Imaginary Time Dynamics of Low Energy Modes in Heisenberg Antiferromagnets
This event is part of the Preliminary Oral Exam.
Examining Committee: : Anders Sandvik, Anatoli Polkovnikov, Emanuel Katz, Shyam Erramilli
Abstract: Monte Carlo (MC) methods have proven incredibly important to our understanding of the equilibrium behaviour of both classical and quantum systems. As the current understanding of equilibrium physics is pretty well established in terms of statistical mechanics and so there has been a push to see how these equilibrium MC methods can be used to probe questions in non-equilibrium physics. For Classical systems standard MC methods have been very successful in probing Kibble-Zurek (KZ) physics by dynamically ramping temperature (or some other parameter) treating time as the number of MC sweeps. For quantum systems, Quantum Monte Carlo (QMC) methods have been adapted to solve the dynamics of the imaginary time Schrodinger equation which has allowed for detailed studies of KZ physics of quantum critical systems as well as measuring part of the quantum geometric tensor. Here we use Imaginary time dynamics study the low energy states of two variations of spin-1/2 Heisenberg Anti-ferromagnets in 2-dimensions. To this end we prepare an initial state with perfect Ne´el order along the z-axis and then evolve with the state in imaginary time with rotationally symmetric Hamiltonian (e.g. evolve with U(τ) = exp(−τH)). We systematically measure the relaxation time of the staggered magnetization along the z-axis as a function of the system size and ﬁnd that the relaxation time diverges as Lz∞. For each system we show that value of z∞ is related to the ﬁnite size scaling of the low energy states of Hamiltonian.