4.6 Letter

Topology and phases in fermionic systems

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IOP PUBLISHING LTD
DOI: 10.1088/1742-5468/2008/01/L01001

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entanglement in extended quantum systems (theory)

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There can exist topological obstructions to continuously deforming a gapped Hamiltonian for free fermions into a trivial form without closing the gap. These topological obstructions are closely related to obstructions to the existence of exponentially localized Wannier functions. We show that by taking two copies of a gapped, free fermionic system with complex conjugate Hamiltonians, it is always possible to overcome these obstructions. This allows us to write the ground state in matrix product form using Grassmann-valued bond variables, and show insensitivity of the ground state density matrix to boundary conditions.

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