Matrix product operator representations

By V. Murg, J. I. Cirac, Bogdan Pirvu, Frank Verstraete. 2008

363 citations recorded by the source corpus.

We show how to construct relevant families of matrix product operators (MPOs) in one and higher dimensions. These form the building blocks for the numerical simulation methods based on matrix product states and projected entangled pair states. In particular, we construct translationally invariant MPOs suitable for time evolution, and show how such descriptions are possible for Hamiltonians with long-range interactions. We show how these tools can be exploited for constructing new algorithms for simulating quantum spin systems.

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

View Paper: https://www.semanticscholar.org/paper/7408cbc870e4006b3fa93fe46dbb767d730d10bb

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

In Condensed Matter Physics

Citations in the corpus

Computations in quantum tensor networks (2012, background): “A pp r o x i m a t i o n e rr o r blocking [3, 4, 3] blocking [4, 2, 4] blocking [5, 5] blocking [6, 4] (b) 10 spins, simultaneous optimization.”
Chiral floquet phases of many-body localized bosons (2016, background): “FDLUs in 1D are well described by MPUs with finite bond dimensions since each local gate in the circuit can be readily represented as a MPU [44,45].”
Preconditioned Low-Rank Methods for High-Dimensional Elliptic PDE Eigenvalue Problems (2011, background): “,[28]) and was also proposed in [26] for the so called TT format.”
The mass spectrum of the Schwinger model with matrix product states (2013, background): “In general this is most easily done when all the terms in the problem Hamiltonian are expressed as a matrix product operator (MPO) [47].”
Matrix product states and projected entangled pair states: Concepts, symmetries, theorems (2020, methodology): “…(Verstraete et al., 2004a; Zwolak and Vidal, 2004) describe mixed states (like those corresponding to thermal equilibrium, or open quantum systems), Hamiltonians (Crosswhite and Bacon, 2008; McCulloch, 2007; Pirvu et al., 2010), or unitary evolution (Cirac et al., 2017b; Şahinoğlu et al., 2018).”
Tensor product methods and entanglement optimization for ab initio quantum chemistry (2014, background): “(191) When the number of block states are kept fixed the truncation error fluctuates within a full sweep (see Fig.”
Tangent-space methods for uniform matrix product states (2018, background): “Algorithm 8 Find the optimal MPS approximation for the fixed point of the MPO Ô(T ) 1: procedure Vumps(O,A, η) .”