arXiv:1309.0816 [quant - ph]
Phys. Rev. X 4, 031019 (2014) DOI: http://dx.doi.org/10.1103/PhysRevX.4.031019
Phys. Rev. Lett. 111, 260401 (2013) http://dx.doi.org/10.1103/PhysRevLett.111.260401
arXiv:1309.2308 [quant - ph]
We study the nonequilibrium dynamics of correlations in quantum lattice models in the presence of long-range interactions decaying asymptotically as a power law. For exponents larger than the lattice dimensionality, a Lieb-Robinson-type bound effectively restricts the spreading of correlations to a causal region, but allows supersonic propagation. We show that this decay is not only sufficient but also necessary.
Modeling and Simulation 3, 520 (2013)
arXiv:1308.3318 [quant-ph]
The paper, authored by T Lunghi, J Kaniewski, F Bussières, R Houlmann, M Tomamichel, A Kent, N Gisin, S Wehner, H Zbinden, has been publised the 1st November 2013 on Phys. Rev. Lett. 111, 180504 (2013)
PoS(LATTICE 2013)332, arXiv:1310.4118 [hep-lat]
The term Tensor Network States (TNS) refers to a number of families of states that represent different ansaetze for the efficient description of the state of a quantum many-body system. Matrix Product States (MPS) are one particular case of TNS, and have become the most precise tool for the numerical study of one dimensional quantum many-body systems, as the basis of the Density Matrix Renormalization Group method. Lattice Gauge Theories (LGT), in their Hamiltonian version, offer a challenging scenario for these techniques.
Physical Review Letters 111, 236805 (2013)
We show that Projected Entangled-Pair States (PEPS) in two spatial dimensions can describe chiral topological states by explicitly constructing a family of such states with a non-trivial Chern number. They are ground states of two different kinds of free-fermion Hamiltonians: (i) local and gapless; (ii) gapped, but with hopping amplitudes that decay according to a power law. We also prove that they are necessarily non-injective, and cannot correspond to exact ground states of gapped, local parent Hamiltonians.
Phys. Rev. Lett. 112, 036402 (2014)
We study the edge physics of gapped quantum systems in the framework of Projected Entangled Pair State (PEPS) models. We show that the effective low-energy model for any region acts on the entanglement degrees of freedom at the boundary, corresponding to physical excitations located at the edge. This allows us to determine the edge Hamiltonian in the vicinity of PEPS models, and we demonstrate that by choosing the appropriate bulk perturbation, the edge Hamiltonian can exhibit a rich phase diagram and phase transitions.
New Journal of Physics 15, 123021 (2013)
We analyze the description of quantum many-body mixed states using matrix product states and operators. We consider two such descriptions: (i) as a matrix product density operator of bond dimension D, and (ii) as a purification that is written as a matrix product state of bond dimension D'. We show that these descriptions are inequivalent in the sense that D' cannot be upper bounded by D only. Then we provide two constructive methods to obtain (ii) out of (i).
Journal of High Energy Physics 11 (2013) 158
We show the feasibility of tensor network solutions for lattice gauge theories in Hamiltonian formulation by applying matrix product states algorithms to the Schwinger model with zero and non-vanishing fermion mass. We introduce new techniques to compute excitations in a system with open boundary conditions, and to identify the states corresponding to low momentum and different quantum numbers in the continuum.