Rigorous RG Algorithms for Low-Energy Eigenstates in 1D Systems
"Discover the rigorous renormalization group algorithms and area laws for low-energy eigenstates in 1D systems. Explore the algorithmic approaches and results for local Hamiltonians and ground state projections."
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Presentation Transcript
Rigorous RG algorithms Rigorous RG algorithms and area laws for low and area laws for low energy eigenstates in 1D energy eigenstates in 1D THOMAS VIDICK CALIFORNIA INSTITUTE OF TECHNOLOGY JOINT WORK WITH ITAI ARAD (TECHNION), ZEPH LANDAU AND UMESH VAZIRANI (UC BERKELEY)
Local Hamiltonians eigenvalues eigenstates
Low-lying states of local Hamiltonians eigenvalues eigenstates
Results eigenvalues eigenstates eigenvalues eigenstates
Outline 1. Approximate ground state projections (AGSP) 2. Viable sets 3. Algorithm
The algorithm Initialization: create viable sets on pairs of qubits Approximation error remains constant throughout!
AGSP construction don t care keep
Summary Area law + efficient algorithms for: (DG) polynomial-size ground space, constant gap (LD) polynomial density of states Features: Iterative tree-like procedure reminiscent of RG Elementary structure is viable set rather than state Operates in delicate constant-approximation regime, controlled by AGSP Questions: Efficient?? [Roberts-Motrunich-V., in progress: benchmark against DMRG] Poly-time algorithm for (LD)? Using MERA? Higher dimension!
