Efficient simulation of one-dimensional quantum many-body systems.

By Guifré Vidal. Physical Review Letters, 2003

1,347 citations recorded by the source corpus.

We present a numerical method to simulate the time evolution, according to a generic Hamiltonian made of local interactions, of quantum spin chains and systems alike. The efficiency of the scheme depends on the amount of entanglement involved in the simulated evolution. Numerical analysis indicates that this method can be used, for instance, to efficiently compute time-dependent properties of low-energy dynamics in sufficiently regular but otherwise arbitrary one-dimensional quantum many-body systems. As by-products, we describe two alternatives to the density matrix renormalization group method.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics

View Paper: https://www.semanticscholar.org/paper/93066c24a03933e9f6e5333c45ba04befc71a9dc

How researchers see this paper

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

In Atomic and Molecular Physics, and Optics

1. Pasquale Calabrese
2. Andrew J. Daley
3. J. Cardy
4. I. Bloch
5. A. Nahum
6. J. Dubail
7. Peter Zoller
8. Frank Verstraete

In Condensed Matter Physics

1. Pasquale Calabrese
2. Andrew J. Daley
3. J. Cardy
4. J. Dubail
5. Frank Verstraete
6. Frank Pollmann
7. I. Bloch
8. J. I. Cirac

Citations in the corpus

• Tangent-space methods for uniform matrix product states (2018, methodology): “One of the many new applications has been the simulation of time evolution, where the MPS formalism has been of crucial value for coming up with algorithms such as the time-evolving block decimation [21–23].”
• Quantum quenches in extended systems (2007, background): “) These striking experimental results have largely motivated the development of new numerical methods to study non-equilibrium dynamics, the most successful one being the time-dependent density matrix renormalization group (DMRG) [6].”
• Quantum simulation with interacting photons (2016, methodology): “In turn for calculating dynamics, Matrix Product State representations of DMRG [193] in form of the TimeEvolving Block Decimation (TEBD) [250, 251, 263] have frequently been applied [110, 107, 95, 128, 198, 225, 202, 25].”
• Improved Simulation of Stabilizer Circuits (2004, positive): “Notably, in a follow-up paper [37], Vidal actually implemented his algorithm and used it to simulate 1-dimensional quantum spin chains consisting of hundreds of spins.”
• One-dimensional quantum liquids: Beyond the Luttinger liquid paradigm (2011, methodology): “…evaluation (Barthel et al., 2009; Feiguin and Huse, 2009; Kohno, 2010; Kokalj and Prelovsek, 2009; White and Affleck, 2008) based on time-dependent extensions of Density Matrix Renormalization Group (DMRG) techniques (De Chiara et al., 2008; Schollwöck, 2005; Vidal, 2003, 2004; White, 1992).”
• Practical quantum advantage in quantum simulation (2022, methodology): “…well when the time-evolving state has limited levels of quantum entanglement 57 , and these methods are often excellent for computing low-energy states or near-equilibrium dynamics, especially in one-dimensional systems with local interactions, where we expect the entanglement to be small 54–56 .”
• Entanglement in many-body systems (2007, methodology): “Tools from quantum information theory also provided important support for numerical methods, as the density matrix renormalization group or the design of new efficient simulation strategies for many-body systems (see for example Verstraete et al., 2004c; Vidal, 2003, 2004).”