Quantum Many-Body Dynamics
We consider isolated interacting quantum systems that are taken out of equilibrium instantaneously (quenched). We study numerically and analytically the probability of finding the initial state later on in time (the so-called fidelity or Loschmidt echo), the relaxation time of the system, and the evolution of few-body observables. The fidelity decays fastest for systems described by full random matrices, where simultaneous many-body interactions are implied.
I will present results for the quench dynamics of one-dimensional interacting bosons under two circumstances. One is when the bosons are in the vicinity of the superfluid-Mott quantum critical point, while the second is when the bosons are in a disordered potential which can drive the system into a Bose glass phase. I will show that the dynamics following a quench can be quite complex by being characterized by three regimes.
We consider quantum quenches in one dimensional Bose gases where we prepare the gas in the ground state of a parabolic trap and then release it into a small cosine potential. This cosine potential breaks the integrability of the 1D gas which absent the potential is described by the Lieb-Liniger model. We explore the consequences of this cosine potential on the thermalization of the gas. We argue that the integrability breaking of the cosine does not immediately lead to ergodicity inasmuch as we demonstrate that there are residual quasi-conserved quantities post-quench.
We describe a new diagnostic for many-body wavefunctions which generalizes the spatial bipartite entanglement entropy. By was of illustration, for a two-component wavefunction of heavy and light particles, a partial (projective) measurement of the coordinates of the heavy (but not light) particles is first performed, and then the entanglement entropy of the projected wavefunction for the light particles is computed.
It has been argued recently that, through a phenomenon of many-body localization, closed quantum systems subject to sufficiently strong disorder would fail to thermalize. In this talk I will describe a real time renormalization group approach, which offers a controlled description of universal dynamics in the localized phase. In particular it explains the ultra-slow entanglement propagation in this state and identifies the emergent conserved quantities which prevent thermalization.
I will discuss a proof of many-body localization for a one-dimensional spin chain with random local interactions. The proof depends on a physically reasonable assumption that limits the amount of level attraction in the system. I construct a sequence of local rotations that completely diagonalizes the Hamiltonian and exhibits the local degrees of freedom.
Isolated, interacting quantum systems in the presence of strong disorder can exist in a many-body localized phase where the assumptions of equilibrium statistical physics are violated. On tuning either the parameters of the Hamiltonian or the energy density, the system is expected to transition into the ergodic phase. While the transition at "infinite temperature" as a function of system parameters has been found numerically but, the transition tuned by energy density has eluded such methods.
Topological phases are often characterized by special edge states confined near the boundaries by an energy gap in the bulk. On raising temperature, these edge states are lost in a clean system due to mobile thermal excitations. Recently however, it has been established that disorder can localize an isolated many body system, potentially allowing for a sharply defined topological phase even in a highly excited state.I will show this to be the case for the topological phase of a one dimensional magnet with quenched disorder, which features spin one-half excitations at the edges.