CONTACTS
 Coordinator
Sebastian Deffner

Quantum Lunch Location:
TDivision Conference Room, TA3,
Building 123, Room 121

Quantum Institute: Visitor Schedule
The Quantum Lunch is regularly held on Thursdays in the Theoretical Division Conference Room, TA3, Building 123, Room 121.
The organizing committee includes Malcolm Boshier (P21), Diego Dalvit (T4), Michael Di Rosa (CPCS), Sebastian Deffner (T4 & CNLS), Changhyun Ryu (P21) , Nikolai Sinitsyn (T4), Rolando Somma (T4), Christopher Ticknor (T1), and Wojciech Zurek (T4).
For more information, or to nominate a speaker, contact Sebastian Deffner.
To add your name to the Quantum Lunch email list, contact Kacy Hopwood.
Thursday October 15, 2015
12:30 PM  2:00 PM
Speaker: David Gosset (Caltech)
Technical Host: Rolando Somma
TOPIC: Gapped and gapless phases of frustrationfree spin1/2 chains
Abstract
We consider a family of translationinvariant quantum spin chains with nearestneighbor interactions and derive necessary and sufficient conditions for these systems to be gapped in the thermodynamic limit. More precisely, let psi be an arbitrary twoqubit state. We consider a chain of n qubits with open boundary conditions and Hamiltonian which is defined as the sum of rank1 projectors onto psi applied to consecutive pairs of qubits. We show that the spectral gap of the Hamiltonian is upper bounded by 1/(n1) if the eigenvalues of a certain twobytwo matrix simply related to psi have equal nonzero 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 the 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. As an extension of our main result, we obtain a complete classification of gapped and gapless phases of frustrationfree translationinvariant spin1/2 chains with nearestneighbor interactions. This is joint work with Sergey Bravyi.
