Local tensor network for strongly correlated projective states

Abstract

The success of tensor network approaches in simulating strongly correlated quantum systems crucially depends on whether the many body states that are relevant for the problem can be encoded in a local tensor network. Despite numerous efforts, strongly correlated projective states, fractional quantum Hall states in particular, have not yet found a local tensor network representation. Here we show that one can encode the calculation of averages of local operators in a Grassmann tensor network which is local. Our construction is explicit, and allows the use of physically motivated trial wavefunctions as starting points in tensor network variational calculations.

4 pages

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Cited by in corpus (22)

• Fractional Quantum Hall Physics in Topological Flat Bands
• Correlation effects in two-dimensional topological insulators
• Exact Matrix Product States for Quantum Hall Wave Functions
• Tensor network trial states for chiral topological phases in two dimensions and a no-go theorem in any dimension
• Projected entangled-pair states can describe chiral topological states
• Compactly-supported Wannier functions and algebraic $K$-theory
• Chiral Topological Phases from Artificial Neural Networks
• Renormalization group constructions of topological quantum liquids and beyond
• Neural network representation of tensor network and chiral states
• Chiral projected entangled-pair state with topological order
• Efficient simulation of Grassmann Tensor Product States
• Tensor network representations of parton wave functions
• Surface codes, quantum circuits, and entanglement phases
• Fermionic tensor network methods
• Rashba coupling and magnetic order in correlated helical liquids
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• Field Tensor Network States
• Finite-Entanglement Scaling of 2D Metals
• Strictly local tensor networks for short-range topological insulators
• Wavefunction Vortex Attachment via Matrix Products: Application to Atomic Fermi Gases in Flat Spin-Orbit Bands
• Grassmann tensor networks
• Tensor network states for the description of quantum many-body systems