators of bond dimension one.”
• Measurement and Entanglement Phase Transitions in All-To-All Quantum Circuits, on Quantum Trees, and in Landau-Ginsburg Theory (2020, methodology): “The operator entanglement [45–49], defined below, is a measure of the amount of quantum information transmitted from the initial to the final time by the nonunitary evolution operator Vm.”
• Entanglement scaling of operators: a conformal field theory approach, with a glimpse of simulability of long-time dynamics in 1  +  1d (2016, methodology): “This was an early observation of Prosen and Pižorn [2]; here we provided an analytic derivation of this fact, relying on the results of [81, 82].”
• Matrix product simulations of non-equilibrium steady states of quantum spin chains (2008, background): “ the density operator ρ. Also, OSEE is different than the ordinary von Neumann entropy of ρ. For instance, OSEE either saturates or grows logarithmically with time in integrable transverse Ising model [42] or in Heisenberg XXZ model in a random magnetic field [43], it saturates or grows linearly with ”
• Operator Entanglement in Local Quantum Circuits I: Chaotic Dual-Unitary Circuits (2019, background): “The idea is to think of a time-dependent operator as a state in an appropriate Hilbert space (the operator-space) and characterise the complexity of its evolution using the entanglement of such a state [30, 31].”
• Velocity-dependent Lyapunov exponents in many-body quantum, semiclassical, and classical chaos (2018, background): “[56] Tomaž Prosen and Iztok Pižorn, “Operator space entanglement entropy in a transverse ising chain,” Physical Review A 76, 032316 (2007).”