Quantum Institute: Visitor Schedule

The Quantum Lunch is regularly held on Thursdays in the Theoretical Division Conference Room, TA-3, Building 123, Room 121.

The organizing committee includes Malcolm Boshier (P-21), Diego Dalvit (T-4), Michael Di Rosa (C-PCS), Sebastian Deffner (T-4 & CNLS), Changhyun Ryu (P-21) , Nikolai Sinitsyn (T-4), Rolando Somma (T-4), Christopher Ticknor (T-1), and Wojciech Zurek (T-4).

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 frustration-free spin-1/2 chains

Abstract
We consider a family of translation-invariant quantum spin chains with nearest-neighbor interactions and derive necessary and sufficient conditions for these systems to be gapped in the thermodynamic limit. More precisely, let psi be an arbitrary two-qubit state. We consider a chain of n qubits with open boundary conditions and Hamiltonian which is defined 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 related 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 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 frustration-free translation-invariant spin-1/2 chains with nearest-neighbor interactions. This is joint work with Sergey Bravyi.