2024/03/15 by Michael Ragone, Ragone, Michael · 2 citations
Physics and Astronomy · #Advanced Chemical Physics Studies #Cold Atom Physics and Bose-Einstein Condensates #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Physics (quant-ph) #Quantum many-body systems
paper · pdf · doi:10.48550/arxiv.2403.09951
openalex publication_date 2024/03/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This thesis studies a pair of symmetry protected topological (SPT) phases which arise when considering one-dimensional quantum spin systems possessing a natural orthogonal group symmetry. Particular attention is given to a family of exactly solvable models whose ground states admit a matrix product state description and generalize the AKLT chain. We call these models ``SO(n) AKLT chains'' and the phase they occupy the ``SO(n) Haldane phase''. We present new results describing their ground state structure and, when n is even, their peculiar O(n)-to-SO(n) symmetry breaking. We also prove that these states have arbitrarily large correlation and injectivity length by increasing n, but all have a 2-local parent Hamiltonian, in contrast to the natural expectation that the interaction range of a parent Hamiltonian should diverge as these quantities diverge. We extend Ogata's definition of an SPT index for a split state for a finite symmetry group G to an SPT index for a compact Lie group G. We then compute this index, which takes values in the second Borel group cohomology H2(SO(n),U(1)), at a single point in each of the SPT phases. The two points have different indices, confirming the two SPT phases are indeed distinct. Chapter 1 contains an introduction with a detailed overview of the contents of this thesis, which includes several chapters of background information before presenting new results in Chapter 7 and Chapter 8.