Matrix product density operators: simulation of finite-temperature and dissipative systems.

By Frank Verstraete, Juan José García-Ripoll, J. I. Cirac. 2004

848 citations recorded by the source corpus.

We show how to simulate numerically the evolution of 1D quantum systems under dissipation as well as in thermal equilibrium. The method applies to both finite and inhomogeneous systems, and it is based on two ideas: (a) a representation for density operators which extends that of matrix product states to mixed states; (b) an algorithm to approximate the evolution (in real or imaginary time) of matrix product states which is variational.

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

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. M. Fishman
2. Frank Pollmann
3. E. Stoudenmire
4. Andrew J. Daley
5. S. White
6. Frank Verstraete
7. L. Vanderstraeten
8. J. Haegeman

In Condensed Matter Physics

1. Frank Pollmann
2. Andrew J. Daley
3. L. Vanderstraeten
4. Frank Verstraete
5. E. Stoudenmire
6. J. Haegeman
7. M. Fishman
8. S. White

In Statistical and Nonlinear Physics

1. Andrew J. Daley
2. E. Stoudenmire
3. S. White
4. M. Fishman
5. J. Dubail
6. Frank Pollmann
7. J. Haegeman
8. P. Nguyen

Citations in the corpus

• Quantum trajectories and open many-body quantum systems (2014, methodology): “Such density matrix representations can be used to represent finite-temperature states [233, 236], though finite temperature dynamics alone (without dissipative processes) can also be represented by use of ancilla states [238], or by sampling minimally entangled states [239].”
• Entanglement of purification: from spin chains to holography (2017, methodology): “When numerically simulating a mixed state ρ̂, one can either represent ρ̂ as a matrix product operator (MPO),[27] or instead purify ρ̂ and represent the purification as a MPS.”
• Operator Hydrodynamics, OTOCs, and Entanglement Growth in Systems without Conservation Laws (2017, methodology): “Our numerical method relies on representing the operator Z0ðtÞ as a MPO, which allows us to apply the two-site unitary gates efficiently.”
• Time-evolution methods for matrix-product states (2019, methodology): “The method can be directly applied in the context of matrix-product states[4–8], as explained in Sec.”
• Tangent-space methods for uniform matrix product states (2018, background): “2 Truncating a uniform MPS The mixed canonical form enables us to truncate an MPS efficiently [12], which is one of the primitive tasks in any MPS toolbox.”
• Entanglement scaling of operators: a conformal field theory approach, with a glimpse of simulability of long-time dynamics in 1  +  1d (2016, background): “In the past two decades, the way we think about quantum many-body systems, as well as the techniques we use to simulate them, have been revolutionized by Tensor Networks; for reviews, see for instance Refs.”
• Cluster mean-field approach to the steady-state phase diagram of dissipative spin systems (2016, methodology): “(1) can be faithfully addressed using a MPO Ansatz for the density matrix [65,66].”