Solving Frustration-Free Spin Systems

Gapped and gapless phases of frustration-free spin-2 chains

An improved 1D area law for frustration-free systems

We present a new proof for the 1D area law for frustration-free systems with a constant gap, which exponentially improves the entropy bound in Hastings 1D area law and which is tight to within a polynomial factor. For particles of dimension d, spectral gap > 0, and interaction strength of, at most, J , our entropy bound is S1D ≤ O(1) · X logX, where X def = (J log d)/ . Our proof is completely ...

Correlation Length versus Gap in Frustration-Free Systems.

Hastings established exponential decay of correlations for ground states of gapped quantum many-body systems. A ground state of a (geometrically) local Hamiltonian with spectral gap ε has correlation length ξ upper bounded as ξ=O(1/ε). In general this bound cannot be improved. Here we study the scaling of the correlation length as a function of the spectral gap in frustration-free local Hamilto...

Improved one-dimensional area law for frustration-free systems

We present a new proof for the 1D area law for frustration-free systems with a constant gap, which exponentially improves the entropy bound in Hastingsâ 1D area law and which is tight to within a polynomial factor. For particles of dimension d , spectral gap > 0, and interaction strength at most J , our entropy bound is S1D O(1) ·X3 log X, where X def = (J log d)/ . Our proof is completely comb...

Contribution to PWA90 Spin Glasses and Frustration

The 1975 EA paper by Sam Edwards and Phil Anderson proposed to understand a class of real materials as frustrated, glassy magnets with a novel type of weak order in time. It launched an exciting period of intense exploration of new directions for understanding random and composite materials. This work has had a lasting impact well beyond materials science, contributing powerful new methods for ...