Using variational methods and hyperbolic lattices to find the ground state of gapless systems

Abstract

The ground state of a system is the foundation state, as all other states of a system are excitations from the ground state. Calculating different observables at the ground state can help us understand the behavior of the system at the ground and excited energy levels. In a quantum system, calculating the ground state is often a hard problem. We explore two approaches to find the ground state of a gapless system. We investigate the Maldacena duality or the AdS/CFT correspondence in our works and calculate the average energy of the ground state of the Conformal Formal Theory lying at the boundary of our 3, 7 hyperbolic space with Anti-de Sitter isometries, using inspiration from Monte Carlo Markov Chain Metropolis sampling algorithm. We also explore the Tensor Renormalization Group theory to compute the ground state of a large quantum lattice using quadratically lesser resources.