Tensor network methods, area laws and topological order in condensed matter
Area laws for entanglement entropies providing insights into the "physical corner" that can be well approximated by tensor network states
Quantum matter exhibits a remarkable wealth of phenomena, originating from basic local laws of interactions.Tensor network states constitute a powerful machinery of numerically solving such systems, as well as analytically characterizing their properties. Notions of topological order or the classification of phases can be elegantly expressed in terms of such tensor networks. At the heart of the insight why tensor network states approximate ground states of locally interacting models well is the area law for the entanglement entropy, defining what is often referred to as the "physical corner of Hilbert space". We are concerned with various aspects of tensor network states, topological order, and scaling laws for entanglement entropies in quantum matter systems, both in the practical-numerical and mathematical-conceptual reading.
Selected group publications
- A tensor network annealing algorithm for two-dimensional thermal states
Physical Review Letters 122, 070502 (2019) - Holography and criticality in matchgate tensor networks
Science Advances 5, eaaw0092 (2019) - Holography and criticality in matchgate tensor networks
Science Advances 5, eaaw0092 (2019) - Time evolution of many-body localized systems in two spatial dimensions
Phyical Review B 102, 235132 (2020) - Efficient variational contraction of two-dimensional tensor networks with a non-trivial unit cell
Quantum 4, 328 (2020) - Single-shot holographic compression from the area law
Physical Review Letters 122, 190501 (2019) - Fermionic orbital optimisation in tensor network states
Physical Review Letters 117, 210402 (2016) - Fermionic topological quantum states as tensor networks
Physical Review B 95, 245127, 574 (2017) - Approximating local observables on projected entangled pair states
Physical Review A 95, 060102 (2017) - A positive tensor network approach for simulating open quantum many-body systems
Physical Review Letters 116, 237201 (2016) - Diagnosing topological edge states via entanglement monogamy
Physical Review Letters 116, 130501 (2016) - Solving frustration-free spin systems
Physical Review Letters 105, 060504 (2010) - Contraction of fermionic operator circuits and the simulation of strongly correlated fermions
Physical Review A 80, 042333 (2009) - Many-body localisation implies that eigenvectors are matrix-product states
Physical Review Letters 114, 170505 (2015) - Matrix product operators and states: NP-hardness and undecidability
Physical Review Letters 113, 160503 (2014) - Wick's theorem for matrix product states
Physical Review Letters 110, 040401 (2013) - Unifying variational methods for simulating quantum many-body systems
Physical Review Letters 100, 130501 (2008) - Entropy, entanglement, and area: analytical results for harmonic lattice systems
Physical Review Letters 94, 060503 (2005) - Statistics dependence of the entanglement entropy
Physical Review Letters 98, 220603 (2007) - Exploring local quantum many-body relaxation by atoms in optical superlattices
Physical Review Letters 101, 063001 (2008) - Unitary circuits for strongly correlated fermions
Physical Review A 81, 050303(R) (2010) - Topological insulators with arbitrarily tunable entanglement
Physical Review B 89, 195120 (2014) - Search for localized Wannier functions of topological band structures via compressed sensing
Physical Review B 90, 115110 (2014) - Tensor network methods with graph enhancement
Physical Review B 84, 125103 (2011) - Real-space renormalization yields finite correlations
Physical Review 105, 010502 (2010)
Group reviews
- Area laws for the entanglement entropy
Reviews of Modern Physics 82, 277 (2010) - Entanglement and tensor network states
Modeling and Simulation 3, 520 (2013) - Quantum many-body systems out of equilibrium
Nature Physics 11, 124 (2015)