702 citations · 2.1k across the 58 of their papers we have counts for
5 papers · 1 filter
The gap of the area-weighted Motzkin spin chain is exponentially small
Lionel Levine, Ramis Movassagh
We prove that the energy gap of the model proposed by Zhang, Ahmadain, and Klich [1] is exponentially small in the square of the system size. In [2] a class of exactly solvable qua…
The gap of Fredkin quantum spin chain is polynomially small
Ramis Movassagh
We prove a new result on the spectral gap and mixing time of a Markov chain with Glauber dynamics on the space of Dyck paths (i.e., Catalan paths) and their generalization, which w…
Generic Local Hamiltonians are Gapless
Ramis Movassagh
We prove that generic quantum local Hamiltonians are gapless. In fact, we prove that there is a continuous density of states above the ground state. The Hamiltonian can be on a lat…
Eigenpairs of Toeplitz and disordered Toeplitz matrices with a Fisher-Hartwig symbol
Ramis Movassagh, Leo P. Kadanoff
Toeplitz matrices have entries that are constant along diagonals. They model directed transport, are at the heart of correlation function calculations of the two-dimensional Ising…
Entanglement and correlation functions of the quantum Motzkin spin-chain
Ramis Movassagh
We present exact results on the exactly solvable spin chain of Bravyi et al [Phys. Rev. Lett. 109, 207202 (2012)]. This model is a spin one chain and has a Hamiltonian that is loca…