Topology and Phases in Fermionic Systems

Details Topology and Phases in Fermionic Systems Topology and Phases in Fermionic Systems

2007-10-17

arxiv.org/abs/0710.3324v1

Physics

Quantum Physics

4 pages, see also arxiv:0710.3299

Scientific paper

10.1088/1742-5468/2008/01/L01001

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 Grassman-valued bond variables, and show insensitivity of the ground state density matrix to boundary conditions.

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