Gaussian matrix product states cannot efficiently describe critical systems
arXiv:2204.02478 · doi:10.1103/PhysRevB.106.235136
Abstract
Gaussian fermionic matrix product states (GfMPS) form a class of ansatz quantum states for 1d systems of noninteracting fermions. We show, for a simple critical model of free hopping fermions, that: (i) any GfMPS approximation to its ground state must have bond dimension scaling superpolynomially with the system size, whereas (ii) there exists a non-Gaussian fermionic MPS approximation to this state with polynomial bond dimension. This proves that, in general, imposing Gaussianity at the level of the tensor network may significantly alter its capability to efficiently approximate critical Gaussian states. We also provide numerical evidence that the required bond dimension is subexponential, and thus can still be simulated with moderate resources.
4 pages, 2 figures + appendices (7 pages, 1 figure)
References in corpus (8)
- Matrix Product States and Projected Entangled Pair States: Concepts, Symmetries, and Theorems
- Matrix product states represent ground states faithfully
- Entropy scaling and simulability by Matrix Product States
- Entanglement hamiltonians in two-dimensional conformal field theory
- Physics at the entangling surface
- Chiral projected entangled-pair state with topological order
- Symmetries and boundary theories for chiral Projected Entangled Pair States
- Skeleton of Matrix-Product-State-Solvable Models Connecting Topological Phases of Matter