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SUMMARY:Gapped and gapless phases of frustration-free spin-1/2 chains - Da
 vid Gosset (Caltech)
DTSTART:20150416T131500Z
DTEND:20150416T141500Z
UID:TALK58496@talks.cam.ac.uk
CONTACT:William Matthews
DESCRIPTION:We consider a family of translation-invariant quantum spin cha
 ins with nearest-neighbor interactions and derive necessary and sufficient
  conditions for these systems to be gapped in the thermodynamic limit. Mor
 e precisely\, let psi be an arbitrary two-qubit state. We consider a chain
  of n qubits with open boundary conditions and Hamiltonian which is define
 d as the sum of rank-1 projectors onto psi applied to consecutive pairs of
  qubits. We show that the spectral gap of the Hamiltonian is upper bounded
  by 1/(n-1) if the eigenvalues of a certain two-by-two matrix simply relat
 ed to psi have equal non-zero absolute value. Otherwise\, the spectral gap
  is lower bounded by a positive constant independent of n (depending only 
 on psi). A key ingredient in the proof is a new operator inequality for th
 e ground space projector which expresses a monotonicity under the partial 
 trace. This monotonicity property appears to be very general and might be 
 interesting in its own right.  This is joint work with Sergey Bravyi.
LOCATION:MR12\,  Centre for Mathematical Sciences\, Wilberforce Road\, Cam
 bridge
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